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THE RADIOACTIVITY OF MANGANESE-56 AND OF IODINE-128

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T H IS D IS S E R T A T IO N H A S BEEN M IC R O F IL M E D E X A C T L Y AS R E C E IV E D .
L ib ra ry
Y, Uwrv,'
THE RADIOACTIVITY- OF MANGANESE56 AND OF IODINE128
by
RALPH HOYT BACON
Subm itted in p a r t i a l f u lf illm e n t o f th e requirem ents
f o r th e degree o f D octor o f Philosophy
at
New York U n iv e rsity
March 1940
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ABSTRACT
The o b je c t o f t h i s work was to determ ine w hether th e
Fermi o r th e Konopinski-Uhlenbeck th e o ry (o r n e ith e r ) p rovides
a s u ita b le e m p iric a l b a s is f o r c la s s if y in g and an aly zin g b e ta ra y s p e c tra , by examining a s c a r e f u lly a s p o s s ib le th e s p e c tra
o f Mn^S and 1^28
th e Wilson cloud chamber and a ls o by
a ttem p tin g to in v e s tig a te th e gamma ra y s accompanying th ese
b eta r a y s .
I n a d d itio n , i n th e course o f t h i s work, an
attem p t has been made to in v e s tig a te c r i t i c a l l y th e o b je c tiv ity
and th e d i f f i c u l t i e s o f applying th e cloud chamber method to such
d e te rm in a tio n s .
The r e s u l t s seem to fav o r th e K-U th e o ry over th e Fermi
th e o ry .
However, i t i s shown t h a t th e e r r o r s o f cloud chamber
measurement a re more se rio u s th an commonly supposed, so th a t
t h i s r e s u l t i s n o t too c o n clu siv e .
n
o
7
>
5
o
CONTENTS
Page
I n t r o d u c t i o n ..........................................................................................................
1
A pparatus ..................................................................................................................
5
E xperim ental D e ta ils .........................................................................................
9
The measurement o f th e m agnetic f i e l d ..........................................
9
The measurement o f th e r a d i i o f c u r v a t u r e ..................................
11
The In flu en ce o f th e m agnetic f i e l d on th e observed shape of
th e s p e c tru m ..................................................................................................
12
The e f f e c t o f th e s iz e and p o s itio n o f th e source on th e ob­
served shape . o f th e s p e c tr u m ..........................................
16
The e f f e c t o f o th e r o p e ra tin g c o n d itio n s in s id e th e chamber
on th e observed shape o f th e s p e c tr u m ...........................................
19
T h e o ry ......................................................................................................................
20
The th e o rie s o f Fermi and o f Konopinski and Uhlenbeek . . .
21
The Compton E f f e c t .....................................................................................
26
R e su lts . . . . . .
.............................................................................................
The p -ra y spectrum o f Mn®® . . . . .
...............................................
29
29
e c
The y -ra y s accompanying the decay o f Mn
/
...................................
41
D iscu ssio n o f th e r e s u l t s ....................................................................
43
The p -ra y spectrum o f I
....................................................................
50
C o n c lu s io n s ..............................................................................................................
53
A cknow ledgm ents......................................................................................................
66
B ibliography ..............................................................................................................
67
INTRODUCTION
The p -ra y spectrum o f Mn56 was f i r s t measured i n th e cloud chamber
by G a e rttn e r, T urin and Crane1 .
Using a m agnetic f i e l d o f 850 g au ss, th e y
found th e spectrum to c o n s is t o f a s in g le K-U group having an e x tra p o la te d
end p o in t a t 6 .5 me* (2 .8 MeV).
The ra d io a c tiv e sample was n o t p laced d i ­
r e c t l y in s id e th e chamber in t h i s work, b u t was p laced in a w e ll i n the
cloud chamber to p , and th e p - p a r tic le s allow ed to e n te r the chamber through
a window in th e w e ll.
th ic k .
This window c o n s is te d of copper f o i l .001 inch
The e f f e c t o f t h i s window upon e le c tr o n s o f v a rio u s e n e rg ie s i s
a fu n c tio n o f th e in c id e n t e le c tr o n energy.
This e f f e c t i s g r e a te r and
more u n c e rta in f o r slow er th an f o r f a s t e le c tr o n s .
The use o f t h i s win­
dow, th e r e f o r e , d e tr a c ts from th e r e l i a b i l i t y o f the measurement o f th e
low energy end o f a spectrum .
This spectrum was l a t e r measured in th e cloud chamber by Brown and
M itc h e ll2 .
Using m agnetic f i e l d s o f 375 and 490 g a u ss, th ey fin d th a t
th e K-U p lo t re s o lv e s i t s e l f in to two groups having e x tra p o la te d end
p o in ts a t 6 .8 me* (3 .0 MeV) and 3 .4 me* (1 .2 MeY).
They placed the r a d i­
o a c tiv e sample in s id e the cloud chamber behind a s e t o f shelves c a lle d
" S o lle r s l i t s ” , which were supposed to c o llim a te the beam o f e le c tro n s
e n te rin g th e v i s i b l e p o rtio n o f th e chamber.
However, th e se ”s l i t s ”
a ls o provided a s e t o f s c a tte r in g s u rfa c e s which should have d e fle c te d
an unknown number o f slow e le c tr o n s in to th e measured beam.
Hence, one
could n o t be c e r ta in whether th e "second group” re p o rte d by Brown and
1 G a e rttn e r, T urin and Crane, Phys. Rev. 49, 793 (1936)
2 Brown and M itc h e ll, Phys. Rev. 50, 593 (1936)
I
%
M itc h e ll was r e a l l y p a r t o f th e p -ra y spectrum o f Mn5® o r due to s c a t t e r ­
in g .
This spectrum was a lso measured i n a p -ra y sp ectro g rap h by A lich anow, A lichanian and Dzelepows .
MeV (7 .3 me*).
They r e p o rt th e end p o in t to be a t 3.2
This does n o t agree w ith th e fin d in g s o f o th e r w orkers.
I t seemed to us t h a t we might be able to remove th e u n c e r ta in tie s
in th e p revious work by means o f a d d itio n a l experim ents.
As th e r e s u l t
o f o u r work, we are ab le to r e p o rt th a t th e upper lim it o f t h i s spectrum
i s a t th e p o in t found by G a e rttn e r, T urin and Crane^; th e second group
announced by Brown and M itc h e ll a c tu a lly does appear to be p a r t o f the
spectrum ; in a d d itio n , we fin d evidence o f a t h ir d group, in th e language
o f th e K-U th e o ry .
The$ -ra y s from Mn5® have been measured by M itc h e ll and Langer4 ,
using coincidence c o u n te rs to determ ine th e e n e rg ie s o f Compton e le c ­
tr o n s .
They o b ta in 1.65 MeV as t h e y - r a y energy, and claim t h a t t h e i r
work shows t h e y - ra y to be monochromatic.
L a te r, Livingood and Seaborg5 measured th e energy o f t h i s y - r a y
by fin d in g th e th ic k n e ss o f lead n ecessary to reduce i t s in te n s i ty to
one h a l f .
The energy th u s o b tain ed i s 1 .2 MeV.
We have measured t h i s y - ra y spectrum by counting the Compton e le c tr o n s em itted from a th in s h e e t o f b a k e lite p laced along a diam eter
3 Alichanow, A lich a n ian and Dzelepow, Nature 136, 257 (1935);
Phys. Z e it. Sow jetunion 10, 78 (1936)
4 M itc h e ll and Langer, Phys. Rev. 52, 137 (1937)
5 Livingood and Seaborg, Phys. Rev. 54, 391 (1938)
3
o f th e cloud chamber.
The d i s t r i b u t i o n o f th e observed e le c tro n s in d i­
c a t e s ^ - r a y l in e s a t about .6 o r .7 MeV, and a t about 1 .7 MeV, p lu s , p e r­
haps, o th e r l i n e s n o t re so lv e d .
As t h i s work was being com pleted, Dunworth
ment, b ased on coincidence co u n tin g .
re p o rte d an o th er measure­
From h is work, he concluded t h a t
th e re a re two lin e s in th e _y -ra y spectrum - one a t about .6 and th e o th e r
a t about 1 .7 MeV, in s u b s ta n tia l agreement w ith ou r r e s u l t s as to the e n e r­
g ie s o f th e l i n e s .
However, th e r e la tiv e i n t e n s i t i e s o f th e two lin e s do
n o t agree w ith th e r e l a t i v e p o p u latio n s o f th e 3 -ra y groups as determ ined
e i t h e r by Brown and M itc h e ll o r by o u rse lv e s .
Two months l a t e r , Langer, M itc h e ll and McDaniel
7
re p o rte d a t h i r d
co in cid en ce counter measurement, from which i t may be concluded th a t
th e re a re a t l e a s t two l i n e s in t h i s y - ra y spectrum , b u t nothing i s in ­
fe rre d w ith reg ard to t h e i r e n e rg ie s.
IgQ
The end p o in t o f the 3 -ra y spectrum o f I
was f i r s t determ ined by
3
Alichanow, A lich an ian and Dzelepow . Our measurements agree w ith th e ir s
as to th e p o s itio n o f t h i s end p o in t, and a lso show th e shape o f th e r e s t
o f th e spectrum .
I n terms o f th e K-T7 th eo ry , th e spectrum c o n s is ts o f
two g ro u p s, having upper l i m i t s a t 1.05 and 2.10 MeV, re s p e c tiv e ly .
How­
e v e r, we were unable to f in d any y - r a j o f s u f f ic ie n t in te n s i ty to account
f o r two groups i n t h i s 3“ra y spectrum . This agreed w ith th e fin d in g s o f
Q
R oberts and Irv in e , who came to th e conclusion th a t i f th e re be any
6 J . V. Dunworth, N ature 143, 1065 (1939)
7 Langer, M itc h e ll and McDaniel,
Phys. Rev. 56, 422 (1939)
8 R oberts and I r v in e , Phys. Rev. 53, 609 (1938)
H
y - ra y accompanying t h i s r a d i o a c ti v ity , th e re must be le s s th an one quan­
tum f o r every te n e le c tro n s observed.
L a te r, a * /- ra y o f about .4 MeV was
q
re p o rte d by Livingood and Seaborg5, b u t n e ith e r th e energy no r the in te n ­
s i t y ag reesw ith th e 3 -ra y spectrum .
F u rth e r work has been done by Tape10.
H is o b se rv a tio n s on the
y - ra y agree w ith o u rs; th o se on th e 3 - p a r tic le s do n o t.
9 Livingood and Seaborg, Phys. Rev. 54, 777 (1938)
10 G. F . Tape, Phys. Rev. 56, 965 (1939)
s
APPARATUS
A c r o s s -s e c tio n o f the cloud chamber i s shown in F igure I .
An a lu ­
minum p is to n , 7 in ch es in d iam eter and 6 in ch es h ig h , mores in a b ra ss
c y lin d e r .
The expansion r a t i o i s a c c u ra te ly and f in e ly c o n tr o lle d by
screw ing th e c y lin d e r in to o r o u t o f th e b ra ss cup which forms th e base
o f the chamber.
The j o i n t between th e c y lin d e r and th e cup i s sealed
w ith Apiezon Q,.
On top o f th e c y lin d e r i s f i t t e d a removable head, as shown in
th e f ig u r e .
I t s p a r ts are h eld to g e th e r w ith g ly p ta l enamel, so t h a t
th e head can be e a s i l y removed and q u ick ly rep la c e d a s a s in g le u n it.
When in p la c e , i t i s se a le d to th e to p o f th e c y lin d e r w ith Apiezon Q,.
D if fe r e n t heads were used f o r d i f f e r e n t purposes:
th e one devised f o r
use in th e measurement o f th e Iodine spectrum i s shown in d e t a i l in
F igure I .
D uring th e expansion, th e chamber was illu m in a te d by s ix 1000w a tt c le a r g la s s photoflood lamps, made s p e c ia lly f o r us by The Westinghouse E l e c tr i c and M anufacturing Company.
lamps exceeds 30,000 ex p an sio n s.
The lif e tim e o f these
C y lin d ric a l le n se s and s u ita b le s l i t s
were used to c o llim a te a f l a t beam o f l i g h t 1 cm h ig h a c ro ss th e cham­
b e r.
I t was found s a ti s f a c t o r y to o p e ra te in a d a rk room w ith th e came­
r a s h u tte r open, and to sim ply f la s h th e photofloods on and o f f very
q u ic k ly .
A lthough th e lamps d id n o t re a c h maximum b r il l i a n c e t h i s
way, th ey s t i l l e m itte d more th a n enough l i g h t to photograph P -ray
tra c k s on s u p e rs e n s itiv e panchrom atic f ilm .
S a tis f a c to r y p ic tu r e s
could be ta k e n w ith as few a s th re e lam ps, so t h a t we were p ro te c te d
a g a in s t lo s s by th e p o s sib le unnoticed f a i lu r e o f one o r more o f them.
Glass Plate
Insulating Washer
Tin Foil Electrode
Cork o r rubber stopper
Glass Ring -~>
Cross section o f chamber head used in measuring
B-rc/y spectrum of f* *
~ ^ |P * s insulating Nut
.. —s *Brass Cylinder
Felt Ring
saturated with grease
Brass Cup
Arm to support fitte r p a p er
co a ted with activa ted iodine
£ Brass Connecting Rod
To Electromagnet
VERTICAL CROSS SECTION
II I I II I 1 I i t
cm.
BOTTOM VIEW OF REMOVED
CHAMBER HEAD
7
The camera, o r ig in a lly designed to measure forked tra c k s i n the
chamber, was a t f i r s t b u i l t w ith two matched Z e iss T essars mounted symme­
t r i c a l l y a s shovra in Figure I I , so t h a t each took a p ic tu re a t r ig h t
an g les to th e o th e r , and each focussed i t s image in th e same p la n e .
This
o b v iated th e n e c e s s ity o f having the film pass over a bent g a te , as i s
th e case when only one le n s i s used fo r ste re o sc o p ic p ic tu r e s 1^ .
T essars were mounted i n 8° wedges as shown.
The
For the p re se n t work, how­
e v e r, i t i s d e s ire d to have one p ic tu re along th e lin e s of fo rc e of the
m agnetic f i e l d in which th e cloud chamber i s immersed, the o th e r p ic tu re
b ein g , i n our c a se , a t 45® to th e f i e l d .
To e f f e c t t h i s change, i t i s
m erely n ecessary to mount one o f the T essars in a f l a t block in s te a d o f
th e xvedge.
However, i t was n o t found necessary to use the 45° view, as
more th an 90$ o f th e t o t a l momentum o f the tra c k s measured la y in the
h o riz o n ta l p la n e, and i t was h a rd ly worthwhile to t r y to measure the
sm all v e r t i c a l components.
The camera was connected through a Geneva sto p and a p a ir of
u n iv e rs a l j o i n t s to the s h a f t o f the r o ta ry sw itches which c o n tro lle d
th e cycle o f o p e ra tio n s.
The c o i l s f o r producing the m agnetic f i e ld have a lre a d y been d eo
s c rib e d 1 .
1
They are much more e f f i c i e n t th an a Helmholz-Gaugain a r ­
rangement - only 2200 w a tts (10 amperes a t 220 v o lts ) being re q u ire d
to produce a uniform f i e l d o f 880 gauss throughout th e volume o f th e
chamber.
11 F . N. D. K u rie, E. S . I . 3, 655 (1932)
12 E. H. Bacon, B. S. I . 7, 423 (1936)
35mm Moving
Ptctura Film
______
and
Commetnd
anhmnal Jom h to tHaft of rotary switch*!
ftm ovabk Wtdgo - ffangk
45*
p
?
EXPERIMENTAL DETAIIS
The Measurement o f th e M agnetic F ie ld
S e v e ra l e x p lo rin g c o i l s , each o f 50 to 100 tu rn s , o f No. 36 c o t­
to n covered copper w ire , were wound on a c c u r a te ly turned c y lin d e rs of 6
to 10 cm d iam eter.
The d iam eter o f No. 36 w ire i s .13 mm, and so the
d iam eter o f each c o i l was known to w ith in .1 mm, o r the e f f e c ti v e area
o f each c o i l was known to w ith in about one p a r t i n 300.
One o f th ese e x p lo rin g c o i l s was connected through th e secondary
o f a stan d a rd m utual inductance (10 m illih e n r ie s ) to a b a l l i s t i c galva­
nom eter.
The c u rre n t through th e prim ary o f t h i s mutual inductance was
re a d to w ith in 1% from a Weston Model 45 ammeter, and was a d ju s te d u n t i l
a d e f le c tio n o f about 20 cm on the galvanom eter sc a le was caused by tu rn ­
in g i t on o r o f f .
That e x p lo rin g c o i l was chosen which produced as n e a r­
l y a s p o s sib le th e same d e f le c tio n on th e galvanom eter sc a le when turned
through e i t h e r 90 o r 180 degrees in th e m agnetic f ie l d being m easured.
As a check, th e re was taken a second s e t o f measurements, u sin g a second
stan d a rd m utual inductance (0 .1 m illih e n ry ) and a d if f e r e n t b a l l i s t i c
galvanom eter.
conds.
Each galvanom eter has a f r e e p erio d of more th a n 25 se­
S uccessive galvanom eter d e f le c tio n s agreed to about a m illim e te r
o r so , o r to w ith in l e s s th an 1$.
I n m easuring such a m agnetic f i e l d , i t i s a convenience to be
a b le to tu r n the f i e l d c u rre n t on o r o f f , r a th e r than to have to r o ta te
th e e x p lo rin g c o i l .
The f i e l d c o i l s r e s t on b ra s s r in g s , 1 /4 inch th ic k , w ith in sid e
d iam eter o f 25 cm and o u tsid e diam eter o f 44 cm.
These r in g s a re sepa­
ro
r a te d by wooden sp acers between which th e l i g h t p asses from th e photo­
flo o d lamps to th e cloud chamber.
These rin g s a c t as a low r e s is ta n c e
secondary c i r c u i t to th e f i e l d c o ils whenever th e f i e l d c u rre n t i s ap­
p lie d o r removed.
They th u s reduce th e tim e c o n sta n t of the f i e l d c o ils
to a v ery sm all f r a c tio n o f a second13.
I t i s thus p o ssib le $ 6 a c c u ra te -
ly/m easure th e m agnetic f i e l d produced by a given f i e l d c u rre n t by tu rn ­
in g i t on o r o f f o r a lso by re v e rs in g i t .
The measurements o f th e m agnetic f i e l d o btained by tu rn in g the
f i e l d c u rre n t on o r o f f agreed to w ith in 1% w ith each o th e r and w ith
those o b tain ed by r o ta tin g th e ex p lo rin g c o i l .
Having th u s o b tain ed th e average valu e o f th e m agnetic f i e l d
w ith in th e volume enclosed by th e e x p lo rin g c o ils (25 to 100 cc) we
th e n took a sm all c o i l c o n s is tin g o f 3500 tu rn s o f No. 40 w ire wound
on a spool 5 mm in diam eter and 7 mm h ig h , and placed i t in v ario u s
p a r ts o f th e f i e l d .
For a given f i e ld c u rre n t, th e magnitude o f the
f i e l d was found to be c o n sta n t to w ith in 1% throughout th e volume oc­
cupied by th e cloud chamber.
This procedure was re p e a te d f o r each value o f th e m agnetic f i e ld
used in t h i s work - 850, 637, 425 and 319 o e rs te d s .
I n a c tu a l p r a c tic e , however, i t was found
h e a tin g o f th e f i e l d c o ils by the f i e l d c u rre n t,
by n o t more th a n
t h a t , owing to
the
the c u rre n t
dim inished
when o p e ra tin g a t 850 gauss, and by l e s s th an 1%
when running a t 319 g au ss.
This e f f e c t was minimized by s ta r t i n g w ith
13 J . C. Maxwell, P h i l . T ran s. Roy. Soc. 155, 576 (1865)
S . G. S ta r lin g , E l e c t r i c i t y and Magnetism f o r M vanced S tudents
(Longmans, Green and Company, F if th E d itio n , 1929) p . 354
th e c u rre n t a t r i f l e h igh (about 1 /2 o f 1%), and by ta k in g only s h o rt
ru n s a t 850 gauss (never more th a n 50 p ic tu r e s in s u c c e ssio n ), follow ed
by lo n g e r runs a t lower f i e l d s .
The f i e l d was th u s known to w ith in 4$
a t a l l tim e s, and to w ith in 2% most o f th e tim e , throughout th e volume
o f th e cloud chamber.
The Measurement o f th e R adii o f C urvature
The developed film was re p la c e d i n th e camera (o r sometimes in a
B alo p tico n ), and p ro je c te d on to a s h e e t o f p ap er.
The ra d iu s o f curva­
tu re o f each tra c k was measured by comparing i t w ith the edges o f a s e t
o f b ra s s d is c s (o r segments in case o f r a d i i la r g e r than 10 cm), having
r a d i i running from 1 /2 to 25 cm in h a l f c e n tim e te r s te p s .
Measurements
o f r a d i i la r g e r th an 10 cm were n o t considered as r e l ia b le as those of
s h o rte r r a d i i , as th e le n g th o f a rc v is ib le would be only about 15 cm
a t m ost.
Such measurements s u ffic e to show th e t o t a l number o f tra c k s
having r a d i i g r e a te r th an 10 cm, b u t c e r ta in ly n o t to show the tru e
shape o f th e spectrum in th e reg io n co n sid ered .
See T ables I I and I I I .
As each tra c k was m easured, an arc was drawn in red p e n c il over
i t s image on th e p a p e r.
This helped to p rev en t one from m issing any
t r a c k s , o r from m easuring th e same one tw ic e .
The v a rio u s f e a tu r e s o f th e cloud chamber method o f measurement
have been d e scrib ed by E u rie , Richardson and Paxton
14
by Fow ler, D e lsa s-
so and L a u ritse n 15 by G a e rttn e r, T urin and Crane1 , and by many o th e r s .
14 E u rie , R ichardson and P axton, Phys. Rev. 49, S70 (1936)
15 Fow ler, D elsasso and L a u ritse n , Phys. Rev. 49, 561 (1936)
To th e rem arks o f th e s e w orkers, we would add th e fo llo w in g co n sid e ra­
tio n s .
The In flu e n c e o f th e M agnetic F ie ld on the Shape o f th e Spectrum
The ap p aren t shape o f a 3 -ra y spectrum , as measured in th e cloud
chamber, depends upon th e s tr e n g th o f th e m agnetic f i e l d used.
This i s
v ery sim ply e x p lain ed when we co n sid e r t h a t tra c k s o f v ery sm all r a d i i
o f c u rv a tu re have sm all p r o b a b ility o f e n te rin g th e v is i b le p o rtio n o f
th e cloud chamber.
E .g ., in th e case o f Mn5®, we measured 12,000 tra c k s
in f o u r d i f f e r e n t f i e l d s .
850 g a u ss.
Of th e s e , 3,000 were measured in a f i e l d o f
The observed d i s t r i b u t i o n o f 1,500 o f th e se i s shown in
Table I and in F igure V I II .
Only 19 tra c k s o f one cm o r l e s s were ob­
se rv e d , y e t th e r e s u l t s a t 319 gauss in d ic a te t h a t th e re must have been
about 600 o f such tr a c k s .
T his e f f e c t can be e a s ily , though n o t a c c u ra te ly , c a lc u la te d from
th e fo llo w in g c o n s id e ra tio n s : we sp e c ify th e d ir e c tio n o f em ission o f
an e le c tr o n by th e angle <f> which th e h o r iz o n ta l component o f i t s i n ­
i t i a l momentum makes w ith th e h o r iz o n ta l tan g en t to th e e m ittin g s u r ­
f a c e , as shown i n F ig u re I I I .
From t h i s f ig u r e , i t i s seen t h a t in
o rd e r f o r th e e le c tr o n to p ass in to th e v i s i b l e p o rtio n o f the chamber,
i t i s n e ce ssary f o r i t s p a th to e i t h e r c ro ss th e c i r c l e o f r a d iu s B,
o r a t l e a s t , to become ta n g e n t to i t .
which t h i s i s p o s sib le a re given by
The an g les o f em ission between
T
—t—
I
•“1
I
\
s -h
I
I---I
I
I
L_.
o.
{p+B) 1= p%A x-2pA cosfawax.
••• cos#m= U - B - 2 p B ) / 2pA
b. when p > (A + B )/2
( p - 5 ) W + 4 * -2pA cot0min.
c o s f a [ A - B f + p B ) / 2pA
c. whv>p4A+-B)/2, pm = 0
D erivation of E quation C1)
Fig. 3
where A * in s id e ra d iu s o f th e cloud chamber * 9 cm
= ra d iu s o f th e e m ittin g surface
B * ra d iu s o f th e v i s i b l e p o rtio n o f th e
f
* ra d iu s o f c u rv a tu re o f th e h o r iz o n ta l p ro je c tio n o f the
e le c tr o n tr a c k .
Now,
can be
cloud chamber
B i s a fu n c tio n o f p o s itio n on th e su rface o f ra d iu s A, as
seen from F igure I I I .
Thus, f o r an e le c tr o n em itted from a p o in t
n e a r th e to p o f th e illu m in a te d p o rtio n o f th e chamber, B i s l e s s than
7 cm, whereas f o r a tr a c k s ta r t i n g from n e a r th e low er edge, B i s about
8 cm.
Now,
th e p r o b a b ility f o r tra c k s o f a given ra d iu s to e n te r in s id e
th e c i r c l e o f rad iu 3 B i s p ro p o rtio n a l to th e d iffe re n c e
where
and
o f em issio n .
max ” ^min^
are in tu rn fu n c tio n s o f th e p o s itio n o f the p o in t
These p r o b a b i li t ie s are p lo tte d in F igure IV, where the
p r o b a b ility f o r a tra c k o f 5 cm r a d iu s em itted h o r iz o n ta lly i n th e mid
plane o f th e chamber to e n te r in s id e the c i r c l e of ra d iu s B i s tak en as
u n ity .
Any e f f e c t s o f th e v e r t i c a l component o f the e le c tr o n ’ s m otion
are n o t in clu d ed in t h i s c a lc u la tio n .
This om ission may, in p a r t a t
l e a s t , account f o r some o f th e d iffe re n c e between th e computed proba­
b i l i t i e s (th e smooth curve) and th e e x p erim en tally observed v a lu e s , a ls o
p lo tte d in th e f ig u r e .
The ex p erim en tal p r o b a b ilit ie s are determ ined in two ways: in
th e f i r s t , we p lo t th e r a t i o , f o r each m agnetie f i e l d used,
number o f tra c k s observed in a given momentum in te r v a l
number demanded by the b e s t K-U curve to f i t the e n tir e d a ta
in th e second, we p lo t from th e s p e c ia l ru n s, d esc rib e d in th e n ex t
Loss of Tracks of Small Radius of C u rv atu re fro m fhe M easured S pecfrum .
,1 2 8
o
•
8
°
o
* - 6 3 7 Gauss
o -3 1 9 G auss
(The condifions applying fofhe derivafion of equafion (1) w ere nof consfanf during fhe measurement of
fhis specfrum, so no calculafion was attempted.)
M n56
e
« 7
T
W
Comparison of Equafion (1) wifh E xperim ent
•-8 5 0 Gauss.e-637 Gauss.o-319 Gauss. ®- pp. 16,18
—
3---------------- 1---------------- 5 "
Radius of C urvature of T r a c k s
12
cm-
paragraph, th e r a t i o
number o f tra c k s o bserved a t 850 gauss i n a given momentum in te r v a l
number to be expected i n th a t in te r v a l from th e 319 gauss curve
The j u s t i f i c a t i o n o f th is procedure a r is e s c h ie f ly from th e f a c t
th a t th e p lo tte d p o in ts group f a i r l y w e ll, and from th e f a c t t h a t the
tre n d i s a fu n c tio n o f th e rad iu s o f c u rv atu re a lo n e , and independent
o f th e f i e l d used, and, th e r e f o r e , independent o f th e tru e momentum o f
the e le c tr o n s being m easured.
The E f f e c t o f th e S ize o f the R adioactive Source on the Observed Shape
of th e Spectrum
The apparent shape o f the spectrum depends, to some e x te n t, upon
the p o s itio n and siz e o f th e source in th e chamber.
In our e a r ly work,
56
the Mn was d ep o sited on f i l t e r papers 3 .5 x 11 cm, which were a ffix e d
to th e g la s s r in g by wads o f Apiezon Q,.
2 x 11 cm were u sed .
I n our l a t e r work, f i l t e r papers
These narrower sources always showed more low en er­
gy tr a c k s in p ro p o rtio n t o the t o t a l y ie ld th a n d id th e wide sources.
This e f f e c t may be e x p la in e d , in p a r t a t l e a s t , as fo llo w s:
The 3 .5 cm so u rc es are approxim ately tw ice a s wide as th e illu m i­
nated p o rtio n o f th e clo u d chamber, whereas th e 2 cm sources are approxi­
m ately th e same w id th .
Now, f o r an e le c tr o n s ta r t i n g from a p o in t near
th e edge o f the w ider so u rce to e n te r th e v is ib le p o rtio n of the chamber,
i t i s n ecessary f o r i t t o have a t l e a s t a c e r ta in minimum v e r t i c a l com­
ponent o f v e lo c ity .
The chance o f having t h i s n ecessary v e r t i c a l com­
ponent o f v e lo c ity , pro v id ed th a t t h i s component be sm all compared to
th e t o t a l v e lo c ity , i s p ro p o rtio n a l to th e t o t a l v e lo c ity .
Kius, e le c ­
tr o n s o f higher e n e rg ie s have g r e a te r chanoe o f e n te rin g the v is ib le
Mn5iL Comparison of fhe Yield of Wide and Narrow Filfer Paper Sources
Yield of Wide Filter Paper
Yield of Narrow Filter Paper
For momenfa greafer fhan 3 me, fhe num ber of tracks in a
single momenfum interval is sm all. However, fhe fofal
number of electrons of momenfa greafer fhan 3 me observed
at each field is proportional to the width of fhe filter paper.
- ________________________________ _2 _ L ° ____________________ _______
o
o
8 5 0 Gauss
•
319 Gauss
0.50 .0 4
0
2
3
4
5
H orizontal Momenfum of fhe O b serv ed
E le c tr o n s
Fig. 5
me — ►
■
p o rtio n o f th e chamber from p o in ts n e a r th e edges o f th e wide source than
have e le c tr o n s o f lower e n e rg ie s , whereas f o r e le c tr o n s s t a r t i n g from
p o in ts n ea r th e mid plane o f the cloud chamber, the d iffe re n c e between
th e p r o b a b ilitie s i s n o t so g r e a t.
To c a lc u la te t h i s r e s u l t was found to be too la b o rio u s ; moreover,
th e c a lc u la tio n in v o lv es to o many u n c e r ta in tie s , due to th e f a c t t h a t th e
illu m in a te d p o rtio n o f th e chamber i s n o t sh a rp ly d e fin e d , th e illu m in a ­
tio n g rad in g o f f from an in te n se beam 1 cm wide to something below the
s e n s i t i v i t y o f th e photographic film in a re g io n about 5 mm th ic k above
and below.
Ue th e r e fo r e took a s e r ie s o f ru n s w ith a broad and a narrow
source in th e chamber to g e th e r (on o p p o site s id e s ) , and measured the
y ie ld s e p a ra te ly from each so u rc e .
Each run c o n s is te d of te n p ic tu re s
a t 850 gauss follow ed by te n a t 319 g au ss, u n t i l a t o t a l o f 2000 tra c k s
was o b ta in e d .
I t was found t h a t th e y ie ld o f low energy tra c k s was th e
same from each so u rce, w hereas th e y ie ld o f h ig h energy tra c k s was pro ­
p o r tio n a l to the w id th o f the so u rce.
See Figure Y.
From t h i s i t would appear t h a t i t i s im portant to c e n te r th e
source on th e mid plane o f the cloud chamber; f o r i f one edge i s placed
too f a r o u t in to th e shadow, th e observed spectrum w i l l approach t h a t
to be expected from a w ider source th a n i s being used.
Undoubtedly,
some o f th e d isc re p a n c ie s d e p ic te d in F ig u res XI and X II can be a s ­
c rib e d , a t l e a s t In p a r t , to f a u lty c e n te rin g o f some o f th e f i l t e r
p a p e rs .
I t seems to us t h a t th e narrow er source y ie ld s the more f a i t h ­
f u l re p ro d u c tio n o f th e tru e spectrum .
In th e f i r s t p la c e , th e c o l l i -
I
19
m ation i s b e t t e r , and seco n d ly, th e o p e ra tin g c o n d itio n s in s id e th e cloud
chamber are more fa v o ra b le .
The w ider f i l t e r papers sometimes s h o rt th e
sweeping v o lta g e and th u s p rev en t th e prod u ctio n o f sharp c le a r tr a c k s .
T h e refo re , only th e r e s u l t s w ith th e narrow er sources w i ll be ex­
h ib ite d h e re , although th e p revious work w i l l be r e f e r r e d to when neces­
s a ry .
The E f f e c t o f O ther O perating C onditions In sid e th e Chamber on the Ob­
served Shape o f th e Spectrum
As i s w e ll known, the co n d itio n s re q u ire d to o b ta in good, c le a r ,
3 -ra y tra c k s are q u ite c r i t i c a l .
only a v ery
Such tra c k s are ob tain ed throughout
sm all range o f expansion r a t i o s .
In ou r c a se , a t
l e a s t , the
optimum expansion r a t i o appeared to be a fu n c tio n o f the room tem p eratu re.
I f th e expansion r a t i o in use approached e i t h e r end o f the u s e fu l ran g e,
th e s e n s i t i v i t y o f the chamber d ecreased , th e lo s s of s e n s i t i v i t y f o r
v ery e n e rg e tic e le c tr o n s being g r e a te r than f o r slow er e le c tr o n s .
That
th is e ffe c t
i s g r e a te r than might be supposed may be in fe rr e d from F ig ­
u re s XI and
X II, where th e d is p a r ity amongst some o f th e runs p lo tte d
may be a s c rib e d , in p a r t a t l e a s t , to v a r ia tio n s in the s e n s i t i v i t y of
th e cloud chamber as a fu n c tio n o f the energy of th e e le c tr o n s being
d e te c te d .
I
THEORY
In d isc u s s in g the p r o p e rtie s o f b e ta p a r t i c l e s , the fo llo w in g
term s and symbols w i l l be used:
e ■ e le c tr o n ic charge
m = r e s t mass o f th e e le c tro n
v = v e lo c ity o f th e e le c tr o n
V)t m end p o in t o f b e ta ra y spectrum
W <■ t o t a l r e l a t i v i s t i c energy o f the e le c tr o n
** me*V 1 + 7j%W0 = end p o in t o f th e spectrum = mcV^ 1 +
E
= k in e tic energy o f the e le c tr o n
- mc*(V 1 + >JX - 1)
For th e motion o f th e e le c tr o n in th e magnetic f i e ld o f th e cloud
chamber we have
from which we e a s i ly o b ta in
3 me
From t h i s we see t h a t
cloud chamber.
m 1700
i s th e q u a n tity a c tu a lly measured by the
I t i s th e re fo re convenient in t h i s work to ex p ress
the
v a rio u s e q u atio n s needed in term s o f 1) e x p l i c i t l y r a th e r th an in term s
o f W o r E as i s
u s u a lly done.
The conversion to fu n c tio n s o f W o r
always be made, i f d e s ire d , by means o f the r e la t io n s
We - (me*)*
E* + 2 me* E
(me*)*
E
can
Zf
The T heories o f Fermi and o f Eonopinski and TJhlanbeck
Modern th e o r ie s o f 3-decay attem p t to p reserv e c o n serv atio n o f enerby and o f n u c le a r s p in .
t r i n o , i s p o s tu la te d .
To do t h i s , an e lu s iv e p a r t i c l e , c a lle d th e neu­
The n e u trin o has n e ith e r charge no r r e s t mass, b u t
only energy and an g u la r momentum.
The Fermi and th e K-U th e o r ie s suppose
t h a t th e e le c tr o n and n e u trin o are e m itted as the r e s u l t o f a t r a n s i t i o n
between two s t a t e s o f th e n ucleus in much th e same way as th e photon i s
em itte d in a s im ila r atom ic p ro c e ss.
The t r a n s i t i o n o f a n u c le a r p a r t i ­
c le from a "n eu tro n s ta t e " to a "p ro to n s ta t e " i s thought to be analogous
to the t r a n s i t i o n o f an atom from an e x c ite d s ta t e to the ground s t a t e .
16
The eq u atio n f i n a l l y o b tain ed by Fermi
may be w r itte n as fo llo w s:
P(W) dW - G * |h |sF(Z,W) f a
-vj*
Vffe - (me*")* V dW
o r , f o r purposes o f comparison with, experim ent,
v r« f
- V i +VTI
(2)
vT ~+ij J~ - VTTjpj Tj^drj
where P(W)dW = p r o b a b ility t h a t an e le c tr o n w i l l be em itted w ith an
energy ly in g between W and IT + dW
N(h)d?7 == number o f e le c tr o n s e m itted w ith momenta ly in g between
mcTJ and mc(fj + djj)
W0
= end p o in t o f th e 3 -ra y
spectrum
= (presum ably) energy o f d is in te g r a tio n
F
= fu n c tio n d e s c rib in g the in te r a c t io n o f the e le c tr o n
w ith th e Coulomb f i e l d o f th e nucleus
f
=
G
= c o n sta n t which m easures the s tr e n g th o f th e coupling
between th e n u c le a r p a r t ic le undergoing the t r a n s i t i o n
( i . e . , th e n eu tro n changing in to a pro to n ) and the
16 E. Ferm i, Z e it. f . P hysik 88, 161 (1934)
21
"e le c tro n -n e u trin o f i e l d " .
M = m a trix elem ent c o n ta in in g th e wave fu n c tio n s of th e chang­
in g p a r t i c l e , and i s analogous to th e m a trix elem ent o f
th e d ip o le moment in o rd in a ry r a d ia tio n th e o ry . D iffe re n t
v a lu e s o f | m) b correspond to "allow ed" and "forbidden"
t r a n s i t i o n s , analogous to d ip o le and quadrupole t r a n s i ­
tio n s in o rd in a ry r a d ia tio n th e o ry .
K = co n sta n t o f p r o p o r tio n a lity , depending upon the number o f
e le c tr o n s co u nted.
I t has been shown
14
t h a t f o r elem ents o f medium atom ic number, f
may be w r itte n in th e r a th e r simple form
ZirtHZnVl +77 k
f =
V_
V l ’+' *
-Sirov Z
ri
where * = 2ire*/hc * 1/137 = f in e s tr u c tu r e c o n s ta n t.
F and f are p lo tte d as fu n c tio n s o f 7} f o r Mn®6 and I ^ 8 i n Figdre VI.
Now, to f u r th e r f a c i l i t a t e comparison w ith experim ent, Equation
(2) may be w r itte n as fo llo w s:
V W Jt = K j v i + 7)a
“ V T T /p -]
which i s th e e q u atio n o f a s t r a i g h t l i n e .
(3)
However, i f one p lo ts VN/f
against Vl + 7)4 , a smooth curve (not a straight line) generally re-
s u its .
In th e s p rin g o f 1935, Eonopinski and Uhlenbeck
17
proposed a
m o d ific a tio n o f F e rm i's th e o ry by in tro d u c in g h ig h er term s in th e e le c tr o n -n e u tr in o in t e r a c t io n .
The eq u atio n r e s u ltin g may be w r itte n
a s:
K [vi + 7 ) J
I f one p lo ts
- VI + })*]
a g a in s t V l + V
(4)
, in many cases a s tr a ig h t
l in e does en su e, p ro v id in g one co n fin es h is a tt e n t io n to the mid p o r-
17 Eonopinski and Uhlenbeck, Phys. Rev. 48, 8 (1935)
/'
F f o r i ' 2®
Fermi's
Functions
Fig. 6
I
2V
tio n s o f th e spectrum .
However, a t th e upper and lower l i m i t s , th e ob­
served p o in ts are q u ite a b i t below the s tr a ig h t lin e determ ined by th e
major p o rtio n o f th e spectrum .
I n o th e r c a se s, th e p lo tte d p o in ts do n o t arran g e them selves in a
s tr a i g h t l i n e , b u t along a curve t h a t su g g ests t h a t th e 3 -ra y s might be
d iv id e d in to two o r more groups.
I t should be emphasized here t h a t the pro cess o f decomposing a 3 ra y spectrum in to groups i s independent o f the v a l i d i t y o f the K-U th eo ry .
This p ro cess was f i r s t suggested by E l l i s and Mott
18
.
They f in d
t h a t th e RaC spectrum can be b u i l t o f fiv e components, each having the
same shape a s th e HaE spectrum , which i s regarded by them as a sim ple
spectrum .
The end p o in ts and r e l a t iv e p o p u latio n s o f th e se f iv e com­
ponents are c o r re la te d w ith th e known e n e rg ie s and i n t e n s i t i e s o f the
y -ra y s accompanying th e RaC - RaC* d is in te g r a tio n .
Now, i t has been shown by s e v e ra l workers 19 t h a t , ex cep t a t th e
end p o in ts , th e 3 -ra y spectrum o f RaE c lo s e ly fo llo w s th e K-U th e o ry .
T h erefo re, i f th e p ro cess suggested by E l l i s and Mott be v a lid a t a l l ,
and i f th e RaE spectrum be sim ple, th e n th e K-U th eo ry a ffo rd s a con­
v e n ie n t implement f o r e f f e c tin g such a r e s o lu tio n in to groups, whether
th e th e o ry i t s e l f be v a lid o r n o t.
But i f th e assum ption t h a t th e RaE
spectrum i s sim ple be in c o r r e c t, th e n th e K-U th eo ry no lo n g er serv es
t h i s purpose, and i t i s n o t c o r re c t to i n t e r p r e t d e p a rtu re s from a
18 E l l i s and M ott, P ro c. Roy. Soc. A141, 502 (1934)
19 E. M. Hyman, Phys. Rev. 51, 1 (1937);
Langer and W hitaker, Phys. Rev. 51, 713 (1937);
The Rev. J . S . O’Conor, S . J . , Phys. Rev. 52, 303 (1937).
zs
s t r a i g h t lim a i n th e K-U p lo t as evidence o f group s tr u c tu r e .
I n the fo llo w in g p ro ced ure, th e r e f o r e , nothing i s assumed a s to the
th e o r e t ic a l v a l i d i t y o f the K-U th e o ry :
E quation (4) i s used m erely as a
convenient method o f e f f e c tin g th e p ro cess proposed by E l l i s and M ott.
VN'/f i s p lo tte d a g a in s t V l ' +
, as shown in F ig u re s IX and XVI.
I t w i l l be observed t h a t f o r t o t a l e n e rg ie s g r e a te r th an 3 me*, th e p o in ts
l i e c lo se to a s t r a i g h t l i n e .
The b e s t s tr a i g h t l in e amongst th e se p o in ts
was found by l e a s t sq u ares and e x tra p o la te d back to the v e r t i c a l a x is .
Next was computed th e momentum d i s t r i b u t i o n o f e le c tr o n s which
would e x a c tly f i t t h i s s t r a i g h t l i n e .
T his th e o r e tic a l d i s t r i b u t i o n was
s u b tra c te d from th e observed d is t r i b u t i o n , and a K-U p lo t o f t h i s d i f ­
fe re n ce was th e n co n stru cted in th e same manner as th e o r ig in a l K-U p l o t .
In th e case o f I ^ 28, th e K-U p lo t o f t h i s d iffe re n c e i s j u s t th e
s tr a i g h t l i n e shown i n F ig u re XVI.
56
I n th e case o f Mn , th e K-U p lo t
o f th e f i r s t d iffe re n c e c o n s is ts o f a s tr a ig h t lin e p o rtio n and a smooth
cu rv e.
By re p e a tin g th e p ro cess ju s t d e sc rib e d , a K-U p lo t o f th e second
d iffe re n c e was o b ta in e d .
T his t h i r d p lo t c o n s is ts o f m erely the s tr a i g h t
lin e shown i n F igure IX.
F in a lly , th ese t h e o r e t ic a l d is tr ib u ti o n s were added to give the
smooth curves shown in F ig u re s VTII and XV; and th e K-U p lo ts o f th e se
th e o r e t ic a l sums were computed to give th e smooth curves shown in F ig­
u re s IX and XVI f o r e n e rg ie s l e s s th an 3 me*.
Fermi p lo ts are a ls o shown.
manner a s the K-U p l o t s .
They were c o n stru c te d i n the same
I t i s seen th a t i t i s n o t f e a s ib le to pass a
s t r a i g h t I'*"** through th e h igh energy t a i l o f th e se p l o t s .
In t h i s con-
n e c tio n , a t t e n t i o n m ight be in v ite d to a re c e n t work by Eonopinski
20
who
shows t h a t beoause o f th e s c a tte r in g o f th e e le c tr o n s i n the 3-ra y so u rce,
a Fermi d i s t r i b u t i o n o f 0 - p a r t ic le s might be d is to r te d in to an apparent
K-U d i s t r i b u t i o n .
This would be a l l r i g h t i f one eould re c o n c ile th e end
p o in ts (upper lim its ) p re d ic te d by th e two th e o r ie s from the same s e t of
d a ta .
The non-agreem ent o f th e "observed" and th e K-U end p o in ts does n o t
have much s ig n if ic a n c e , a s long as th e "observed" end p o in t i s below the
K-U upper l i m i t .
As can be seen from th e T ables, one would have to ob­
serve more th a n a m illio n tra c k s in o rd e r to have a reasonable chance o f
fin d in g an e le c tr o n o f energy w ith in 100 keV o f th e K-U upper l i m i t .
The Compton E f f e c t
When an e n e rg e tic photon s tr i k e s a r e l a t i v e l y f r e e e le c tr o n a t
com parative r e s t w ith r e s p e c t to th e o b se rv e r, the e le c tr o n i s e je c te d
w ith c o n sid e ra b le v e lo c ity , and an o th er, l e s s e n e rg e tic photon i s pro­
duced, w ith v e lo c ity in such a d ir e c tio n as to s a t i s f y the fo llo w in g
energy and momentum r e l a t io n s :
h v - h P" + me*(VI +
- 1)
hP
0
where h
p
* energy o f the in c id e n t photon
hp'/'c * momentum o f th e in c id e n t photon
hi/'
=* energy o f the s c a tte re d photon
20 E. J . E onopinski, B u lle tin o f th e American P h y sic a l S o c ie ty ,
Chicago M eeting, December 1939, Paper No. 14.
m eV
Energy
of Incident Quanta
2. 0 -
0 .5 -
1
M o m en tu m
2
of E le c tr o n s
4
3
E je c te d
me
in F o r w a r d O ir e c t io n
b y C o m p to n E f f e c t
F ig. 7 ..................
ZQ
h ii'/c
y
■ momentum o f th e s c a tte r e d photon
- d ir e c tio n o f motion o f th e s c a tte re d photon
<j> * d ir e c tio n o f motion o f th e r e c o i l e le c tr o n .
E lim in a tin g hi*' and ip from th e se me o b ta in
me* (Vl + u * - 1)
" 7] cos ^ - (vT"+jjl + 1)
______
=
V
me* (VI + * - 1 + h )
g
,
when)? =
(5)
0
The second o f E quations (5) i s p lo tte d in F igure V II.
Thus, i f 7] and
ured a t once.
could be measured e x a c tly , h.tJ could be meas­
Now, th e r e c o i l e le c tr o n s are em itte d from a th i n sh eet
o f bake11te (su rfa c e d e n s ity 100 mg/cm*), and th e r e fo r e , because o f e le c tr o n s c a tte r in g in t h i s s h e e t, one can be c e r ta in o f n e i th e r the
i n i t i a l v alue o f
A
s ta tis tic a l
nor o f .
method, th e r e fo r e , based on the form ula o f K lein
and N is h in a ^ has been evolved by R ichardson and K u r ie ^ f o r determ in ­
in g th e e n e rg ie s o f th e y - ra y li n e s i n term s o f th e measured v alu es
o f T| and (j>.
T his i s th e method used by u s .
21 K lein and N ish in a, Z e i t , f . Physik 52 , 853 (1928)
22 R ichardson and K u rie, Phys. Rev. 50, 999 (1936)
r
19
RESULTS
The Bet a -ra y Spectrum o f lih5®.
The work on th e 3 -ra y spectrum o f Mn56 may be d iv id e d in to two
p a r ts - t h a t done d u rin g th e summer o f 1937, and t h a t done d u rin g th e
w in te r o f 1937-1938.
D uring th e f i r s t p a r t o f t h i s work, we bad b u t
50 mg o f radium mixed w ith b ery lliu m ; d u rin g th e second p a r t , we had
200 mg Ra + Be.
We ir r a d i a t e d o v ern ig h t two pounds o f NaMnO^ w ith th e n eu tro n s
from th e 50 mg so u rc e .
I n th e morning, th e permanganate was d isso lv e d
i n as l i t t l e d i s t i l l e d w ater a s p o s s ib le .
NaMnO was used because o f
i t s g r e a te r r a p i d it y o f s o lu tio n and a ls o because o f i t s g r e a te r s o lu ­
b i l i t y - s e v e ra l tim es t h a t o f KMnO^.
The s o lu tio n was th e n f i l t e r e d ,
u sing a Buchner fu n n e l 11 cm in d iam eter.
56
The Mn was d ep o site d a s an
in so lu b le oxide on th e f i l t e r p ap er, which becomes th o roughly impreg­
n ated w ith v a rio u s manganese compounds by th e passage o f th e f i r s t few
cc o f t h i s s o lu tio n .
A second run was made w ith a f r e s h sample o f NaMn04 .
The so lu ­
tio n was preserved each tim e , and in succeeding ru n s, th e two s o lu tio n s ,
poured to g e th e r, were i r r a d i a t e d .
With two e x c e p tio n s, th e i n t e n s i t i e s
o b tain ed were about th e same each tim e - about 150,000 d is in te g r a tio n s
p e r m in u te.
(On th e se two o cc a sio n s, th e i n t e n s i t i e s were so g r e a t t h a t
a few h o u rs - approxim ately two h a l f - l i v e s - had to be allow ed to e la p s e
b efo re th e samples were u sable in the cloud chamber.J The mass o f th e
t o t a l d e p o s it on th e f i l t e r papers in th e se ru n s was from 70 to 100 mg
(about one mg/cm*).
30
The f i l t e r paper c o n ta in in g the a c tiv e d e p o s it was th en o u t in to
two s t r i p s , 3 .5 z 11 cm, and th e s t r i p s a ffix e d to th e in s id e o f the
g la s s r in g by means o f sm all wads o f Apiezon Q a t the c o rn e rs .
was th en b o lte d in to p lace and s e a le d .
The head
The chamber was then f i l l e d w ith
helium (sometimes w ith hydrogen) f o r some o f the ru n s, and l e f t f i l l e d
w ith a i r f o r o th e r s .
I t was found th a t th e gas in th e chamber had a l ­
most no e f f e c t on th e m ajor p o rtio n o f th e spectrum.
I n g e n e ra l, two hours o r more elap se d between th e time an i r r a d i ­
a tio n ceased and th e time photographing began.
However, th e a c t i v i t y
was s t i l l g r e a t enough to be u sab le f o r two o r th re e h a l f - l i v e s .
Four d i f f e r e n t m agnetic f i e l d s were used i n t h i s work - 850, 637,
425 and 319 o e r s te d s .
A s h o rt ru n w ith 212 o e rs te d s was a lso made: i t
shows n o th in g more th an does th e 319 gauss ru n , and i s th e re fo re om it­
te d from th e d is c u s s io n f o r sake o f b r e v ity .
The r e s u l t s 23 o f th e ru n s w ith th e th re e h ig h er f i e l d s may be
summarized as fo llo w s:
The 850 gauss ru n s d u p lic a te d alm ost e x a c tly th e curve o f G aertt n e r , T urin and Crane1 : th e observed e le c tr o n s seemed to f i t a s in g le
K-U group having an upper l i m i t a t 6.58 - .10 me* (2.84 1 .05 MeV).
The ru n s a t 637 and 425 gauss seemed to support the work o f Brown and
n
appeared
M itc h e ll : th e observed e le c tr o n s Ato f i t in to two groups, having up­
p e r lim its a t 6 .5 5 and 3.25 me* (2.80 and 1.15 MeV), r e s p e c tiv e ly .
The end p o in ts found by Brown and M itc h e ll are 6 .8 and 3 .4 me* (2 .9
and 1 .2 MeV), r e s p e c tiv e ly .
23 Bacon, Grisewood and van d e r Merwe, Phys. Bev. 5£, 668 (1937)
3!
The d iffe re n c e between th e p o s itio n s o f th e upper l i m i t as d e te r ­
mined by Brown end M itc h e ll and t h a t as determ ined by G a e rttn e r, T urin
and Crane o r by o u rse lv e s may be e a s ily ex p lain ed as fo llo w s:
The s tro n g e s t f i e l d used by Brown and M itc h e ll was 490 g au ss.
In
t h i s f i e l d , a 2 MeV e le c tr o n , f o r in s ta n c e , t r a v e ls in an a rc o f 17 cm
r a d iu s .
The a p e rtu re o f t h e i r cloud chamber i s o n ly 13 cm in diam eter
- much too s h o rt a chord f o r m easuring such an a rc w ith the d e s ire d ac­
curacy and, th e r e f o r e , th e v alu e o f th e end p o in t as given by them i s
n o t a s r e l i a b l e a s i t would have been had th ey used a f i e l d o f , say,
800 g a u ss.
Since th e c h a r a c t e r i s t i c s o f th e second group are found only by
s u b tr a c tio n , i t fo llo w s t h a t a displacem ent o f th e assumed end p o in t
o f th e most e n e rg e tic group would be accompanied by a s h i f t o f th e value
to be found f o r th e upper l i m i t of th e second group.
A s h o rt ru n a t 319 gauss (and one a t 212) seemed to in d ic a te a
t h i r d group w ith an end p o in t a t about 2 .2 me* ( .6 MeV).
We decided
to re p e a t th e se ru n s b efo re announcing t h i s r e s u l t , but were prevented
from doing so im m ediately by th e sudden appearance o f some unknown con­
tam inant in th e chamber i n th e middle of th e summer.
P rev io u s to t h a t tim e , th e n a tu r a l background o f the chamber had
been one tr a c k ( i . e . , one tr a c k which would have been m istaken f o r a
prim ary e le c tr o n from a ra d io a c tiv e body had th e r e been one p laced in
th e chamber) every seven expansions.
tim e.
T his was checked from time to
These fo re ig n tra c k s were assumed to have n e g lig ib le e f f e c t on
th e measurement o f a spectrum , as we u s u a lly had from f iv e to tw enty
tra c k s on a p ic tu r e .
However, we disco v ered on August 11, 1937 th a t
t h i s background had suddenly jumped to about th re e such tra c k s p e r ex­
p a n sio n .
We secured new g la ssw a re , a new p is to n and had th e b ra ss c y lin ­
d e r and cup tu rn e d on th e la th e to remove any contam inated s u rfa c e ,
were th u s a b le to reduce t h i s background to 60 such tra c k s in 100 ex­
p a n sio n s.
A spectrum o f th e se tr a c k s , a t d if f e r e n t f i e l d s , was tak en
between each ru n from th e n on, and t h i s spectrum s u b tra c te d from the ob­
served s p e c tra o f Mn56 and I 128.
Meanwhile, we acq u ired th e new n eu tro n source co n ta in in g 200 mg
mixed w ith Be.
We now c u t o u r f i l t e r papers in to s t r i p s 2 x 11 cm.
Even so , th e i n i t i a l a c t i v i t y was on a few o ccasio n s so in te n s e th a t a
few h a l f - l i v e s , on one o ccasio n f iv e h a l f - l i v e s , were allow ed to e la p se
b e fo re photographing began, u n t i l the a c t i v i t y subsided to a s u ita b le
le v e l - n o t more than 20 to 25 tra c k s p er p ic tu r e .
I n c id e n ta lly , t h i s
stu d y in g o f samples o f d i f f e r e n t ages d id n o t b e tra y any r e a l d iffe re n c e
in th e h a l f - l i v e s o f th e v a rio u s groups in to which th e spectrum may be
d iv id e d i f one uses th e K-U th eo ry to d e sc rib e i t .
As mentioned above, th e r e s u l t s o f th e se ru n s , tak en a t 850, 637
and 319 g au ss, and shown in F ig u res V III, IX and X, d i f f e r from th o se
o f th e prev io u s summer only in t h a t th e ap parent r e l a t iv e p o p u la tio n s
o f th e low energy groups now seem to be g r e a te r th an they d id a t f i r s t .
I n a l l , e i g h t ru n s were made, in c lu d in g runs w ith new samples o f KMnO^
and a new box o f f i l t e r p ap ers f o r each ru n , and th e background meas­
ured w ith th e decayed source s t i l l in the chamber a few days l a t e r
(each day °> 10 h a l f - l i v e s ) .
Ihe m utual concordance amongst th e se runs
may be judged from an in s p e c tio n o f F ig u res XI and X II.
The f i d e l i t y
w ith which t h i s spectrum appears to fo llo w th e K-U th e o ry may be ob-
I n te r v a l
Momentum
B eta Ray S p e c tru m of Mn56
8 5 0 Gauss
6 3 7 Gauss
Number
of Electrons
in Each
Gauss
H orizontal
Com ponent
of the M om entum of
Fig. 8
me—
the O b s e r v e d E l e c t r o n s
M n ^ K - U Plof
,
8 5 0 Gauss
0
6 3 7 Gauss
a
319 Gauss
Energy of fhe Emiffed E lecfro n s
Fig. 9
9
8
7
6
5-
Mn56— Fermi
Plot
Althothe plowed points between 3.4 and
5.1 p itfa ll quite accurately on a straight line,
it is not possible to resolve this spectrum
further by this m ethod, as the Fermi Plot of
the differential is a smooth curve thru which
if is impossible to pass a significant straight
line.
4-
850 Gauss
637 Gauss
3-
210E nergy of E m itte d
E l e c tr o n s
me*
I
3i
TABLE I
3-ray Spectrum of Mn®6
2f>
Obs.
%
C alo.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
19
63
135
185
238
175
144
111
91
70
58
46
40
35
28
20
14
8
4
4
2
2
0
1
0
7 .5
16.3
26.9
38.0
48.5
57.2
63.4
67.0
67.8
66.0
62.1
56.4
49.4
4 1 .7
34.2
26.7
19.9
14.1
9 .3
5.6
3 .0
1 .4
.5
.1
.009
6x10" 6
T o ta l
1493
B el. Pop.
Calo.
87.6
175.0
242
278
264
219
150
86.7
41.3
15.0
1 .8
.01
-
NI I I
C alc.
T o ta l
C ale.
160
29 2
310
240
114
35
255
384
579
556
426
301
216
154
109
81
64
56
49
42
34
27
20
14
9
6
3
1
1 /2
1/10
10"6
783
1560
1155i
2
4
3
3498
850 Gauss
D if f .
Obs
K-U
-365
-513
-421
-241
- 63
- 41
- 10
+ 2
+ 10
+ 6
+ 2
- 3
- 2
+ 1
+ 1
0
0
.00
.05
.11
.24
.44
.79
.81
.94
1.02
1.12
1.09
1.02
.94
.96
1.02
1.05
1.00
1.00
Cale
.00
.00
.21
.60
.75
.83
.90
.94
.98
1.00
1 .02
1 .0 4
1.06
1 .0 7
1.09
1.03
.97
.96
.9 4
.93
37
TABLE I I
0 -ra y Spectrum o f Mn®6 -
637 Gauss
T o tal
D if f .
Obs
K-U
Calc
164
305
402
475
469
384
333
257
199
155
117
90
70
58
51
47
43
38
33
28
-297
-378
-381
-307
-185
-116
- 33
0
+ 7
0
- 4
- 1
- 7
0
- 1
0
0
0
- 6
.00
.04
.11
.24
.35
.57
.74
.91
1.00
1.04
1.00
.95
.98
.88
1.00
.98
1.00
1.00
1.00
.70
.00
.00
.21
.60
.75
.83
.90
.94
.98
1.00
1.02
1.04
1.06
1.07
1.09
1.03
.97
.96
.94
.93
+
1.01
.9 +
2p
Obs.
si
C ale.
N il
C a le.
N lII
C ale.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
8
44
112
162
220
247
234
199
162
117
86
69
51
51
46
43
38
33
22
4 .6
9 .6
16
22
29
36
42
47
52
54
56
56
55
53.5
50.5
47
43
38
33
28
54
107
160
201
226
230
213
182
142
101
61
34
15
4 .5
.7
.008
105
188
826
252
214
118
78
28
5
Und.
68
Over
98
97
T o ta l
2023
870
.1
97
1732
1214
1
3816
Und. = Undetermined , i . e . , tra c k s whose ra d iu s o f cu rv a tu re could not
be measured w ith th e d e s ir e d accu racy .
I n a l l , th e r e were 110 such
tr a c k s , o f which 42 a re in clu d ed amongst the 98 "o v er 20" and the r e ­
maining 68 had d ia m e ters o f curvature between 10 and 20 cm.
39
TABIE I I I
Un56
- 319 Gauss
Obs.
NI
C alc.
C alc.
% II
C ale.
T o ta l
C alo.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
46
84
141
188
229
255
258
255
247
200
158
134
137
96
64
65
63
41
1 .2
2 .5
3 .8
5 .2
6 .8
8 .5
10.2
12.1
14.0
16.0
17.7
19.5
21.2
22.8
24.3
25.7
26.8
28.0
28.8
29.5
14.5
29.3
43.8
58.1
72.2
8 6 .3
102
109
116
122
124
123.8
120.3
115.0
109.0
98.5
8 7 .1
76.6
65.4
54.5
29.6
57.4
83.0
104
123
136
141
140
132
118
101
81.2
61.2
43.0
27.8
15.7
7.7
2.9
.7
.07
46
89
129
167
202
231
253
261
262
256
242
223
202
181
161
140
122
108
95
84
Und.
362
Over
685
634
154
10"5
788
946
1890
1405
4246
2p
T o tal
3708
D if f .
Obs.
K-U
-46
-89
-83
-83
-59
-43
-24
- 6
- 4
- 1
+ 5
.00
.00
.35
.50
.70
.81
.90
.98
.98
1.00
1.02
-371
Calc
.00
.00
.21
.60
.75
.83
.90
.94
.98
1.00
1.02
1.04
1.06
1.07
1.09
1.03
.97
.96
.94
.93
The o b je c t o f th e se measurements was m erely to observe th e shape o f th e
r i s i n g p o rtio n o f th e curve below about 250 Kv ( i . e . , below diam eters
I
o f 12 cm). T h e refo re , l e s s tim e and e f f o r t were sp en t on a d i f f i c u l t y
measured tr a c k o f d iam eter g r e a te r th a n 12 cm th an would have been sp en t
on a tr a c k o f s im ila r cu rv a tu re a t 850 g au ss.
Mrf-Mutual Concordance Amongst the Runs
319 Gauss
© December 8,1937
■ December 21,1937
• January 14.1938
e February 17.1938
• January, 1939
i
• •
850 Gauss
© December 6.1937
□ December 20,1937
■ December 21,1937
s January. 1939
0 Close agreement among
two or more points.
©
e«
0
2
s s
©
s
I
©
□
0
—r
05
1
1.5
T
2
i
2.5
3
T
3.5
“ I--------
4
4,5
me—*
Horizontal Component of Momentum of Observed Electrons
Fig.11
Mn5- 6 3 7 Gauss
January 14,1938
December 21.1937
December 7,1937
February 17,1938
Concordance among Fhe Runs
Fig. 12
served by examining T ables I , I I and I I I .
The Gamma Hays accompanying th e Decay o f Mn56.
The s o lu tio n o f NaMn04 , now c o n ta in in g 5 pounds in 5 g a llo n s o f
d i s t i l l e d w a te r, was i r r a d i a t e d o v ern ig h t and f i l t e r e d in th e morning.
The s t i l l m o ist f i l t e r paper was th en r o ll e d and compressed in to as
t i g h t a wad as p o s s ib le (about 5 mm in d iam eter) and p laced in a r e s t
between th e f i e l d c o i l s , in th e m id-plane o f the cloud chamber.
Owing
to th e weakness o f t h i s y - r a y so u rc e , as compared to th e so u rces used
by Richardson and K urie22, f o r in s ta n c e , i t was n o t f e a s ib le to p lace
i t a s f a r from th e chamber a s th ey d id .
There i s th u s in tro d u ced in to
th e measurements o f th e angle between th e observed d ir e c tio n o f the
i n i t i a l m otion o f th e e je c te d e le c tr o n and th e assumed d ir e c tio n o f
th e motion o f th e in c id e n t photon a sm all e r r o r (o f n o t more th an 5°
in th e w orst in s ta n c e ) .
As a check on t h i s work, we measured th e energy o f the a n n ih i­
l a t i o n r a d ia tio n from the Cu p o s itro n e m itte r s formed by th e bombardment o f a n ic k e l f o i l by p ro to n s in th e Columbia c y c lo tro n
24
.
As me­
t a l l i c n ic k e l would d is tu r b th e m agnetic f i e l d , th e ir r a d i a te d f o i l
was d isso lv e d in HNOg, and th e sm all mass o f Ni (NOgIg was l a i d i n the
56
same p lace a s had been th e Mn b e fo re .
The r e s u l t s o f th e se m easure­
ments a re shown i n F igure X III.
For com parison, th e re i s a ls o drawn
22
to a p p ro p ria te s c a le th e r e s u l t o b tain ed by R ichardson and K urie
who
used a lamina o f about one q u a rte r th e su rfa c e d e n s ity o f o u rs to meas-
24 We ta k e t h i s o p p o rtu n ity to e x p re ss ou r a p p re c ia tio n to P ro fe s so r
J . R. Dunning and D r. E. T. Booth f o r t h e i r kindness and i n t e r e s t .
o
Data obtained by
Richardson and Kur i e . Phys
Rev.50,999 (1936). Electrons
ejected from radiator 4 0
mq/cm2 by annihilation radi­
ation from N® 250 Gauss.
Elecfrons ejected from
radiator 100 mq/fcm2by an­
nihilation from Cu isotopes
excited by bombarding Ni
with protons. 425 Gauss.
T
3
T
3.5
4 me-
Electrons emitted from
radiator 100 mq/6m2by
gamma rays accompany iny the decay of Mn?? 425
Gauss.
tme
Horizontal Component of the Momentum of Electrons Ejected
by the Gamma Rays
Fig. 13
¥3
u re th e a n n ih ila tio n r a d ia tio n from N13.
The r e s u l t s
25
o f o u r measurements, as sh o rn in F igure X III, seem
to in d ic a te a y - ra y lin e a t about 600 o r 700 keV, and perhaps one a t a bout 1 .7 MeV.
However, th e complete i n t e r p r e t a t i o n i s n o t c le a r - i t i s
probable t h a t th e re are o th e r lin e s a l s o .
For th e r e la tiv e i n t e n s i t i e s ,
we o b ta in
Sum o f th e i n t e n s i t i e s o f a l l li n e s below .7 MeV v g
Sum o f th e i n t e n s i t i e s o f a l l li n e s above .7 MeV
g
These r e s u l t s agree w ith th o se o f Dunworth ; th e r e s t of o u r an aly ses
o f th e se d a ta do n o t.
e/*
D iscu ssio n o f th e R e su lts o f Measurements o f th e R a d io a c tiv ity o f Mn
Tobegin w ith , i t should be p o in ted
cfi
Mn
.
o u t t h a t the y - r a y s from
are q u ite in te n se compared w ith th e t o t a l a c t i v i t y .
In Table IV
i s a com parison o f t h i s a c t i v i t y w ith t h a t o f s e v e ra l o th e r elem ents.
56
F u rth e r, when th e samples o f Mn were placed in s id e the cloud chamber,
th e number o f e le c tr o n tra c k s a s c rib a b le to the y - r a y s was eq u a l to
about one f i f t h o f th e number a s c rib e d to the prim ary 0 -ra y d i s i n t e ­
g r a tio n s .
Ho a tte m p t was made to determ ine th e momentum d is tr i b u t i o n
o f th ese secondary e le c tr o n s , as th ey were e m itte d from a l l over the
chamber, c h ie f ly from th e w a lls .
Hence, th e an g le between th e i n i t i a l
m otion o f th ese e le c tro n s and th e m otion o f th e in c id e n t quanta was
e n t i r e l y unknown, a s was a lso the depth from which they were e m itted ,
and th e r e fo r e , th e spectrum o f th e s e e le c tro n s would be q u ite meaning­
le ss .
25 Bacon, Grisewood and van d e r Merwe, P hys. Rev. 56, 1168 (1939)
TABLE IV.
The r e l a t i v e gamma a c t i v i t i e s o f a few ra d io a c tiv e is o to p e s .
I o n iz a tio n chamber and e le c tro sc o p e measurements.
Element
y /to ta l
O bserver
Cu62 (e+)
Cu61 (e+ )
Cu64
2n63 (e+ )
.012
.016
.010
.014
Chas. V. S t r a in , Phys. Rev. 54, 1032 (1938)
"
"
m
n t i
"
«
«
i»
«
"
"
*
"
"
Fe59
.04
Livingood and Seaborg, Phys. Rev. 54, 51 (38)
Mn51 (e+)
Mn52 (e+)
Mn56 (e “ )
.0016
.2
.04
Livingood and Seaborg, Phys. Rev. 54, 392 (38)
«
«
i»
«
it *
ft
"
"
"
"
"
n
1 ^
(e“ )
l “ | (e “ )
t j s (•:>
I 130 ( • )
.1
.0015
Livingood and Seaborg, Phys. Rev. 54, 777 (38)
(e “ )
Mn56 (e “ )
.0 1
.04
.04
ft
ft
ft
ft
ft
ft
ft
tf
ft
ft
ft
ft
ft
It
ft
tf
ft
W. J . Horvath
(unpublished)
G eiger co u n te r measurements.
In
(e " )
.02
V. J . H orvath
(unpublished)
I 128 (e~)
.00068
Bacon and H ornbostel
Mu58 (e“ )
.018
Bacon, H ornbostel and Horvath
ft
Hs
Now, th e f i l t e r p ap ers covered ahourt o n e -s ix th o f the a re a o f the
in s id e o f th e g la s s r in g , so t h a t one tw e n ty - f if th to o n e - t h ir t i e t h of
th e e le c tr o n s regarded a s p rim a rie s were probably se c o n d aries e je c te d
from th e source by th e
y -ra y s.
As most o f these secondary e le c tro n s
a re o f low en erg y , i t i s probable th a t a p o rtio n o f the " th ir d group"
r e a l l y c o n s is ts o f secondary e le c tr o n s .
Secondly, th e f i l t e r papers were p laced so c lo se to the g la s s r in g
t h a t a number o f e le c tr o n s in c id e n t upon i t must have been r e f le c t e d
back in to th e v is ib le p o rtio n o f th e chamber.
These r e f le c te d e le c tr o n s
would have l o s t some o f t h e i r k in e tic energy in th e p ro c e ss .
F u rth e r,
many slow e le c tr o n s l o s t ap p re c ia b le a p p o rtio n s o f t h e i r energy in e s ­
caping from th e source in th e f i r s t p la c e , so th a t th e y were measured
as even slow er e le c tr o n s .
The low energy end o f th e spectrum i s th e r e ­
by enhanced, and th e " t h i r d group" i s th u s probably en larg ed beyond
i t s tru e s iz e .
The adherence o f t h i s " th ir d group" to the observed K-U lin e i s ,
th e r e fo r e , regarded as a b i t a c c id e n ta l.
However, i t i s n o t l i k e l y
th a t th e e n t i r e " t h i r d group" c o n s is ts m erely o f se c o n d a rie s, as i t s
r e l a t i v e p o p u latio n i s to o g r e a t:
t h i s " th ir d group" accounts f o r
o n e -th ird o f a l l th e e le c tr o n s counted a t 319 g a u ss.
The tru e popu­
l a t i o n and upper li m i t o f th e " t h ir d group", th e r e f o r e , are n o t r e ­
garded as w e ll determ ined by ou r ex p erim en ts, b u t th ese q u a n titie s
a re n o t b e lie v e d to be v ery d if f e r e n t from th e observed v a lu e s .
I t m ight be urged t h a t th e " th ir d group" re p re s e n ts th e p a r t i a l
i n t e r n a l co n v ersio n o f a y - r a y lin e o f about 600 o r 700 keV,
This
p o s s i b i l i t y cannot be d e f i n i t e l y excluded, b u t i t seems v e ry u n lik e ly .
r
*lo
As w i l l be seen in th e n ex t few parag rap h s, th e observed unconverted i n ­
t e n s i t y o f t h i s lin e i s q u ite g re a t a lre a d y , so t h a t , u n le ss th e re be
s e v e ra l l i n e s o f about t h i s energy in t h i s spectrum , th e p o s s i b i l i t y o f
stro n g i n te r n a l co nversion seems to be r a th e r sm all.
I n th e coincidence cou n ting experim ents, b o th Dunworth® and Langer,
M itc h e ll and McDaniel
n
fin d t h a t th e re i s a t l e a s t one y - r a y lin e ac­
companying th e h ig h e st energy e le c tr o n group; and Dunworth fin d s th a t
th is
y - r a y l in e i s th e one having energy about 600 keV.
From t h i s , i t
would appear t h a t th e most e n e rg e tic 0 -ra y t r a n s i t i o n from Mn
an e x c ite d s t a t e o f Fe
le a d s to
a t l e a s t 600 keV above th e ground s t a t e .
Dunworth th en c o r r e la te s th e 1 .7 MeV y - r a y observed by him w ith
th e d iffe re n c e in energy between th e f i r s t two 0 -ra y groups, and sup­
poses th a t th e l e s s e n e rg e tic 0 -ra y t r a n s i t i o n i s follow ed by two y r a y s , th e 1 .7 and th e .6 MeV in tu r n , a s shown in F igure XEV(a).
The
fin d in g s o f Langer, M itc h e ll and McDaniel a ls o suggest t h i s .
Now, th e second group o f 0 -ra y s i s tw ice as in te n se as the most
e n e rg e tic group.
The h igh energy y - r a y , th e r e f o r e , should, according
to Dunworth*s p ic tu r e , be tw o -th ird s as in te n se as th e low energy y ra y .
Dunworth, however, (and we a ls o ) fin d th a t th e h ig h energy y -
ra y i s on ly tw o - f if th s a s in te n se as th e low energy y - r a y , le a d in g
him to th e co n clu sio n t h a t th e second group i s only tw o -th ird s a s i n ­
ten se as th e most e n e rg e tic group.
There a re s e v e ra l ways o f c o r r e la tin g th e observed r a t i o o f the
i n t e n s i t i e s o f th e y - r a y l i n e s w ith th e observed r a t i o o f th e in t e n s i ­
t i e s o f th e 0 -ra y g roups.
(c) and ( d ) .
Three o f th e se are shown in F ig u res ZIV (b),
Each in v o lv es the su p p o sitio n t h a t th e re are two o r more
-3-
_J2_
_£_
X Dunworth's p ic £ . Sim plest m o d ili£ . Another possible
lu re does not a g r e e
c a llo n of Dun w o rth 's te r m sc h e m e , based
with the o b s e rv e d in -sc h em e, to a c c o u n t on the a ssu m p tio n th a t
tensities of the b e ta - simultaneously to r the th e re is a g a m m a ra y g roups.
observed in te n s itie s lin e a t a bout 1.1 MeV
of both the g a m m a r a y lin e s and th e '
b e t a - r a y groups.
Note: —
» g a m m a -ra y .
........
_d_
_£_
jL Possible diagram
to account lo r lha
th ird b e t a - r a y group,
a s w ell a s tor th e
observed in te n sitie s
of the o th e r m o re
c e r t a i n com ponents
of this sp e c tru m .
t ,Possible scheme,
based on Fragmentary
Fermi Analysis of the
Beta-Ray Spectrum ,
In order to account
to r the observed in­
tensities ot the gammaray lines ot about
0 .6 MeV, other trans­
itions must a ls o occur.
» b e ta - ray .
m
l i n e s o f approxim ately 600 to 700 keV, n o t reso lv e d e i t h e r by Dunworth
o r by o u rs e lv e s .
The sim p le st o f th e se i s F igure xrv(b), which m erely
supposes t h a t each o f th e p ro c e sse s co n sid ered by Dunworth i s follow ed
by a n o th e r y - r a y l i n e o f about 600 o r 700 keV.
By c o n s u ltin g Table V, i t i s seen th a t th e
y - r a y background i s
la rg e compared to t h a t observed in o th e r a c t i v i t i e s .
F u rth e r, by in 7
s p e c tio n o f F ig u re 2 in th e p aper o f Langer, M itc h e ll and McDaniel , i t
i s observed t h a t th e re i s an ab ru p t change in th e r a t i o o f 3 - y c o in c i­
dences p e r 3 - p a r t i c l e counted a t a 0 -ra y energy o f about .7 MeV.
i s j u s t th e energy o f our t h i r d group.
This
Remembering t h a t the e f f ic ie n c y
o f th e counting system f o r d e te c tin g th e e le c tr o n s o f t h i s group ( th e ir
mean energy i s o n ly 180 keV) i s sm all compared to t h a t f o r th e h ig h e r
g ro u p s, we see t h a t th e r e must be a la rg e number o f quanta accompanying
t h i s group.
Now, i t i s p o s s ib le to i n f e r from th e r a th e r d if f u s e d i s t r i ­
b u tio n o f e le c tr o n s having momenta between 1.75 and 2 .5 me in Figure
X III t h a t th e r e i s a y - r a y l i n e o f about 1 .1 MeV having something
l e s s th a n tw ice th e i n t e n s i t y o f th e 1 .7 MeV l i n e .
I f one assumes
t h a t t h i s l in e r e a l l y e x i s t s , i t i s p o s sib le to c o n s tru c t th e energy
le v e l diagram s i n F ig u re s XTV(c) and ( d ) .
F ig u re XTV(c) a tte m p ts to
keep th e number o f 3~ray groups a t only two; F igure XEV(d) a tte m p ts to
account fo r the e x is te n c e o f the t h i r d group.
Of c o u rse , th e se two p o s s i b i l i t i e s are n o t th e o n ly o n es.
I t is
p o s s ib le to c o n s tru c t o th e r energy le v e l schemes which w i l l account f o r
th e p re se n t o b se rv a tio n s o f th e 3“pay® and th e y —
r a y s , usin g the K-U
th e o ry to an aly se th e 0 -ra y spectrum .
56
TABIE V Mn
- Summary o f R esu lts
B eta Ray Spectrum
Group I
EM P o in t
Obs.
K-U
Group I I
Group I I I
R el. EM P o in t R el. EM P o in t R el.
Pop.
K-U
Pop.
K-U
Pop.
Observer
2 .5 MeV
6 .0 me* 6.58 me*
2
3 .2 5 me*
4
2 me*
T his Work
2 .5 MeV
6 .0 me* 6 .8 me*
3
3 .4 me*
7
Hot
Observed
2 .5 MeV
6 .0 me* 6 .5 me*
1
Hot Observed
3 .2 MeV
(EM p o in t o n ly determ ined)
7.3 me*
3
Brown aM
M itc h e ll
G ., T .,
and C.
A. y A. i
and D.
(B e ta -ra y sp ectrograph)
1
3
(In fe re n c e from gamma ra y d a ta )
I*, t
f
and McD.
3
2
(In fere n c e from gamma ra y d a ta )
Dunworth
Gamma Ray Spectrum
Probable number
of lin e s
P robable
E n e rg ies
At l e a s t 2
1 .7 MeV
.6 MeV
1 .2 MeV 7
1
2
2
This
Work
Hot
Observed
1
2
L ., M.t
aM McD.
2
1 .7 MeV
.6 MeV
2
5
Dunworth
7
1 .2
At l e a s t 2
Probable
I n te n s i t i e s
Observer
(A bsorption measurement) Livingood
aM Seaborg
J5o
F in a lly , ad o p tin g th e su g g estio n o f Eonopinski20 th a t an ap p aren t
E-U d i s t r i b u t i o n o f e le c tr o n s i s r e a l l y a d is t o r t e d Fermi d i s t r i b u t i o n ,
we have t r i e d to see what could be in fe rr e d from th e Fermi p l o t in F ig­
ure X.
Assuming t h a t th e d i s t o r t i o n above 3 me* (1 MeV) i s v e ry sm all,
we found by l e a s t sq u ares th e b e s t s tr a ig h t lin e amongst the p o in ts
p lo tte d between 3 .6 and 5 .6 mo* (1 .3 and 2 .3 MeV).
Having done t h i s ,
one can p o s tu la te two groups o f energy 5 .8 and 3 .6 me* (2 .4 and 1 .3 MeV)
r e s p e c tiv e ly , b u t th e f i t i s so bad t h a t i t i s im possible to say any­
th in g about th e r e l a t iv e p o p u latio n o f th e second group on t h i s scheme,
n o r about th e e x iste n c e o f any low er groups.
The energy le v e l diagram
r e s u l t i n g from t h i s i s shown in F igure X IV (e).
The R a d io a c tiv ity , o f I
lOO
A s a tu ra te d s o lu tio n o f about 1500 grams o f KEOg was i r r a d i a t e d
f o r about an hour w ith th e n eu tro n s from 200 mg Ra mixed w ith Be.
Be­
fo re each i r r a d i a t i o n , th e re was added to the s o lu tio n about 1/10 gram
o f KE and a tra c e o f NH^OH.
A fte r the i r r a d i a t i o n , th e combining w eight
(about 1/15 gram) o f AgNOj was added, th e s o lu tio n was f i l t e r e d , and
IOQ
th e I
was d ep o sited a s Agl on th e f i l t e r p a p e r. I n t h i s way, we were
a b le to o b ta in i n i t i a l a c t i v i t i e s o f 150,000 o r more d is in te g r a tio n s
p e r m inu te.
The f i l t e r paper was th en fa ste n e d to a b a k e lite su pport
and in s e r te d through a hole in the to p g la s s p la te in to th e cloud cham­
b er.
T his procedure was re p eated about 40 tim es - u n t i l about 1350
tra c k s had been photographed - 654 tra c k s in a f i e l d o f 637 gauss and
710 tra c k s i n 319 g a u ss.
Because o f th e s h o r t p erio d o f i ^ 2® and beeause of th e tim e con-
I
57
sumed in th e f i l t r a t i o n p ro c e ss , e t c . , i t was n e cessary to d ev ise some
method o f in s e r tin g th e specimen in to th e chamber and o f re n d e rin g th e
chamber s e n s itiv e as q u ic k ly as p o s s ib le .
The method o f a f f ix in g th e
f i l t e r p ap ers to th e in s id e o f th e g la s s r in g and th e n s e a lin g th e head
i n p la c e , w hile q u ite r a p id , i s n o t ra p id enough.
th e head shown in d e t a i l i n Figure I .
We then c o n stru c te d
The s t i l l m oist f i l t e r p ap er, a -
bout 2 x 11 cm, was h e ld on th e b a k e lite arm by sim ply c o a tin g t h i s arm
w ith a t h i n la y e r o f v a s e lin e .
This arm and th e b a k e lite plug su p p o rt­
ing i t were th e n in s e r te d in to the hole in th e to p , and th e jo in t sealed
w ith Apiezon Q,.
I t was found p o ssib le to g e t th e chamber in to s e n s itiv e
o p e ra tio n in some tim es as few as f iv e o r te n expansions a f t e r s e a lin g
th is jo in t.
The perform ance was n o t too r e l i a b l e however, some tim es
f o r ty o r f i f t y m inutes ela p se d b e fo re th e chamber became s e n s it iv e , in
which ease t h a t p a r t ic u la r ru n was l o s t .
A lso , the cycle o f o p e ra tio n s
had to be lengthened to one minute (in s te a d o f 24 seconds, th e cycle
used i n our o th e r work), a s th e presence o f the arm seems to r e ta rd
th e p ro cess by which th e chamber comes to e q u ilib riu m a f t e r each ex­
p an sio n .
A simi l a r b ra s s su p port was found to be even worse.
The re su lts^ ® , shown in F ig u res XV, XVI and XVII and i n Tables VI
and V II, may be summarized a s fo llo w s:
The observed e le c tr o n s appear
to have e n e rg ie s up to about 1.85 MeV.
The K-U p lo t a p p a re n tly shows
two groups, having upper l i m i ts a t 3.06 and 5.10 - .10 me* (1.05 and
2.10 - .0 5 MeV), r e s p e c tiv e ly .
The agreem ent w ith th e K-U th eo ry i s
as c lo se a s can be ex p ected from th e sm all number o f tra c k s counted:
26 Bacon, Orisewood and van d e r Merwe, Phys. Rev. 54, 315 (1938)
-
"
*
'
" f t
IS
>
L.
0>
Beta Ray Spectrum of I
E
3
C
a*
E
o
2
f •
u
<0
• 319 G auss- 7 1 0 T racks
0 637 G a u s s-6 5 4 Tracks
UJ
M mmi
c
(A
JC
u
•a
l.
t.
a»
E
3
II
z
AJ3
1
Horizonfal
2
3
4
Components of the M omenta
Fig. 15
-Aft.", ft
’ . 'ft ft
■ - -v ft ' -ft
Vft'
V .C Jft
*
•/ ;
\ ’f t f t f- \
V. ft >
ftft;7 f t ”
WM list:
ft—
ft.:.ft
■'/
.
• - \ •«■■. .
"■ ^..ftft-.ftft.J;
•
f tftft.-ftftftftft-.'ft
f -7 _■*
_
ft-'-.
' f t f t f t ‘ % f t f t f t f t f t - f t f t f t . f t ’f t ,
‘
. . . . . . . . A,
ft •
. '
ftft
■
.128
K - U P lot
319 G au ss
6 3 7 G auss
E n e r g y of E m it t e d E le c tro n
F i g . 16
f 28- Fermi Plot
•
319 Gauss
X 637 Gauss
2
3
4
Energy of Emitted
E lectro ns
Fig.17
me*
I
S'S"
TABLE 71
j.128
- 637 Gauss
Obs.
%
C alc.
Nn
C alc.
T o ta l
C alc.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
17
39
60
78
89
91
75
54
34
27
21
15
11
10
7
5
4
3
1
1
1
1
0
0
3 .7
7 .4
11.1
14.9
17.9
20.4
22.3
23.2
23.5
22.8
21.5
19.0
17.3
14.8
12.1
9 .6
7.2
5 .2
3 .5
2 .2
1.3
.6
.23
.06
.008
5x10
30.8
58.5
80.0
95.0
97.6
92.0
79.0
61.2
42.8
36.1
13.2
5 .2
1.3
4
10“5
35
66
91
110
116
112
101
84
66
59
35
24
19
15
12
10
7
5
4
2
1
1/2
1 /4
T o tal
644
282
693
975
3
7
zp
R el. Pop.
D if f .
-35
-66
-74
-71
-56
-34
-12
+ 7
+ 9
- 5
- 1
+ 3
+ 2
0
- 1
0
0
0
0
+ 1
0
+ 1/2
+ 3/4
+ 1
0
0
Obs.
C alc.
.00
.00
.IB
.36
.52
.70
.89
1.09
1.14
.90
.98
1.12
1.12
1.00
.94
S t,
TABLE 711
I 128
319 Gauss
Obs.
NI
C alc.
%I
C alc.
T o ta l
C alc.
D if f .
Obs.
K-U
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
9
14
19
28
33
43
43
42
42
35
39
33
35
31
29
26
19
.7
1 .4
2 .1
2 .8
3 .5
4 .2
4 .9
5 .7
6.3
6 .8
7.3
7.8
8 .2
8 .5
8 .7
8 .9
8 .9
8 .9
8 .9
8 .7
5.9
11.7
17.2
22.2
26.3
30.5
33.4
35.6
36.9
37.1
36.6
35.0
32.8
30.0
26.8
23.3
19.8
16.3
13.0
9.9
7
13
19
25
30
35
38
41
43
44
44
43
41
3 8.5
35.5
32
29
25
22
19
- 7
-13
-19
-16
-16
-16
-10
- 8
0
- 1
- 2
- 1
•• 6
+ 1/2
- 5/2
+ 3
+ 2
+ 4
+ 4
0
.00
.00
.00
.34
.46
.54
.70
.81
1.00
.98
.96
.98
.86
1.01
.95
1.08
1.07
1.15
1.19
1.01
Und.
70
Over
120
92
20.0
112
+ 8
1.07
T o ta l
710
215
520
735
2p
Und. = Undetermined, i . e . , cu rv atu re n o t measurable to th e d e s ire d ac­
cu racy .
Owing to th e d i f f i c u l t i e s encountered in th e o p e ra tio n o f th e
chamber (due to the s h o rt h a l f - l i f e ) , th e se tra c k s are s c a tte r e d through­
out th e spectrum .
The f ig u r e s above are th e b e s t f i t o f the K-U th eo ry
to th e measured tr a c k s .
SI
a s can ba seen from T&bles IV and V, th e K-U th eo ry p r e d ic ts th a t n o t
more than one e le c tr o n o u t o f 1300 w i l l have energy ly in g between 1.85
and 2 .1 0 MeV.
I n t h i s co n n ectio n , i t i s d i f f i c u l t to understand th e re c e n t work
o f Tape10.
He s t a t e s i n h i s a b s tr a c t:
"The o r ig in a l Fermi th eo ry i s in
b e t t e r agreement w ith th e ex p erim en tal d a ta , the Kurie p l o t s being l i n e a r
o v er a co n sid e ra b le range to th e end p o in t."
N e v e rth e le ss, in F igures 3,
5 and 7 o f h is p ap er, th e K-U p lo ts are s tr a ig h t li n e s w hile the Fermi
p lo ts a re smooth curves convex toward th e o r ig in :
in h is F igure 9, both
cu rv es a re convex toward th e o r ig in , due to the presence o f two r a d io a c tiv e is o to p e s ( I
id Q
and I
T3T
) i n the chamber a t the same tim e.
He f u r th e r s t a t e s , w ith reg ard to F igure 2 in h is p ap e r ( h is to gram o f th e observed momenta o f 1330 e le c tr o n s from I
128
):
"Below 2500
Hp ( i . e . , below about 1 .5 me) the spectrum has very l i t t l e s ig n if ic a n c e .
That t h i s i s t r u e comes from th e c r i t e r i a used i n tr a c k s e le c tio n .
From th e demand th a t a tr a c k be a t l e a s t 10 cm long . . . .
i t i s seen
t h a t f o r a f i e l d o f 448 o e rs te d s , th e low er end o f the spectrum lo se s
s ig n ific a n c e around 2500 Hp."
The e f f e c t o f t h i s c r i t e r i o n f o r t r a c k s e le c tio n upon th e r e l a ­
t i v e p r o b a b ility o f tra c k s of d i f f e r e n t r a d i i of cu rv atu re being meas­
ured can be c a lc u la te d by means o f an argument s im ila r to t h a t used f o r
d e riv in g E quation (1) o f t h i s paper (F igure I I I ) .
U n til such a c a lc u ­
l a t i o n i s made, i t cannot be s ta te d d e f i n it e l y a t what v a lu e of th e
momentum T ap e's spectrum lo s e s s ig n if ic a n c e .
As f o r th e upper l i m i t , th e disagreem ent between T a p e 's spectrum
and ou rs i s o f e s p e c ia l i n t e r e s t .
3 .9 .2 6
P rev io u s measurements ' '
were made
5«
on I
1 28
a c tiv a te d w ith slow n e u tro n s, and a l l agree i n p la c in g th e upper
Igp
l im it a t 2 .1 MeV; T ap e's measurements were made on I
a c tiv a te d by deu-
te ro n s .
P rev io u s attem p ts to fin d d iff e r e n c e s in the 0 -ra y s p e c tra of
p o ly g en etie iso to p e s a s a fu n c tio n o f th e method o f e x c ita tio n have n o t
1OQ
been s u c c e s s fu l. I t may be t h a t I
produced by deuteron bombardment
i s formed i n a s t a t e d if f e r e n t from th a t produced by slow n eu tro n bom­
bardm ent.
However, sin ce no chem istry was perform ed on th e samples
placed in th e cloud chamber by Tape, i t i s im possible to s ta te d e f i n ite ly
th e cause o f th e d iffe re n c e between h is upper l im i t and t h a t o f o th e r
w orkers.
The su p p o sitio n o f two groups in th e 0 -ra y spectrum o f I
128
sug­
g e s ts t h a t e i t h e r th e groups have d i f f e r e n t p e rio d s, o r e ls e th a t th e re
be y - ra y s whose energy accounts f o r th e energy d iff e r e n c e between th e
two g roups.
We measured th e p erio d very c a r e f u lly on the G eiger co u n ter sev er­
a l tim e s, fo llo w in g one ru n through tw elve h a l f - l i v e s (see F igure XVII).
The p erio d was found t o be s in g le to w ith in one m inute, being eq u al to
2 6 - 1 m in u tes.
We a ls o looked f o r a y - r a y .
We wrapped a f r e s h ly prepared f i l ­
t e r paper around a b ra s s c y lin d e r whose w a lls are about 3 mm th ic k , and
p laced t h i s over th e G eiger c o u n te r.
p e r m inute.
The count th u s o b tain ed was 3 5
We th e n slip p e d th e b ra s s c y lin d e r o u t from the f i l t e r
p ap er, and o b tain ed a count (c o rre c te d f o r decay) o f 5i,6oo p e r m inute.
Using th e f ig u r e s o f Sizoo and Willemson27 as to th e r e l a t iv e e f f i e i e n -
27 Sizoo and W illemson, P h y sica 5 , l ° & (1938).
Counting
Time
30
in M i n u t e s
60
90
120
1000
500
Counts in 5-Minute
Intervals
Decay of I128
Half-Life
25.6 Min
270
300
100
50
180
210
240
Minutes after Activation Had
Fig. 18
C eased
330
bo
cy o f th e co u n ter fo r d e te c tin g photons and e le c tr o n s , we concluded t h a t ,
i f th e re be any y - ra y o f one MeV em itted a t a l l , th e r e was c e r ta in ly
l e s s th an one photon f o r ev ery 10 e le c tr o n s .
Q
in g s o f R oberts and Irv in e .
This agreed w ith th e f in d -
L a te r, a y -r a y o f v ery sm all i n t e n s i ty , having energy o f .4 MeV
was re p o rte d by Livingood and Seaborg9 ; b u t n e ith e r the energy nor th e
i n t e n s i t y o f t h i s y - r a y can be c o r re la te d w ith th e 3 -ra y spectrum .
I t i s p o s s ib le , o f co u rse, t h a t most o f the y - r a y i n t e n s i t y i s
i n t e r n a l l y co n v erted , le a v in g b u t v ery l i t t l e to be measured a s y - r a d i ­
a tio n .
U n fo rtu n a te ly , however, the cloud chamber cannot be r e l ie d upon
to ,alw a y s d e te c t an i n t e r n a l conversion l i n e .
I n 1937, S tew a rt, Lawson and Cork®® measured in th e cloud cham­
b e r th e d i s t r i b u t i o n o f th e e le c tr o n s from one o f th e ra d io a c tiv e is o ­
to p es o f stro n tiu m .
They found th e se e le c tr o n s to have a continuous
d i s t r i b u t i o n o u t to 600 kV, w ith a K-U end p o in t o f 650 kV.
Two y ears
l a t e r , t h i s same a c t i v i t y was measured in th e cloud chamber ag ain by
duBridge and M arsh all89, who ob tain ed a r e s u l t ag reein g alm ost e x a c tly
w ith t h a t o f S tew art e t a l . .
DuBridge and M arshall th en placed a sam­
p le o f t h i s iso to p e in a 3 -ra y sp e ctro g rap h , i n which th ey were a b le to
observe b u t a s in g le i n t e r n a l conversion lin e a t about 360 kV, due to a
y - r a y o f about 370 kV (b in d in g energy o f th e K e le c tr o n i n stro n tiu m =
14 kV).
28 S te w a rt, Lawson and Cork, P hys. Rev. 52, 901 (1937)
29 duBridge and M arsh all, Phys. Rev. 56, 629 (1939)
Assuming t h a t t h i s s o r t o f th in g could happen ag ain , i t i s reason­
ab le to suppose t h a t th e second group observed by us in th e 3 -ra y spec128
trum o f i* * " i s r e a l l y a d i s t o r t e d i n te r n a l conversion lin e o f perhaps
500 kV, due to a y - r a y o f about 525 kV (b in d in g o f the K e le c tr o n in io ­
d in e - 28 kV).
T his i s in only rough agreement th e r e s u l t s o f Livingood and Sea9
borg , whose measurements o f th e a b s o rp tio n o f th e y - r a y i n le a d in d i ­
c a te a v e ry weak " / - r a y lin e o f about 400 kV.
However, th e se workers
s t a t e i n reg ard to th e a b so rp tio n o f th e 0 -ra y s i n aluminium:
"The down­
ward c u rv atu re o f th e p lo t su g g ests the presence o f an o th er component,
p o s sib ly a m ono-kinetic l in e due to an in t e r n a ll y converted y - r a y ."
However, i f t h i s e x p la n a tio n be adopted, i t i s n e cessary to p o stu ­
l a t e t h a t th e low en erg y e le c tr o n s , owing to t h e i r la rg e number, must
r e p re s e n t th e u n resolved su p e rp o s itio n o f s e v e ra l t r a n s i t i o n s .
TABLE T i l l
I
128
-
Summary o f R e su lts
B eta Ray Spectrum
Group I
Group I I
R el.
Pop.
End P o in t
K-U
Rel
Pop.
Observer
1 .8 5 MeV
4 .6 me* 5.10 me*
3
3.06 me*
7
T his Work
2 .1 MeV
5 .1 mo*
(End p o in t o n ly determ ined)
(B eta ra y sp eetro g rap h )
A, A and D
2 .1 MeV
5 .1 mo*
(A bsorption measurements)
Livingood and
Seaborg
End P o in t
Obs
K-U
2 .4 MeV
5 .8 me* 6 .8 me*
5 .3 me*
(Cloud chamber}
K-U
Perm!
Tape
Gamma Ray Spectrum
P robable
Energy
Probable
I n te n s i ty
O bserver
Too weak to measure
This Work
Too weak to measure
R oberts and
Irv in e
Too weak to measure
Tape
.4 MeV
Livingood and
Seaborg
CONCLUSIONS
Our r e s u l t s appear to lend somewhat g r e a te r su pport to th e K-U
th e o ry th an to th e o r ig in a l Fermi th e o ry o f b e ta decay.
cord w ith th e fin d in g s o f most o b s e rv e rs.
This i s in ac­
T his ap p aren t agreement w ith
th e K-U th e o ry h as been a s c rib e d by Kbnopinski
20
to th e d i s t o r t i o n o f
th e tru e spectrum by th e s c a tte r in g o f th e e le c tr o n s i n th e 3 -ra y so u rc e .
I n sup p o rt o f t h i s e x p la n a tio n i s th e r e c e n t work o f T y ler
30
and o f Law-
31
s o n , who f in d , t h a t as th e source i s made th in n e r, th e observed spec­
trum d e p a rts from th e K-U and begins to approach th e Fermi d is tr ib u t io n ;
a g a in s t t h i s e x p la n a tio n i s the work o f R ichardson and Isig h -S m ith
32
,
who, upon m easuring th e 3 -ra y spectrum o f ThC a s a gas (bism uth t r i ­
m ethyl) i n th e cloud chamber, fin d c lo se agreement w ith th e K-U th e o ry ,
even to th e la rg e number o f v ery slow e le c tr o n s p o s tu la te d by the K-U
th e o ry f o r elem ents o f h ig h atom ic number.
Perhaps i t m ight be mentioned in p assin g t h a t , a t th e o th e r end
o f th e p e rio d ic ta b le , Fow ler, D elsasso and L a u ritse n
K-U end p o in t o f the
15
fin d t h a t the
spectrum ag rees w ith th e d is in te g r a tio n d a ta ,
whereas a low er end p o in t does n o t.
I f we attem p t to choose between th e Fermi and th e K-U th e o ry by
co n sid e rin g o n ly th e upper re g io n o f the spectrum , where th e s c a tte r in g
contem plated by Kbnopinski i s probably v ery sm all, we f in d , th a t in th e
30 A. W. T y le r, Phys. Rev. 56, 125 (1939)
31 J. L. Lawson, P hys. Rev. 56, 131 (1939)
32 H. 0 . W. R ichardson and A lice Ieig h -S m lth , P ro c. Roy. Soc. 162, 391
(1937)
56
case o f Mn
, th e two th e o r ie s can be brought in to p r a c t i c a l agreement
o ver th e range from 1 .2 to 2 .1 MeV.
This i s c le a r ly brought o u t in F ig ­
ure XIX, which showB, on en larg ed s c a le , th e d a ta o f F igure V I II , to g e th e r
w ith th e b e s t Fermi d i s t r i b u t i o n to f i t th e d a ta between th e lim its men­
tio n e d .
I n view o f t h i s , i t m ight perhaps b e s t be s a id t h a t th e cloud
chamber i s in cap ab le o f d is tin g u is h in g between th e two th e o r ie s , a t
l e a s t i n t h i s c a se .
Confidence in cloud chamber measurements i s f u r th e r shaken by
c o n s id e ra tio n o f th e disagreem ent between th e chamber and the 3 -ra y spectro g ra p h re p o rte d by duBridge and M arshall
29
.
T h eir work shows th a t th e
cloud chamber can make some e le c tr o n s appear to have more energy than
th e y r e a l l y p o s se s s.
The agreem ent between th e 1 .7 MeV y - r a y l in e and th e d i f f e r ence i n energy o f two groups i n th e Mn
spectrum i s q u ite s tr ik in g ,
and would seem to su p p o rt th e K-U a n a ly s is o f t h i s spectrum .
However,
we have shown in F igure XIV (e) th a t one may c o r r e la te t h i s y -ra y lin e
w ith a p o s s ib le Fermi a n a ly s is .
• 850 Gauss
o 637 Gauss
Best K-U Distribution
Best Fermi Distribution
The eleven points between
the arrow s fit either curve
equally well.
me
Comparison of Fermi and K-U Groups
Fig. 19
ACKNOWLEDGMENTS
The au th o r w ishes to ex p ress h is a p p re c ia tio n to P ro fe s so r C arol
Willem van d e r Merwe f o r h i s c o n sta n t I n te r e s t and v alu ab le su g g estio n s
throughout t h i s work; to Mr. Edgar Norman Grisewood f o r h is g e n e ro sity
and p a tien c e in m easuring thousands of tra c k s ; to D octors John Horab o s te l and W illiam J . Horvath f o r t h e i r a s s is ta n c e w ith th e G eiger
co u n ter measurements; to D octor Frank A. V alente f o r ex ecu tin g the
draw ings; and to Mr. W alter T urnbull o f the U n iv e rsity machine shop
f o r h is su g g estio n s and i n t e r e s t in th e c o n s tru c tio n o f th e ap p a ra tu s.
r
11
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Alichanow, A llc h an lan and Dzelepow, N ature 136, 257 (1935);
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Livingood and Seaborg, Phys. Rev. 54 , 391 (1938)
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R oberts and I r v i n e , Phys. Rev. 53, 609 (1938)
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G. P . Tape, Phys. Rev. 56, 965 (1939)
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E l l i s and M ott, P ro c . Roy. Soc. A141, 502 (1934)
19.
E. M. Lyman, Phys. Rev. 51, 1 (1937);
Langer and W hitaker, Phys. Rbv. 51, 713 (1937);
The Rev. J . S . O'Conor, S . J . , Phys. Rev. 52, 303 (1937)
20.
E. J . K bnopinski, Phys. Rev. 57, 68 (1940)
21.
K lein and N ish in a, Z e it . f . P hysik 52, 853 (1928)
a
BIBLIOGRAPHY continued
22.
R ichard son and K u rie, P hys. B ar. 50, 999 (1936)
23. Bacon, Grisewood
and van d e r Merwe, Phys. Rev.
52, 668 (1937)
25. Bacon, Grisewood and van d e r Merwe, Phys. Rev.
Phys. Rev. 57, 240 (1940)
56,1168 (1939);
26. Bacon, Grisewood
54, 315 (1938)
and van d e r Merwe, P hys. Rev.
27. Sizoo and W illem sen, F hysica 5, 105 (1938)
28.
S te w a rt, Lawson and Cork, Phys. Rev. 52, 901 (1937)
29. duBridge and M arsh all, Phys. Rev. 56, 629 (1939)
30. A. W. T y le r, Phys. Rev. 56, 125 (1939)
31. J . L. Lawson, Phys. Rev. 56, 131 (1939)
32. H. 0 . W. R ichardson and A lice Leigh-Sm ith, P ro c . Roy. Soc. A162,
391 (1937)
FIGURES
Figure
Page
I
Diagram o f cloud chamber and p a r ts
6
II
Diagram o f o r ig i n a l o p tic a l system
8
III
D e riv a tio n o f eq u a tio n
IV
Comparison o f eq u atio n I w ith experim ent
15
V
Comparative y ie ld o f wide and narrow sources i n the
cloud chamber
17
VI
F e rm i's fu n c tio n s f o r Mn56 and I 128
S3
VII
Graph o f eq u a tio n
27
V III
D is tr ib u tio n o f th e h o riz o n ta l momenta o f e le c tr o n s
from Mn56
33
IX
K-U p lo t o f th e 0 -ra y spectrum o f Mn
34
X
56
Fermi p lo t o f th e 3 -ra y spectrum o f Mn
35
XI
Concordance amongst s e v e ra l runs a t 850 and a t 319
gauss
39
XII
Concordance amongst s e v e ra l runs a t 637 gauss
40
X III
D is tr ib u tio n o f th e h o riz o n ta l momenta o f e le c tro n s
e je c te d by th e y -ra y s from Mn56
(1)
13
(5)
42
C fl
47
XIV
P o ss ib le le v e l diagrams to d e s c rib e th e decay o f Mh
XV
XVI
D is tr ib u tio n o f th e h o riz o n ta l momenta o f e le c tro n s
from I 3-28
log
K-U p lo t o f th e 3 -ra y spectrum o f I
XVII
Fermi p lo t o f th e 3 -ra y spectrum o f 1**°
54
XVIII
H a lf l i f e o f I 128
59
XIX
Comparison o f Fermi and K-U an aly ses o f th e 3 -ra y
spectrum o f Mn65
65
Igg
52
53
TABLES
Page
Table
I
II
III
IV
Tha 3 -ra y spectrum o f M n^ - o b se rv a tio n s in th e
f i o l d o f 850 gauss
36
The 3 -ra y spectrum o f Mn56 - o b se rv a tio n s in th e
f i e l d o f 637 gauss
37
The 3 -ra y spectrum o f Mn56 - o b se rv a tio n s in th e
f i e l d o f 637 gauss
38
The r e l a t iv e y -ra y a c t i v i t i e s o f a few r a d io a c tiv e
iso to p e s
44
Summary o f th e measurements on th e r a d io a c tiv ity
49
VI
VII
V III
The 3 -ra y spectrum o f I
f i e l d o f 637 gauss
1OQ
- o b se rv a tio n s i n the
The 3 -ra y spectrum o f i ^ 88 - o b se rv a tio n s i n the
f i e l d o f 319 gauss
55
56
Summ|j*g o f th e measurements on th e r a d io a c tiv ity
62
TABLES
Page
Table
I
II
III
IV
V
VI
V II
V III
The 0 -ray spectrum o f Mu56 - o b serv atio n s in th e
f i e l d o f 850 gauss
36
The 3 -ray spectrum o f Mn5® - o b serv a tio n s in th e
f i e l d o f 637 gauss
37
The 3 -ray spectrum o f Mn56 - o b serv a tio n s in the
f i e l d o f 637 gauss
38
The r e l a t iv e y -ra y a c t i v i t i e s o f a few ra d io a c tiv e
iso to p e s
44
Summary o f th e measurements on the r a d io a c tiv ity
o f Mn
49
The 3-ra y spectrum o f 1^® - o b serv atio n s in the
f i e l d o f 637 gauss
55
T*he 3 -ray spectrum o f 1^28 _ o b serv atio n s i n the
f i e l d o f 319 gauss
56
Summ^gg o f th e measurements on th e r a d io a c tiv ity
62
M e th o d of P rodu cing U niform M agnetic Field
$
.R
a l p h ..
H
oyt.
B acon
•I
!
I
■'%
i
Reprin-.eJ from T he R e v ie w
of
Sc ie n t if ic I n j i k c m e n i s , Vol. 7, Xo. 11, N ovem ber, 19,16
I
%
N OV E MB E R ,
1936
R .
S.
I .
V O L U ME 7
P r i n t e d in U . S. A
Method of Producing Uniform Magnetic Field
R a l p h H o y t B a c o n ',
Department o f Physics, New York University, W ashington Square, New York City
(R eceived M ay 22, 1936)
E have had to design a pair of coils to
produce a uniform m agnetic field for use
with a cloud cham ber originally constructed to
stu d y and m easure forked tracks. In order to
keep o u t of the way of the optical system , it
was necessary to construct the coils of unusual
cross section, and it was found possible to devise
such coils so as to produce a very uniform
m agnetic field. T he m ethod is merely to vary
th e num ber of am pere turns per square c e n ti­
m eter in different p arts of the coil.
We divided the cross section into centim eter
squares, and assum ed th a t the windings in each
square produced substantially the same effect as
a filam entary current through the center of each
square. T he error introduced by this assum ption
is small, and affects chiefly the calculation of
th e m agnitude of the field, not its uniform ity.
Since there will be a large num ber (say 50 or 100)
of such squares, the effect of those which are
cut by the actual coil m ay be taken as pro­
portional to the area within the actual coil, as
the error introduced by this procedure again
affects chiefly the calculation of the m agnitude
of the field, rather than the uniform ity. The
resultant field is the sum of the fields of all these
elements. T he field was com puted for four p o in ts:
two points in the plane m idway between the two
coils—one on the axis, th e other 6 cm from the
axis of the coils; and two points similarly placed
in the plane one centim eter from this plane.
Of the expansions available for com puting the
field due to a circular current, perhaps the most
convenient is th a t g i v e n by G ray,1 modified to
suit the present case:
W
H x=
3V
a2r
3 y2
45 y4
35 y 6
= 2irn I —I 1 + - — ( 0 2 _ 4 * S ) +
(a4—12a?x2+ 8x4) + ---------(5«'; - 120«4.r-+240«-.r4- 64xr’)
3.y
r3L
4 r4
64 r8
256 r 12
+ etc.
3V
H y=
a2xy[ 5 y 2
35 y4
= 3wnl
1-|-------(3a2—4.r2)d— •—(5a4—20a2a;2+ 8 r ,) + e tc .
3y
rh L 8r 1
64 rH
w here V = p o te n tia l clue to c ircu lar c u rre n t,
//* = axial com ponent of field due to c ircular c u rre n t,
H y = rad ial com p o n en t of field due to c ircular c u rre n t,
a = m ean ra d iu s of e le m en tary c e n tim e te r cross
section,
.v = d istan c e from m idplane of e le m en tary cross
section to point w here I I is being calculated,
r = (a-’-f-.r2)*,
y = d istan c e from axis of coil to point w here I I is
being calculated, cf. Fig. 1,
n = n u m b er of tu rn s per square centimeter,
/ = c u rre n t (in e.m .u .) in each tu rn .
.T, y, a n d a can be chosen so as to be w hole num bers.
I t will be noticed im m ediately, th a t for ele­
m ents for which a > 2 x , the axial com ponent of
the field increases as we leave the axis, whereas
for elem ents for which a < 2x, the field decreases
as y increases. T he radial com ponents tu rn out
to be negligibly small in the region studied.
M oreover, on the m idplane between the two
coils, they exactly cancel out; in any other plane
near this plane, m ost of the radial com ponents
are still exactly canceled out, leaving b u t a
small rem ainder of radial com ponents due to
the elem ents along the upper and lower edges
of the coils: these are the only radial com ponents
th a t have to be com puted a t all. A similar
simplification applies to the calculation of the
axial com ponents a t a point off the plane of
sym m etry.
As a result of these com putations, it was
found th a t we could construct a pair of coils,
w ith the cross section shown in Fig. 2 (necessary
to avoid obstructing the line of sight of the
stereoscopic cam era), which, if uniform ly wound
1 A. G ray , A bsolute M easurem ents in E lectricity and
M agnetism , 2nd E d itio n (M acm illan, 1921), pp. 210-212,
797.
423
424
RALPH
HOYT
BACON
■
B
\
i
/
(ft
o
o
A
r
I
—|
1
u.
o
(ft
X
<
_____ ^
F iig
F
g .. 1. Show ing
„ th e q. u a n titie s used in c o m .p u tin g th e
m agnetic field d u e to a circu lar c u rre n t, a = ra d iu s of fila­
m e n ta ry c u rre n t, x —d istan c e from p lan e of filam en tary
c u rre n t to p o in t w here H is being com puted, y = distan ce
from axis of fila m en tary c u rre n t to th is p o in t, r = (a2+x*)*.
w ith th e same size wire throughout, would
produce a field ab o u t 3 percent greater a t the
points for which y = 6 cm th an a t the correspond­
ing p oint on the axis. T he next step was to divide
th e cross section of the coils into two or more
regions, such th a t th e variations in the field
produced by one such region would neutralize,
as far as possible, the variations in the field pro­
duced by the rem ainder of th e coils. For practical
reasons, it is not feasible to divide th e coils along
the cone a = 2x (x m easured from the plane of
sym m etry) b u t ra th e r to have the divisions
between sections either parallel or perpendicular
to th e axis.
E ach coil was therefore divided into three
regions, as shown by th e letters A . B and C in
Fig. 2. According to th e com putations, the field
T
I. Comparing the observed and the computed m agni­
tudes and uniform ities o f the field due to the coils as
one continuous unit, and due to each pair of
regions A , (A -f-B ) and C.
able
H x on ax is
W h o le coil
in series
(A +B )
l i x a t y = 6 cm
V a ria tio n
C o m p u te d
O b se rv ed
4 .40 m / —250 /
218 /
4 .5 5 m / = 2 5 8 /
227 /
3 .2 %
4.0
C o m p u te d
O b se rv ed
1.8 5 m / = 105 /
95 .2 1
1.95 m / = 110 /
100 .9 /
5.2
5.5
C o m p u te d
O b se rv ed
3 .4 0 m / = 193 /
166 /
3 .58 m / = 203 /
173 /
5.0
4.7
C o m p u te d
O b se rv ed
1.00 m / = 5 6 . 7 /
50 .6 /
.97 m / = 5 5 .0 /
4 9 .3 /
3.0
3.0
I = c u r r e n t in a m p e re s.
W h e n (A + iJ ) a n d C w e re co n n e c te d in p a ra lle l o n th e 110-volt line,
(A 4--B) d rew a b o u t 1.5 a m p e re s , C , a b o u t 3.5 a m p e re s , a n d to g e th e r
th e y p ro d u c e d a field of a b o u t 440 g a u s s , o r 88 g a u s s p er am p e re ,
u n ifo rm to w ith in th e e x p e rim e n ta l erro r. T h e c o m p u te d v a lu e s fo r th is
c o n n e c tio n a r e 97 g a u s s p e r a m p e re o n th e ax is, a n d 99 g a u s s p er a m p e re
a t y =6 cm .
.................
\
F ig . 2. Show ing how th e cross sections of th e coils were
divided in o rd e r to produce a uniform field by a d ju stin g
th e n u m b er of a m p e re tu rn s per sq u are c e n tim e te r in each
region. T h e odd sh a p e is necessary to keep o u t of th e w ay
of th e previously designed o p tic a l system . T h e d o tte d
rectangle in th e c en ter show s th e region in w hich th e
uniform field is desired.
due to region A alone would be ab o u t 5 percent
greater a t y —t cm th an a t y = 0; th a t due to
region (A + B ) , taken as one unit, ab o u t 5 percent
greater a t y = 6 cm th a n a t y = 0; whereas th a t
due to C alone would be about 3 percent less a t
y = 6 cm th an on the axis. I t was further found
th a t if we m ake n l in region C twice as great as
in region {A-\-B), the re su ltan t field would be
2 percent greater a t y = 6 cm th an a t y = 0; if n l
be four tim es as great in C as in (A-\-B), the
variation would become only 1 percent. If n l be
three tim es as great in C as in A , and only A and
C be used, then the variation would decrease to
ab o u t 1/4 percent.
I t was decided to wind each region w ith No. 16
enam eled wire, so th a t th e various regions
could be connected in series or parallel with
each other as desired. By m eans of rheostats,
any desired com bination of n l in th e various
regions can be obtained. I t was assum ed th a t
the wire could be wound 56.7 tu rn s per square
centim eter, and could carry 8 or 10 am peres for
the few seconds th a t the coil is on a t an y one
time. T he coil will operate on a m axim um of
220 volts, with th e corresponding regions always
in series. Regions A and B have cross sections
of 26 square centim eters each, region C, 20
square centim eters, m aking 144 square centi­
m eters in th e pair of coils. T he experim ental and
com puted constants of each pair of regions A ,
{A-\-B), and C are given in T able I.
I t should be em phasized th a t the object of the
UNIFORM
MAGNETIC
above procedure is not to predict w ith great
precision th e m agnitude of th e field, b u t rath er
th e uniform ity to be expected.*
* O f course, no one w ould use such c o m p u ted v a lu e s for
th e m ag n itu d e o f th e field in a n y ex p erim en tal w ork,
an y w a y : ra th e r, e x p erim en tally d e te rm in e d va lu e s of th e
field w ould be used in all cases.
FIELD
425
I t is believed th a t this m ethod of winding
coils in different p a rts should prove to be of
service to those who have to design coils to
produce very uniform fields, particularly when
the size and shape of th e coils m ay no t be freely
chosen.
$
$
L A N C A S T E R P R E S S , I N C . , L A N C A S T E R , PA .
R eprinted fro m
T
he
668,
P
h y s ic a l
R
e v ie w
,
Vol. 52, No. 6,
Septem ber 15, 1937
P lin te d in U . S. A.
The /3-Ray Spectrum of Mn56
We h ave m easured th e /3-ray spectrum of M n 56 excited
by bom b ard in g N a M n O i solution w ith n e u tro n s from a
R a-B e source. U sing a field of 850 gauss, we o b tain a single
g roup w ith a K -U e n d -p o in t a t 6.5 me2, in ag reem en t w ith
G a e rttn e r, T u rin a n d C ra n e . 1 U sing a field of 425 gauss,'
we o b tain c u rv es sim ilar to th o se of Brown and M itch e ll ,2
w ith en d -p o in ts a t 3.4 a n d 6.5 me2, respectively. W ith a
field of 637 gauss, th e sp e c tru m again show s th e tw o
groups w ith th e sam e en d -p o in ts as found w ith 425 gauss,
b u t w ith th e re la tiv e population of th e low er energy group
g re atly dim inished. M ore th a n 1300 trac k s were m easured
for each field.
T h is w ork th e n confirm s th e existence of th e low energy
gro u p re p o rte d by Brown a n d M itchell. We a ttrib u te the
discrepancy b etw een th e ir re su lts and those of G a erttn er,
T u rin a n d C rane to th e suppression of som e of th e trac k s
of th e low energy gro u p b y th e stro n g e r m agnetic fields,
b u t our w ork does not perm it us to draw conclusions as to
th e u ltim ate origin of the low en erg y group.
R a l p h H. B a c o n
E d g a r N. G r i s e w o o d
C a r e l W. v a n d e r M e r w e
N ew Y ork U n iv ersity ,
W a sh in g to n S q u a re College,
A u g u st 31, 1937.
1 G a e rttn e r, T u rin a n d C ran e, P h y s. R ev . 49, 793 (1936).
2 B row n a n d M itc h ell, P h y s. R ev . 50, 593 (1936).
R eprinted from
T
he
P
h y s ic a l
R e v i e w , Vol. 56,
P rin te d in U . S. A.
N o. 11, 1168, D ecem ber 1, 1939
The Radioactivity of Mn66
W e h a v e a tte m p te d to m easure th e 7 -rays from M n 66
b y coun tin g th e electrons ejected from a th in lam ina in
th e W ilson cloud ch am b er. T hese electrons fit an energy
group having a n e x tra p o la ted e n d -p o in t betw een 1.50 and
1.75 me2, in dicating a 7 -ray line of 600-700 kev. T h ere is,
how ever, m ark ed straggling o u t to a b o u t 3.90 me2, which
m ay in d ic a te a 7 -ray line a t a b o u t 1.7 M ev. T hese findings
agree w ith th o se of D un w o rth ,1 except th a t th e in te rp re ta ­
tion of th e flat d istrib u tio n betw een 1.75 a n d 3.90 me2 is
n o t clear. I t is possible t h a t th ere a re o th e r lines betw een
th e tw o m entioned.
T h a t such m ig h t be th e case is suggested b y th e results
o b tain e d b y o th e r w orkers. If one exam ines th e curves
published b y Seaborg a n d L ivingood 2 a n d b y Langer,
M itchell a n d M c D a n iel ,3 it is seen th e 7 -ray backg round
is high com pared to th e m easured 0-ray in te n sity . T h ere
are th ree possible explanations of th is: (a) th e n u m b er of
q u a n ta p e r d isin te g ra tio n is large, (b) th ere a re v e ry m any
electrons (presu m ab ly of low energy) th a t a re n o t being
detected b y th e c o u n tin g system , o r (c) som e com bination
of th e above tw o possibilities.
O u r m easurem ents of th e /3-ray sp ectru m in d ic a te th a t
(c) is th e m ost likely.
R. H. B aco n
E . N . G r is e w o o d
C . W. V a n d er M e r w e
D e p a r tm e n t of P h y sics,
N ew Y o rk U n iv e rsity ,
W a sh in g to n S q u a re C ollege,
N e w Y o rk , N ew Y o rk ,
N o v e m b e r 17, 1939.
j
1 J . V . D u n w o rth , N a tu r e 143, 1065 (1939).
* G . T . S eab o rg a n d J . J . L iv in g o o d , P h y s. R e v . 54, 397 (1938).
9 L a n g er, M itc h e ll a n d M cD an iel, P h y s. R e v . 56, 422 (1939).
R e p rin te d fro m T
h e P h y s ic a l R e v i e w , V o l. 57, N o . 3,
240, F e b r u a ry 1, 1940
P rin ted in U . S. A.
Erratum: The Radioactivity of M n56
(P hys. R ev. 56, 1168 (1939))
T h e energy groups referred to in th e second sentence of
th e le tte r were a ctu ally p lo tte d a s m o m en tu m groups.
All th ro u g h th e le tte r me2 should re ad me.
R.
H.
E. N.
C. W .
B acon
G
r is e w o o d
van
der
M
erw e
D e p a r tm e n t of P h y sics,
N ew Y o rk U n iv e rsity ,
W a sh in g to n S q u a re C ollege,
N ew Y o rk , N ew Y o rk ,
J a n u a ry 6, 1940.
L ib r a r y
N . Y . U n iv .
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