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Elastic Scattering of Polarized Neutrons by 3He at Low Energy.

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Annalen dcr I’lixsik. 7. Folge, Band 39, Heft 6, 1982, 8. 408--426
J. A. I h r t h . Lcipzig
Elastic Scattering of Polarized Neutrons by ’He
a t Low Energy
Istituto di Fisica dcll‘UniversitB, Padova
Istituto N:izion:de di Pisicn Nudeare, 8ezionc di Padova
Tstituto di l+’isic;c dcll‘Univwsit8, Padova. I talia
A b s t r a c t . E:l,istic scattering by j H e tor t.67, 2.43, :LO, 3.4 and 7.8 MeV neutron beam.; of
known polarinition W ~ L Smetisirred at seven angles from 2.3” to 15.?)‘ using A high pressure g i s scintillation counter. The gcometric.tl and ninltiplc scattering effect6 were accounted for by the Monte
Carlo technique. The corrected results were (*omparedwith previous experimental d&i and with
the existing predictions based on microsropic calculittions and phenomenological ;milyses.
Elastische Htreiiiirig polarisierter riicdrigenergetischer Neutroncn an “Ha
I n h n l t s u b r r s i c h t . Die elastische Stretiring von Neiitronenstrahlen mit beknnntcr Polarisation w i d ;in 3 H ~bei
> BinschulJencrgien von 1,67, “43, 3,0, R,4 und 7,s MeV und Einschuhvinkcln
von 25‘’ bis 156 ’ rnittels eincs Hochdrock-Gas-RcintillatorzHhlersuncsrsueht.
D:e Effektc t k r geomet,rischcrinnd Vielfiichstreuungen werden niittcls Monte-(:nrlo-~~ethodci~
berucksichtigt.
Die korrigicrteri Ilesiiltate n-erclcn init friiheren experimentellen Daten und mit Ergebnissen
vcrglicbcn, die t i i d mikroskopixchen Llrchnnngen und phiinomenologischon Thcorien beruhen.
1. Introductiori
Even though nuich work has been clone by both experimentalists and theoreticians
in the past few years, the problem of the excited unbound states of 4He is still open,
apart perhaps for a few states all of which are near 20 MeV excitation energy [ I].
Traditionally the meeting point of scattering experiments and theories remains at
the level of phase-shifts, since if their energy function is conveniently yaramctrized,
one obtains information on nuclear properties of the conipound system. However the
extraction of an iinanibiguous set of phase shifts is often a non soluble problem if one
analyzes cross section and polarization data related to a unique scatt,ering experiment,
certainly in the case of A = 4 if only first order polarization observables (“double
scattering data”) have been considered or inelastic channels were present. A confiriliation
of this situation is a recent analysis [2] of p3He elastic scattering performed using
all available data.
I )
Work performed a t the Laboratori IV:wion;ili di Legnaro (Padova).
IElastic Sc;ittering of T'olarized Keutrons by 3He at Low Energy
409
The way to obtain unambiguous solutions was suggested by BAZ[3] and it lies
(I)]-nucleon reactions. Following this
in the contemporary analysis of all [(A = 3)
direction in the past a few authors 14-61 with some simplifications or collateral
assumptions have attained important results on the low lying states of the 4Henucleus
on the basis of the scarse existing experimental data.
Recently the amount of experimental data, expecially regarding polarization, has
increased, but not sufficiently considering the reactions involving the 4He nucleus as
a compound system. This is particularly true for the polarization data in elastic scattering of neutrons by 3He.
For this reaction, in the past, polarization measurements were carried out a t three
angles, a t 1.10 and 2.16 MeV [7], and in a more extended angular range a t 3.33 and
7.90 MeV 181. More recent measurements with 3 MeV partially polarized neutrons [9]
appear to be in disagreement with the earlier data as occurs with measurements at
8.0 MeV [lo] of a more complete experiment extending up to the higher energies of
12.0 and t7.1 MeV.
The aim of the present expcrirnent is an improvement of the polarization data
referring to r ~ - ~ H
elastic
e
scattering in the low energy range, hoping that a comprehensive
analysis of various, different observables will permit an unambiguous solution of the
problern of the level struct>ureof the 4He nucleus.
Moreover these data can be compared directly with the predictions of recent microscopic calculations which appear to be successful [ll].
Our measurements were carried out a t 1.67, 2.43, 3.0, 3.4 and 7.8 MeV lab. energies
a t seven angles between 25" and 155" and preliminary results a t 2.43 and 3.0,MeV
were published previously [ 121.
+
2. Experimental Proccduro
2.1. I'olarimoter and Keutron Sources
The experimental apparatus, already employed in polarization ineasureirients with
solid and liquid targets [13, 141 a t Laboratori Nazionali di Legnaro, was used with
a gaseous 3He target2) a t a pressure of about LO7 Pa, with 8-9% of Xe.
The experiniental method, employing the time-of-flight technique in connection
with the pulsed beam facilities of the Legnaro Van de Graaff accelerator, exploits the
scintillation in the gas target following the neutron helinm interaction.
The gas target assenibly, the electronic circuitry and other experimental details
have been described elsewhere [ 161.
As a source of partially polarized neutrons we used the reaction 31iT(p, n ) at the
lowest energy of 1.67 MeV, extracting the neutron beam a t 33" with a spread of about
&0.08 MeV. The polarization of the neutron beam was assumed to he 0.28 [l6]. A t
intermediate energies the reaction 12C(d,n ) was employed extracting neutron beams
of 2.43 & 0. LO and 3.0 f 0.1 MeV a t 25" and 20" respectively with polarizations of
-0.47 [17] and -0.11 [15].
F o r the remaining measurements we exploited the fact that the reaction gBe(cx,n )
provided two groups of neutrons, quite well separated (in suitable conditions), corresponding to the ground state and first excited level respectively of thc residual nucleus.
With an alpha beam of 2.55 MeV mean energy and a beryllium target -0.3 mg/cm2
0.17 MeV and 3.38 & 0.16
t]hick we obtained contemporaneously neutrons of 7.80
MeV at, 45" for which both polarizations were 0.33 according to ref. [ 171. A s shown
-
?)
'I'hc 3He gas. 99.9°() grade,
W.;LSfurnished
by Mommto, Miamisburg, Ohio.
410
L. DRIGO
et al.
in ref. [15], a t these energies the fast timing technique, using a sufficient time-of-flight
base, made i t possible t o make a reliable separation of the contribution of the two
neutron groups, routing in different parts of the data acquisition system the respective
time-of-flight spectra of scattered particles. Small contributions of the highest energy
neutrons to the lower peak have not been taken into account because their amount
produced a n error lower than the statistical one. Typical time-of-flight spectra are
is indicated as a dotted line. The data were
shown in fig. 1, where the background
collected in 60 hours.
-2 nskhannel
1500e
v)
90"
25'
c
135"
3
0
1
I
3'0
5i)
'
7b
9'0
*
30
50 ' 7b
Channels
9'0
'
'
50
'
7'0
Fig. 1. Experimental time-of-flight spectra for 2.43 MeV neutrons scattered by the
90" and 135" (lab.).
~
'
L
9'0
'
cell
S
at 95
,
2.2. Data Handling and Corrections
The analysis of the time-of-flight spectra, accomplished with a H1' LOO0 computer
system, does not give the final results, as usually occurs in neutron measurements.
The data obtained are encumbered with errors because of the finite dimension of the
gas scatterer and detectors, but above all because of the effects of the massive container
and of r~-Xeinelastic scattering.
In fact, in experiments involving a gas target at a high pressure, the counters
detect neutrons both scattered directly by the gas anti rescattered by the container.
Moreover, one has to take into account direct inelastic neutrons whose corresponding
y-rays were detected in the gas cell. These effects are particularly important at angles
for which the n-"e
cross section is sinaller.
The correction procedure, based on the Monte Carlo method and described in detail
in ref. [ 151, was used with a ccrtain ariionnt of iuiprovernents, regarding essentially
the inelastic effects and tlie y detection. The code gives the expected values for the
left-right ratios which are to be conipared with the experimental ones, as one feeds
beam polarization and an input analysirig poivcr agular distrihution at each energy.
For the collisions of neutrons \\ ith the "iron" cell, we considered the elastic and
inelastic reactions mine tlie data c l i i o t o r l in ref. 1131. For t h e cvaluation of t h e inter-
Elastic Scattering of Polarized Neutrons by 3He at Low Energy
ill
action with the gas of the y-rays corresponding to different excited levels of the iron
isotopes we considered a fictitious excited level a t a suitable energy with a cross section
evaluated according the data given in ref. [MI.For the inelastic scattering on Xethe
evaluated cross-sections furnished by N.E.A. [19] were used. Finally the table in ref.
[20] made it possible to calculate the effects of the y-ray interactions in the gas scatterer.
For the n-3He elastic scattering two different sets of input data, originating both
from theoretical calculations and from the phenomenological analysis of experimental
results, were employed. The results of M.C. calculations are dicussed in the next section.
With neutrons of the highest energy the three-body breakup reaction 3He(n, d ) p , n
is energetically allowed (& = -5.494 MeV).
However its effect was not taken into account because of the probable smallness
of its cross section [21] and because the time-of-flight of neutrons emerging from this
reaction was beyond our experimental limit a t least for the counters placed a t 8 > 25'.
At this energy (7.8 MeV) we extracted the polarization data a t the backward angles
sepairating (in the time-of-flight spectra) the contribution of the direct elastic scattering
by W e from all the detected neutrons. These direct neutrons appeared as a sufficiently
well defined peak over a smeared-out distribution. This was possible with minor reliability a t 90" because of the very small value of the cross section and not possible
obviously a t the forward angles where contributions of' the same shape overlapped.
However for the latter angles the smallness of the analysing power renders the other
contributions of little value in the final results. Thus the only correction applied to
the data manipulated in this fashion was the geometrical one, taking into account
the double scattering on 3He. The same method was followed in ref. [12] where we
compared our 2.43 and 3 MeV polarization data with the previous contrasting measurement,s [8, 91.
This procedure was also followed for the 1Zio data when possible. I n fact at, this
angle it was very difficult to separate the background contributions from those caused
by double scattering and inelastic effects. This difficulty becomes apparent when
examining the size of errors.
3. Results and a Comparison with Related Data arid Predictions
I n Table 1 the experimental asymmetries (exp.) are shown as obtained from the
present experimctit a t different angles and energies.
In this table our experimental data are compared with the results of the Monte
Carlo calculation performed following the procedure explained in the preceding section.
Set I (HH) shows the asymmetries evaluated using as input for the correction procedure
cross section and polarization data deduced from the microscopical calculations of
HEIS5 and H \CKICNI:ROK>II [ 111 covering the whole range of our measurements. Set
I1 (135) corresponds to asymmetries resulting from the correction procedurc using
input data deduced from the charge-invariant phase-shift :malysis of 13 UWI' and SinGEEV [6] limited however up to about 3 MeV. The H H and 13s input analysing powcrs
are displayed in Pigs. 2 - 4 as continuous and dotted lines respectivcly.
The rows and columns marked by a) in Table 1 are experimental data evaluated
in the simplified manner explained in the preccding section, and M.( '. c:Llciilations
taking into account only geometrical corrections.
The errors reported in the experimental data are a quadratic cotnhination of the
statistical ones with the crrors derived by the background evaluation. In the Monte
Carlo calculations the errors indicated are only statistical, evaluated as in ref. [15],
without taking into account thr. errorq of the nciitron k)(,illn polarization arid of tht:
othei- iripnt dat:~.
T,. DRIWet
413
;tI.
Tnblr 1. Comparison between experimciitnl asymmetries m d Monte Carlo calculatious
elab
h',
exp
25j0 HH
13S
CXp
1.m M ~ V
+
0.013 0.028
0.019 -c 0.013
0.048 -t 0.013
0.030
4.5' HH O.Oli7
13s
CXP
6.5" H H
RS
CXP
90" HH
HS
0.087
A
0.023
4
0.01:1
+ 0.013
0.074 4 0,023
0.108
0.012
0.100 f 0.013
+
0.064
0.029
0.092 3 0.01:1
0.070
0.01:1
+
113" HH
BS
0.027 f- 0.0:10
0.0.-,9
0.013
0.040 t 0.012
t'xp
132 HH
SS
0.041 i- 0.038
0.038 -1 0.012
0.027 t 0.012
pup
+
C'XP
155' H H
")
13s
-
2.41 MeV
7.8 MeVL)
*
0.016 4-0.013
0.008 0.017
-0.025
0.017
-
3.4 MeV
3.0 MeV
0.005 0.009 -0.007 4-0.02:$
0.001 0.017 -0.025 5 O.OL8
0.007 L 0.017
0.002 & 0.017
+
+
+
+
0.057 I! 0.01:1
0.002 i O.oO!r
--0.034
O.O?L
0.033 i O.Otci
0.00.5
0.01 f i
0.023
0.017
0.087 4 0.016 -0.014 t O.Ol(i
0.014 i 0.017
+
0.092 f 0.027
-0.093 0.006
+
0.120 i 0.01(i -0.017 i 0.011
0.01 i
0.147 4- 0.011; -0.032
0.033 & 0.011,
0.1.5!1 t 0.016
+
0.04li 3i 0.0%7
O . l l ( i i_ 0.01G
0.112 i-0.01fi
0.1 fi0 i 0,02<5
0.172
0.017
O.l(i0 f 0.017
0.038 f 0.014
0.037 -10.017
0.033 i0.017
0.048
0.05:I
0.234 t 0.017
0.183 + 0.017
0.10d _t 0.08.5
o.:$lo
0.014
0.101 I 0.027 -0.027 1 0.014
-0.125 t 0.019 -0.031
0.017
0.017
0.104 t 0.020 -0.fP27
0.074 1 0.0:{7
0.17:) -I 0.018
0.128 3 0.018
0.174
0.0X8 4 0.057
0.104
0.020
0.081 1 0.01!)
0.080
0.159
0.0.58 1 0.09-I
0.070
(I.fP?!)
0.047 i 0.0")
ll.020
0.077
~
-
-
O.O(i5 41 0.032 -0.0:10
0.07!1 k 0.023 -0.017
0.065 t 0.023
0.012
~
0.0:IT + 0.035 -0.02.5
-0.0.50 r. 0.0:34 -0.014
-0.OX1 _1 0.035 -0.011
+
+
+ 0.016
:1
0.019
0.011)
-L
0.0:10
I.
+ O.O"(i
0 02li
+
+
+
-
0.280
i 0.04(i
t f).012
t 0.042
,
O.OI0
1
0.oso
0.OOY
") P:wti:illy corrected
As one can see, the HH arid BS predictions are, on the whole, satisfirctory a t the
three lowest energies, although they appear a little too high in respect to exp. data at
forward angles for set] 11 and sornetinies a t backward angles for set I . A t 3.38 MeV
a systematic discrepancy, very large at backward ilngles, arises betweeri the experimental data and predictions of set J and T I which show only slight differences between
them.
The discontinuity between our experimental data at 3 and 3.38 MeV, not justified
h.v any of thc theoretical predictions suggests that the bcam polarization value used
a t 3.38 MeV IS too high.
Unfortiniately for this cncrgy, we have no further incasiirenients of the beam
polarization after the paper referred to in [I 71, as, o n the contrary, we had at 3.0 Me\'
where we solved a siniilnr problcni 1151.
A discrepancy of minor iniportance again arises at 7.80 MeV with rc.spwt to the HH
predictions.
For a comparison of our results with existing experimental data, our corrected
analysing power of the d H e elastic reaction at different angles and energies can hr
extracted from the experimental asymmetries moctdying the inpiit polarization ciirves
in the correction program, until the resulting asymmetries are statistically consistent
with the experimental ones. Lacking an airtonlatized code this "groping" procedure
is tedious and may lead to arrtbigiioiis results. So we nwle only a fen trials with t h e
Elastic Scattering of Polarized Neutrons by 3He a t I,ow Energy
413
minimum alteration of BS and HH predictions, taking into account the experimental
and Monte Carlo errors we have evaluated “ad oculum” a band of analysing powers
considering the values in the middle as “corrected”. They are displayed in figs. 2-4
as square points with errors obtained as a quadratic combination of experimental and
Monte Carlo deviations. All the input polarization curves, included among the shown
errors, would probably give asymmetries in agreement with the experimental ones.
I n the same figures the experimental data of HOLLAXDYWORT et al. a t 3 MeV [9] and
LISOWSKI
et al. a t 8 MeV [lo] are shown as white and black circles respectively. The
triangles in figs. 3 and 4 are the data of BEHOFe t al. [8] a t 3.33 and 7.9 MeV modified
using the values suggested in ref. [17] for the neutron beam polarization.
E,,,= 1.67 MeV
-HH
.-E ? .
g
E,,= 2.43MeV
I
1.
.5
I
0
,
-.5
cos
Fig. 2. Experimental data of %-“He
anulysing power (w present work) at 1.67 and 2.33 MeV, coinpared n i t h the predictions in ref. [ll] (HH) and ref. [GI (BS).
The agreement with other analysing powers is quite satisfactory for the forward
angles, while for the backward angles, apart from the 3 MeV data, the agreement is
lacking, particularly at 7.8 MeV where our polarization data appear intermediate
[ 101 and BEHOF’B
[8].
between LISOWSKT’S
However a t the latter energy we applied an incomplete correction to the data as
noted in the previous section. But guided by preceding analogous evaluations we
estimate the possible differences between the partial [ 121 or full correction [16] procedures t o be of the order of the experimental errors for analysing power values near
to the rnaxitnutn and negligible in all other cases.
1,. DRIC~O
ct nl.
-HH
0.5.-
--- B S
0.
L
B
1
Q
I
Pig. 3. Experimental data of n-"e analysing power ( present work, 0 ref. 191 ant1
at 3.0 and 3.4 MeV, cornpared with the predictions in ref. [Ill (HH) and ref. [ (il (JZS).
E,,-H
1.
A
ref. L8])
A
ref.,
7.8 MeV
H
.5
0
I
-1.
-.5
=os %M.
Fig. 4. Experiincsiital data of m-8Heanalysing power (m present work, 0 ref. [lo] and
compared with tlw predictions in ref. [U] (HH) :md G . M. Hale (HA) at 7.5 MeV.
[a])
Elaritic Swtttc,ring of Polarized Neutrons by 3He a t Low Energy
415
Moreover the 90' point is critical, a t this energy, because the applied geometrical
corrections are important. They reduce the measured analysing power to about 113
and are very dependent on the input polarization curve.
Recently after an exchange of letters we received from G.M. Hale the predictions
of the n-"e
analysing power obtained from his R-matrix analysis of the reactions
involving the *He system. The general trend is similar for all the low energies (13.4MeV)
to the BS predictions, pratically coinciding a t 1.67 and 2.43MeV, and being intermediate between the H H and BS curves a t 3.0 and 3.4 MeV. At 7.8 MeV Hale's predictions, displayed in fig. 4 as point-line curve (HA), show the sole significant disagreement with our data in the zero-crossing position.
4. Conclusions
Our measurements enrich the polarization data of the n-3He elastic reaction at low
energies ( 53.0 MeV) confirming HOLLANDSWORTH'S
results a t 3.0 MeV. They indicate
a t the same time that only few improvements in the predictions are necessary a t the
lowest energy (1.67 MeV).
For the other two energies we believe that new measurements are necessary of the
beam polarization a t 3.4 MeV and of the analysing power a t 7.8 MeV, expecially near
t9 = 120' C.M. where the differences among the experimental data are more evident.
As long as these uncertainties are left, any analysis leading to definite conclusions
ahont the 4He states will remain problematic.
References
FIARMAN,
S.; MEYERHOF,
W. E.: Nucl. Phys. A 206 (1973) 1.
SZALOKY,
G.; SEILER,F.: Nucl. Phys. A 303 (1978) 57.
BAZ,A. 1.: Sov. Phys. JEPT 5 (1957) 403.
JIEYWRHOI', W. E.; MC ELEARNEY,
J . N.: ?u'~cl.I'hys. 74 (I%;.!) 533.
[a] 'U'ERTTZ,C.; MEYERHOF,
W. E.: Nucl. Phys. A 121 (1968) 38.
[G] BARIT,1. YA.; SERGEEV,
V. A. : Sov. Phys. JETP 13 (1971j 708.
Ti] SEAGRAVR,
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L.; SIMMONS,
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[8] REHOW,
A. I?.; HEVEZI,J. M.; SPALEK,
G.: Nucl. Phys. 84 (IlflXi) 290.
HOLLATYDSWORTH,~~.
E.; GILPA4TBICK. 11.;BULHER,
W. P.: Phys. Rev. C 5 (1972) 3!1*5.
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P. W.; RHEA,T. C.; WAT,TES,
R. L.; BUSCH,
C. E . ; CLEGIGI,
T. B.: Nucl. Phys. A 259
(1976) 61.
[ll] HEISS,P.; HACKENBROIVR,
H. H.: Niicl. Phys. '1 YO2 (1953) 333.
[12] DRIGO,L.; TORNIELLI,
G.; ZANNONI,
G.: Lett. R'uovo Cimento IS (1977) 30G.
[13] DRTCO,
L.; MANDUCHI,c. ; b10SCHIN1, G. ;RGSSO fir JNDUCHI, &I. T. ;TORNIELLI,
G . ; ZANNONI,c.:
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[14] DRIGO,L.: TORNIELLI,
G.; ZANNONI,
G . : Nuovo ('omento A 31 (197G) 1.
[I51 DRIGO,
I,.; TORNIELLI,
G . ; ZAXXONI.G . : Nucl. Instr. Meth. 166 (1979) 261.
[ l G l SMITH,
J. I<.; THORNTON,
6. T.: Nucl. Phys. A 186 (1972) 161.
[li I W a ~ i m tB.
, I,. : Polarization Phenomena in Piucle.ir Reactions (eds. BARSOHALL,
H. H. ; HAEHERLI, W.) Madison, Wis. 1971, p. 317.
1181 GOLUBERG.
M. D.; MUGHABGHAB,
S. F.; M u c u ~ u oB.
, A.; M ~ YV.
, M.: Neutron Cross Sections, Brookhaven Nat. Lab. Report BNL-325, 2nd ed. 19GG, vol. 2 A.
113
[21
131
[4l
416
L. DRIGOet id.
[19] N. E. A. Neutron Data Compilation Centre 91190 GIF-SUR-YVETTE (France).
A. H.; NIJGH,G. J.; VAN LIESHOUT,
R.: Nuclear Spectroscopy Tables, Amsterdam:
[20] WAPSTRA,
North-Holland 1959, p. 66.
[all DROSG,M.; MC DANIELS,D. K.; HOPKINS,
J. C.; SEIGRAVE, J. D.; SHERMAN,
R. H.; KERR,
E. C.: Phys. Rev. C 9 (1974) 179.
Bei der Redaktion eingegangen am 27. Februar 1981, revidiertes Manuskript a,m 1G. Juni 1982.
Anschr. d. Verf.: Drs. L. DRIGO,G. TORNIELLI,
G. ZANNONI Istituto di Fisica ,,G. Galilei"
Via Marzolo 8 1-35100 Padova
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