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Further Experiments on the BLOCH-SIEGERT Effect.

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CARRELLI,
BRESCIA
and GROSSETTI:Experiments on the B L O O H - S I ~ OEffect
ERT
205
Further Experiments on the B~ocw-S~ro~rt
Effect
By A. CARRELLI,G. BRESCIAand E. GROSSETTI
With 3 Figures
Abstract
I n this work we have tried to show that fields of perturbing radiofrequency (obtained
by modulating the radiofrequency field), besides produoing a displacement of frequency
of the line of resonance in nuclear magnetic resonance (the BLOOE-SIEGBRT
effect), also
produce variations of intensity between the line of nuclear resonance and the line due to
the perturbing fields when the threa lines are partially superimposed.
It is known that magnetic resonance occurs when the LARMOB
precession
of magnetic moments of the nuclei, immersed in a constant magnetic field H,,
coincides with the rotation frequency of a magnetic field HI, rotating in a plane
normal t o the direction of the constant magnetic field H,,.
Now BLOCH
and SIEQERThave shown t h a t if to the rotating field of frequency v,, corresponding to the LARMOR
frequency, another rotating field of
frequency v' is added, near vo and of H' intensity, the frequency a t which
resonance occurs is displaced from initial value by a quantity Avo expressed as:
Equation (1) is arrived a t by imagining a system of axes rotating around
the axis of field H,,, with a frequency v ' ; in such a case the LAEMOBfrequency
is reduced t o the value v, - v', and in this system, through which dipoles
Fig. 1.
H'in wrst.
rotate with the frequency vo - v', the constant magnetic field which produces
2RV'
the LARMOR rotation has the value H , - - (fig. 1). Now the perturbing
Y
field H' m u s t be added t o this field (and H' is a constant for this system of
206
Annalen der Physik
*
7. Folge
*
Band 19, Heft 3/4
*
1967
rotating a.xes). Thus the LARMOR
rotation in this systema of axes occurs with
a frequency
Y
= -l / ( H o -
,> + HI2 and occurs along the
2nd
2
a;
axis. How-
ever, according to BLOCH
~ ~ ~ . S I E ~because
E B T , of the low value of H’ the a
axis for all practical purposes coincides with the axis of field H,; t o pass on
again to fixed axes, in respect to which measurement will be made, one must
add the rotation frequency Y’ and thus because of the presence of the rotating
field H‘ the frequency becomes
-~
--;-) +
f ( H 0 - 9nv‘
2
HI2
+
Y’.
2n
From this one reaches equation (1) by easy calculations, taking into consideration the fact that there are two perturbing fields. Fig. 1 illustrates the points
discussed above; it is to be noted, however, that BLOCH
and SIEGERTmaintain that since H’ is very small the rotation of the dipoles actually takes place
always in the direction of the field H,.
The experiment which serves t o confirm this effect was performed by
L ~ S C H[l]
E with a special device; in place of a single perturbed field of intensity
H’ and frequency v’ (to take a n example higher than the LARMOR
frequency yo)
he modulated with a certain frequency Y: the frequency ot the rotating field
in such a way that, in addition t o the original rotating field two others also
come into play-one with a frequency of v, - Y;, the other with frequency
v,
Y: and each with intensity H‘ which depends on the extent of the modulation. More precisely, if we take as an example a modulation of 40%, the intensity
of the field H’ relative to the two perturbing frequencies has a value of 20%
of the intensity of field HI, which produces the nuclear magnetic resonance.
Consequently, in accord witahthe prediction of BLOCH
and SIEQERT,
in place
Y: one finds that
of the three lines of resonance of frequencies yo - Y:, v,, Y,
t h e lines Y, - Y; and Y,
Y; have approached the fundamental frequency of
Avo as given by formula (1).
The experiment has fully confirmed the predictions of the theory. More
recently the same experiment was repeated under more precise experimental
conditions and the relation written above was carefully verified by a series of
frequency value [2] making evident the behaviour of Avo as a function of the
difference of frequency according to equation (1).
L~SCHE’S
experiment was carried out for a frequency of 13 MHz with lines
of approximately 0.700 KHz in width; more modern research, on the other
hand, has been carried out with much thinner resonance lines on the order of
10 Hz, permitting the perturbing frequency t o be brought much closer t o the
frequency of LARYOR.Thus i t has been possible t o predict a much greater
value of Avo and consequently more accurate measurements.
I n the present experiments we proposed to work essentially under conditions in which the value of field H’ would be rather large, so that we could
not regard that the rotation of the dipoles may take place along the axis of
field H,.
Using LOSCHE’R
method we found the width of the lines in our experiment
was a t most 3.5 KHz. If the two lines of perturbing resonance are indeed
Y; = 4.0 KHz apart; a portion of one of the three lines of resonance has parts
i n common (and the closer v’ is to yo, the more marked is this condition).
+
+
+
CARRELLI,BRESCIA
and
GRoSsETTI:
Experiments on the BLOCH-SIEOERT
Effect
207
The significance of this finding is that for R certain value of magnetic field
H, which produces LARMOR’S
rotation, the resonance for some dipoles corresponds to one frequency, say vb, while for other dipoles the resonance will correspond, simultaneously, to a. different radiofrequency, say v,,
v; or v, - v i .
When the lines are not superimposed the resonance for every value of the field
is produced by one sole radiofrequency.
The experiments were conducted up to modulation values of 60%. Under
our experimental conditions the oscillating currents generate a maximum
value of the perturbing rotating magnetic field of about 0.3 oersted. Taking
into consideration thc values of times T,and T, of the liquid used (water with
known concentration of Fe) we have been able to establish that for the oscillating current used, H‘ have values which shows that they are already beyond
the maximum intensity of the maximum signal, which is obtained by a value
H L of the field a t rotating frequency. I n other words, the condition is one in
which HA > H L .
Without modulation the signal had been seen on an oscillograph and in
addition h i d been registered on an ESTERLINE-ANGUS recorder which gives the
derivative of the signals. With modulation only the registration of the derivative could be obtained; the signals themselves, precisely because of the
modulation, were not clearly visible on the oscilloscope.
As is well known from theory, the intensity of the registered signal depends
on the difference between the phase of tension of the reference furnished to
the phase detector, and the phase of the signal. We have observed that without
modulation the amplitude of the oscillograph signal and the amplitude of the
signal of the recorder are different. That is, upon varying the value of the
radiofrequency current, the amplitude of the signal on the recorder does not
correspond t o that measured on t.he oscillograph. The figures we obtained on
the oscillograph for various values of t.he rotating field agree well with those
obtained by other workers.
This difference in intensity can be interpreted by supposing that in the
sequency from the low frequency amplifier to the recorder a difference in
phase is produced, proportional to the value of the radiofrequency current,
which has as effect a variation of intensity of the signal from the value seen
on the oscillograph to that registered.
It is t o be noted t h a t in our recordings (which coniprise a frequency band
between the two extremes of t.he three signals of the order of 10- 15 KHz) the
two lateral signals always have the same intensity ; therefore this variation
in phase does not depend on the frequency of the signal.
In our own measurements, with vb rather small, i t is not possible to show
the BLOCH-SIEQERT
effect because the width of the lines is fairly marked.
Once we had established the graduation of the recording apparatus we
could vary the modulation to use rather low values if I (the intensity of the
radiofrequency current and therefore of the perturbing field).
I n a series of measurements with I = 0.4 ( H b = 0.5 oersted) and with signals
2 KHz wide, i t turned out that the intensity of the two lateral signals, 5 KHz
from the central one, does not agree with the expected intensity, inasmuch as
the intensity of the central signal is lower than was foreseen. Further, we were
able to show that this effect. is more cospicuous when vb is smaller - that is,
when it passes 4 KHz -.
+
208
Annalen der Physik
*
7. Folge
Band 19, Heft 3/4
*
1967
The same thing can be said for higher values of I (I = 0.6).
It is apparent therefore that the action of the two perturbing fields not
effect) whiuh has
only produces variations of frequency (the BLOCK-SIEOEBT
already been clearly demonstrated experimentally, but in addition varies the
relative intensity of the three signals.
Thus we proceded to experiment under conditions in which the three signals
were clearly superimposed. This can be done by raising the inhomogeneity of
field H,,, reducing the value of vh and by letting the field of the two lateral
signals be intensified (by raising the intensity I of the oscillating current in
the coil). Working with signale of the width of 2.86KHz and with lateral
signals of frequencies rather distant from the 3.6 KHz of the prinoipal frequency
signal, one succeeds in getting the three signals clearly superimposed.
We proceeded by keeping constant the modulation (60%) and the value
of vb = 5 KHz and by varying the intensity I of the oscillating current, which
leads to a change in intensity of the field of radiofrequency Hh and consequently
of the perturbing field H'.
The recordings we obtained permitted us to measure the intensity of the
central line and of the lateral lines.
behaves as a function of the radiofrequency current,
Fig. 2 shows that
I,
and anologoualy that the intensity of the central signal is relatively diminished.
I c - central linc intensity
C
I - bierdl line intensity
a5
1.0
Ccumnt intensity
I5
Fig. 2.
By keeping a constant value of I such aa to produce a field of loersted
in the coil, we proceeded to vary the modulation up to SOY0, which gives a
value of H' = 0.3; and we measured the intensity of the central signal and
of the two lateral signals. Fig. 3 shows the ratio between intenmties of the
central and lateral lines, on the ordinates, and the depth of modulation on the
abscissas.
mod. depth
Fig. 3.
It is apparent that the relative intensity of the central signal dimishes
rapidly with the rising values of the perturbing field H' (from 0.1 to 0.3 oersted).
CARBELLI, BRESCIA
and GROSSETTI: Experiments on the BLOCH-SIEUERT
Effect
209
The theoretical interpretation of the BLOCH-SIEGERT
effect, as set forth
above, demands that the value of the angle through which the dipoles rotate
because of the presence of a perturbing field must be practically zero, so that
the rotation may take place along the direction of the magnetic field H,.
Under the experimental conditions in which H' = 0.3 08, H' = 0.1 oe that is, in the conditions obtaining in some of our experiments in which the
central signal almost disappears, one can calculate that the angle which the
axis of the dipoles makes with the axis of the constant magnetic field is about
18' and therefore no longer negligible.
We must also add that there are two perturbing magnetic fields: according
to the BLOCH-SIEGERT
theory each of them produces a variation of Avo and
the two variations are additive. Under our experimental conditions the two perturbing fields can produce a total inclination of the axis of the dipoles in respect
to field Ho which is also not neghgible and which demonstrates that the conditions are markedly different from those considered heretofore. The theory
therefore calls for a revision from which one can justify the modalities we
encountered.
References
[l] LOSOHE,A., Ann. Physik 20 (1967) 178.
[Z] BENOIT-OTTAWI,
H., C. R. Acad. Sci. 260 (1960) 2886.
Napoli (Italia), Istituto di Fisica Sperimentale, UniversitB.
Bei der Redaktion eingegangen am 23. Juli 1966.
14
Ann. Physil;. 7. Folge, Bd. 10
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