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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