Ramaswamy, M K

English

IACS Institutional Repository

*Supported in part by the U. S. Atomic Energy Commission. [On leave from tho University of Mysore, India. 285 The principle of the present experiment is extremely simple. If we have a gamma counter which detects the 1.28 Me V gamma ray and a beta 2.6 year Na-22 decays by positron emission and electron-capture to the first.excited state of Ne-22 at 1.28 MeV followed by a gamma ray of this energy to the ground state. The decay scheme is shown in figure 1. The spin of Na-22 has been measured to be 3 (Mack, 1950). The spin of the 1.28 Me V state of Ne-22 is 2+ from systematics of even-even nuclei (Scharff-Goldhaber, 1953). Hence the transition 3+-)2+ follows the selection rule 6.J = 1, No and is therefore pure Gamow-Teller. The electron-capture to positron branching ratio in the decay of Na-22 has been extensively studied. A summary of previous work is given in a very recent paper by Konijn et al (1959). So far the best reported value is that of Sherr and Miller (1954) who obtained c/j3+ = 0.110±0.006 by an elegant experiment, and by comparing with the theoretical value of 0.1135±0.0020 estimated the Fierz interference term to be ( -1+2) % . Since all the present interpretations of Fierz interference are based on this experiment we have been prompted to attempt a more precise determination of this ratio, if possible. INTRODUCTION . ABSTRACT. Tho amount of posit.ron omission in tho decay of Na-22 has been dotor- mined to bo 0.899±0 003 us ing n ··rr ·Ju t i b t . ill . . . . . . · - ·~ " p s JC e ,a scmt.i ut.ion spoct.romot.or rn conjunction wrt.h d~ubl~ and triple coineidonee techniques. This loads to an E/[3+ rat io of 0.112±0.004 which IS slightly better than the best earlier result .of Shorr and Miller. Comparison of the measured value with tho t-hocrct.ica l ratio of 0.113:3 ± 0.002 leads to a value for tho Fierz inter- ference term boT = -0.004± 0.012, showing tho extreme sn~allnoss of the cross torm in allowed Gamow-Teller transitions. In tho append ix a brief summary of the st.at.us of tho Fiorz t.orm as revealed by our studios and other work is prosontcd. M. K RAMASWAl\1Yt DEP1UITl\IBN'.l'. 0 p T F nvsrcs, HE JonNs Hor-rcrxs UNIVERSITY, BAL'rnwm:-18, i\LuwLAND (USA) (Received for publication, .May 14, 1959) 34 A REINVESTIGATION OF THE DECA y OF Na~22* ^86 M. K. Rarmswamycounter which detects the positrons, then assuming that all the positrons are counted wo can write for the beta-1.28 coincidencesas ^and foj’ the gajnma rayN j-2^  — ^0^1-28 =  ^where N q is the transition rate,/+ =  the fraction of ilecays bypositron emissionand (7 i .2b — the efficiency for detecting the! 28 MeV gamma ray. The ratio of a to h then yields/+, from which the c//?+ ratio can be computed. This is iiossiblo provided the entire positron spectrum can be measured.Na22Fig. 1. Docay Scheme of Na-22We liave emi)h)yed a 4tt iilastic scintillation counter for detecting the positrons and a NaT(Tl) counter for the 1.28 MeV gamma ray. The gamma counter is biased to accept only the photopoak. The effectiveness of the 47t plastic scintillation counter for measuring the shapes of beta siiectra has been demonstrated by the work of Johnson et al (1956) and more recently by Robinson and Langer (1958), and is substantiated by the present experiments.A Na-22 source from a HCl solution was evaporated on a 0.0001" mylar foil and covered with a similar foil. The 477- counter was formed in t^ he following way. Two plastic cylinders, each 3mm thick and 1 cm in diameter were chosen. One of the cylinders had a depression 1/2 mm deep and 1/2 cm in diameter. The Na-22 sandwich was placed in the depression. The two cylinders were pressedA Reinvestigation of the Decay of Na-22 287together to form the 47t counter. A cone-shaped light pipe 1-1/2" long having a well at the apex was mounted on a DuMont 6292 phototube. To the bottom of the well the 47t plastic scintillation crystal was cemented by means of Canada balsam. The sides of the well had been painted white to ensure good light col­lection. The top of the well had a thin alummiura foil whitened inside. The gamma counter was a 2" cube Nal(Tl) crystal which had a resolution of 1 1 % for 0 661 MoV gamma ray of Cs-137. The 47t counter had a resolution of 16% for the 0.624 MoV -conversion lino of Cs-137. The entire assembly of crystal and counters was surrounded by 2 " of lead at 4 ".l ^ X P E R I M E N T A LThe general features of the 4n counter were investigated by a P-32 source using plastic cylinders, each 5mm thick and 1 cm in diameter. A Pormi plot ofl*’ip. 2. Fonui plot of P-32 apootrum taken with a 4ir plastio scintillation spectrometer.Note the end-point at 1.72 MoV.ilie spectrum is shown in figure 2 . An end-point of 1.72 MeV is indicated, in good agreement with the value in the literature (King, 1954). Experiments on Na- 2 2  were started with plastics of dimensions described in the Introduction The gamma counter was set on the photopeak of the 1.28 MoV gamma ray. The peak had a width of 3.5 volts at 35 volts. This was used to gate the 20-channel analyzer. The positron spectrum coincident with the 1.28 MeV gamma ray is shown in figure 3. Energy calibration of the siiectrometer was obtained by using external gamma rays of Na-22(0.511 MeV), and Cs-137(0.661 Mev). The Compton edges located at 3/4 of the maximum were used. The calibration is also shown in figure 3(c). The calibration curve intercepted the axis corresponding lo zero pulse height at 18 KeV in agreement with similar observations by Johnson <1^ al (1956).288 M, K. RamaswamyBecause of the fact that the plastic chosen had dimensions somewhat greater than the range of positrons, one would expect that the observed beta spectrumFig. 3.(a) Coniimioxia curve— b^el-a spectrum of Nu^22 in Air plastm coimtor coincident with the 1.28 MoV gamma ray.(b) Dotted curve— l^iota spectrum of Na»22 in triple coincidence with the 1.28 MeV gumma I’ay and the two aimiliilation quanta. Tho Hpcctnuii is normalized to the doubles spec­trum (beta-1 28*) above 50 K!oV to 1/10%.(c) Enorgy calibration of tho 497 plastic counter using Compj/On edges of 0.511 (Na-22) and 0.661 (Cs-137) MeV.(d) Compton distribution of Na-22 gamma rays in 47t plastic counter (with positrons com­pletely stopped by Incite) coincident with tho annihilation radiation and the 1.28 MeV gamma ray.may not be the correct one, but somewhat distorted by the simultaneous detec­tion of a beta partude and its associated Compton electron. Thus the effect would be qualitatively to shift the spectrum towards higher energy, without changing the area under the sxioctrum.In  order, therefore, to obtain the undistorted spectrum, tho beta spectrum was measured in triple coincidence with tho 1.28 MoV gamma ray and the two annihilation quanta. Tho experimental arrangement and a functional diagram of the electronic circuitry are shown in figure 4. Pulses from the two 0.61 iMeV counters and the 1.28 MeV counter were fed to a triple coincidence circuit, whose output Avas used to gate the 20-channel analyzer. The positron spectrum gated by the triples is shown also in figure 3, normalized to the doubles spectrum beyond 50 KeV. Tho statistical error for each point on the triples spectrum varied from 2 to 4%. The doubles and the triples spectra arc indeed displaced as expected. To obtain a quantitative justification for the siiectral displacement, the positronsA Reinvestigation of the Decay of Na-22 289were completely stopped in just enough lucite and the Compton distribution was obtained in coincidentie with the annihilation radiation and the 1.28 MeV gamma ray. The spectrum thus obtained is shown as curve d in iigure 11 and is seen to be similar to the one that is obtained using an external source except for the absence of edge effects.4. Block diagram of experimental eot-up for Na-22 studios.If the assertion that the cffecd of the Compton distribution due to annihila­tion radiation is simply to shift the doubles spectrum is indeed correct, then it must be possible to express the doubles spectrum d{h) in terms of the triples spectrum t{h'), and the Compton distribution C{h—h'). In other words, we should be able to writed{h) t{h/) G{h-h’)h.A niimorical calculation was iiarriod out to test this assumption. For an assumed Compton of 0% the agreement from point to point was 3^% . The assumption of 6 % is not inconsistent with the dimensions of the plastitj and the Compton cross-section (the choice of 6 % is not critical, since the triples spectrum itself was known to 2-4%). The agreement thus obtained provides quantitative justification for the assertion made earlier.lt must bo pointed out in this connec­tion that the effect of the inner bremsstrahlung is to displace the true spectrum m a direction opposite to that due to the Compton distribution but because of the weakness of the effect, the Compton effect predominates. The preservation of areas under the doubles and triples spectra is indicated by the fact that the two areas could be normalized to within 1 /1 0 %.Since the lowest energy observed was around 40 KeV, an extrapolation of the spectrum to zero energy has to be made in order to obtain the area under the whole beta spectrum. To do this, the following procedure was adopted. The ideal290 M ,  K .Fermi flpectnim connected for flcreening was plotted. The spectrum was distorted for finite resolution at various points of the spectrum by folding in a gaussian of the proper width. The assumption was made that the half-width varied as the square root of the energy over the entire energy range. Choosing various en­ergies (designated as to the right of was obtained. I t  wasdetermined that below 50 KeV the area under the beta-spectrum with and without resolutioji correction differed only by 1/10% and amounted to 5.3% of the area under the beta-spectrum beyond 50 KoV. Thus the area under the ideal Fermi distribution was taken as the correct area. This when added to the area duo to the remaining portion of the doubles spectrum (which had been corrected by the Compton distribution to get the undisplaced spectrum) would give the total area.In order to test for any iiossible systematic; errors the ratio of area to the right of and the entire area from 50 KeV up to the maximum energy was plotted as a function of both for the ideal Fermi spectrum corrected for finite resolution, and the actual doubles beta spectrum corrected to the triples spectrum. The result is displayed in figure 5 . I t  is observed that the data of three different runsFig. 5. Study of aystematic errors in tlio Na-22 experiment.are consistent within themselves to 1 -1 /2 % and with the theoretical plot to within 1 %. This may he taken as evidence for the absence of any systematic errors.The experiments wore repeated with and without shielding. The effect of ehaniiel width on the gamma ray side was next studied, A different source wasA Reinvestigation of the Decay of Ra~22 291made and the experiments repeated. In each case consistent results were ob­tained. Throughout the course of the experiments the counters were periodically chocked. The energy calibration of the beta spectrometer was carried out before and after each run. The overall statistical error in the double run was 1/10 to 2 /1 0 %. Altogether seven runs were made.R E S U L T SThe data from six of the runs are assembled in Table I together with explana­tion. The average value of is calculated to bo 0.899±0.003. This yields an average e//?+ ratio of 0.112±0.004.Apart from statistical orrtjr, the other uncertainty is due to the folding of the Compton distribution, and in the estimation of the areas under the beta and gamma spectrum. A calculation was made to see how much error would bo intro­duced if the half-width of the gaussian curve deviated from obeying the law. Dependences jiroportional to E^-  ^ and were investigated. From this it was concluded that the error introduced is less than 1 / 1 0 % in the final result.Finally an error in the determination of the end-point of the positron spectrum would introduce an error in the value of Because of the assumed linearityill energy scale, this would tend to introduce a linear systematic en’or(as distin­guished from any due to the apparatus itself). In Table 2 the end -points are tabu­lated for various runs together with uncertainties. From this table the systematic error introduced in this way is estimated to bo less than 1-2%. Thus allowing for this our kjp-  ^ ratio would at worst becomee//y+ =  0.112+0.005resulting in the Fierz term (see Discussion)=. -0.004+0.013.D I S C U S S I O NThe c.onipuicd value of ejp+ is somewhat better than that of Sherr and Miller. The theoretical value of e//C is 0.1135+0.0020, when corrected for screening and 6.5% L-(;apture (Rose and Jackson, 1949). The value of < W "i>  for W 2.061 for Na-22 is 0.7. The Fierz term is computed from the expressionj  _______\__________2 [ l+ jR /R p < “ lF ~ i> ]== -  0.004+0.012.Na-2 2  is perhaps the ideal case for determining the Fierz term because of the low Z involved. I t  is very unfortunate that the end-point of the positron spectrum IS not known well enough to attempt any further refinement in experimental292 M, K.TABLE I4". y-ray oh. width =  3.5 vollflSour00No. 1 2. No Fihiold. oh.width“ 3.5 voltH3. No flhiold ch. width =  3 voltH4". y-ray ch. widLh =  3.5 voltsNo. 3 .5, No shield oh.width—3.5 volts0. No shield oh. width =  3 volts(a) (b) (c) (d)1.28 ( >  .50 kov) 1 28 ( >  0 kov) Nj.aa cpB A =  (b)/(c)64 08d_0.18 67.48+0.19 75.21+0.11 0.898+0.00364 23iO  19 67 03-1-0.20 75 24 +  0.15 0.900+ 0.00357.82:^0.22 60 88 +  0.2.3 67.76 +  0 15 0.899 +  0.00448.31i0 .14 50.87 +  0 15 56 62 +  0 10 0.900+0 00348.07 +  0 17 50 62 +  0.18 56 31 +  0.11 0899 +  0.00442 78+0.13 45.05 +  0.14 .50 11+0 10 0.899+0.003U O l+0.003 Average value of£/i8^  ^ 0 ioi±o.qo3__8/800 -t ()“ 003 = 0 .112 ±  o'. 004/ h =  0 899^0.003TABLE IIEnd-point energies of positron spectrumKun No End-point (koV)1 646 +  112 541 +  103 648 +  114 539 +  105 540 +  106 644+11TABLE IIISummary of results on Fierz termNucleus Transition Wo bgjt RoforonceGa-68 lt->2+ 4 70 -0.03 +  0.02 Ramaswamy, 1960Co-58 2+->2+ 1.924 -0.004+0.014 „ 1968Nor-22 3+->2+ 2.061 -0 004+0.012 present workA Reinvesiigation of the Decay of Na-22 293techniques to measure ej/i+ ratio. In any case it has been demonstrated that the plastic scintillation counter can be effectively used m the study of beta spectra and precision results obtained if analyzed with caution.C O N C L U S I O N SA reinvestigation of the electron capture to positron branching ratio in the decay of Na-22 has been made with somewhat greater precision than has been possible before, using a 47t plastic scintillator and a gamma counter m coniunction Avith double and triple coincidence techniques. The result for ratio is 0.112 J2 O.OO4 . I t  is suggested that the beta spectrum end-point bo measured with greater precision to make much more meaningful estimates of the Fioi’z term. I t  would he further of interest to measure //?“*" ratios in unique forbidden transitions allowed only by Gamow-Tellor selection rules.A C K N O W L E D G M E N T SThe author wishes to thanlc Professor L. Madansky for valuable suggestions and illuminating discussions.APPENDIXS U M M A R Y  OK F 1 E R Z I  N T E Jt F E R E N C E I N  J3 E T A D E C A YIn this section the conclusions regarding the status of Fierz interference in Gamow-Tellor transitions as indicated by our measurements reported here and elsewhere are summarised (I’able III).Gerhart (Gerhart, 1958) has made an excellent analysis of Fierz interference m Fermi transitions and concludes =  0.00:h0.12. A brief review of Fierz interference m beta-decay has been recently given by the author(Ramaswamy, 1959). From Table 3 one sees that the best evidence for the smallness of the Fierz term in G-T interaction comes from Na-22. Konijn et al have summarized (lata regarding the Fierz term as determined by the ratio technique. They conclude that = ~  0.007 JzlhO 10.From evidence presented above and from Gerhart’s analysis one can conclude that the Fierz term in allowed transitions is practically zero. Before parity nonconservation was discovered the Fierz term in G—T transition could be express­ed as294 M. K . BamaswamyThe smallnesB of b could be interpreted as implying that or O^jC^ wassmall . With the discovery that parity is not conserved in beta-decay, the defi­nition of b has acquired the extended form ^ fP - - --Ir {C\Cr,* +  Oa Gt *)whereC' ,^ are the j)arity conserving and2'^  are the jiarity non-conserving coui)liiig (ionstants.The *s denote complex conjugation resulting from a possible violation of time reversal invariance.With the new definition of 6, the smalhiess of h meansRe{C\G^*-[-G^'Cy*) =  0.This implies that£ j '  = _Nothing more can be said concerning the coupling constants unless the relation between the parity conserving and non-consorving coupling constants is known. Tt is now established from electron polarization measurcraonts on pure Gamow- Teller transitions that G^jG^' 'TT — 1Thus the parity conserving and non-conserving couidmg constants scorn to have SCbout the same strength. The loss of definitiveness of the Fiorz term is one of the consequences of the discovery of parity non-conservation.R E F E R E N 0 10 SGerhart, J. B., 1958, Vkya. Rev., 110, 897.Gertrude Goldhabor, 1953, 90, 587.Johnaon, Johueon and Longer, 1956, Phys. Rev., 102, 1142.King, K. W , 1954, Revs. Mod. Phys., 26, 327.Konijn, van Nooijon, Hagedoorn and Wapatra, 1959, Nuclear Phys., 9, 296.Mack, J. E., 1950, Revs Mod. Phys., 22 64. _Rainaswainy, M. K., 1959, Nuclear Physics 10, 205.Ramaswamy, M. K., 1958, Bull. Am. Phys. Soc., 2, 3, 357.Ph.D. Disaertation, Johns IHopkma University, 1959 (unpiihliahod).Ramaswamy, M. K., 1959, submitted to Ourrent Science.Robinson, R. L., and Longer, L. M., 1958, Phys. Rev., 109, 1255.Rose, M. E. and Jackson, J., 1949, Phys. Rev., 76, 1540.Sherr, R. and Miller, R. H., 1954, 93, 1076.

A Reinvestigation of the Decay of Na-22

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A Reinvestigation of the Decay of Na-22

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