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Internal bremsstrahlung from P32 and Y90
Nuclear Physics 31 (1962) 3 2 2 - - 3 3 4 ; (~) North-Holland Publishing Co., Amsterdam Not to
be reproduced by photoprint or microfilm without written permission from the publisher
INTERNAL B R E M S S T R A H L U N G FROM ps2 AND ygo M. A. H A K E E M t A N D M A X G O O D R I C H
Department o/ Physics and Astronomy, Louisiana State University Received 2 J u n e 1961 T h e i n t e r n a l b r e m s s t r a h l u n g s p e c t r a of t h e allowed b e t a e m i t t e r ]?s2 a n d t h e first forb i d d e n b e t a e m i t t e r yg0 h a v e been s t u d i e d w i t h a scintillation s p e c t r o m e t e r a n d c o m p a r e d w i t h available calculations. T h e e x p e r i m e n t a l s p e c t r u m of ]?s2 does n o t agree e x a c t l y w i t h K n i p p , U h l e n b e c k a n d Bloch's t h e o r y for allowed b e t a t r a n s i t i o n s . T h e d e v i a t i o n s are n o t very large b u t t h e y are significant a n d c a n be explained v e r y well b y t h e C o u l o m b corrections proposed b y Lewis a n d Ford. T h e observed s p e c t r u m of yg0 is in considerable d i s a g r e e m e n t w i t h t h e e x t e n s i o n of K n i p p , U h l e n b e c k a n d B l o c h ' s t h e o r y for first f o r b i d d e n b e t a t r a n s i t i o n s w i t h t e n s o r i n t e r a c t i o n s . T h e C o u l o m b correction in this case is q u i t e i n a d e q u a t e to a c c o u n t for t h e deviation. T h e o b s e r v e d p h o t o n excess m a y be arising f r o m d e t o u r t r a n s i t i o n s ; a n a s s u m p t i o n s u p p o r t e d b y calculations of Lewis a n d Ford.
Abstract:
1. Introduction A number of measurements on the internal bremsstrahlung (IB) accompanying beta decay have been reported 1)**. These measurements are usually compared with the theory originally given by Knipp and Uhlenbeck 2) and by Bloch 3) for allowed beta emitters and further developed by Chang and Falkoff 4) and Madansky et al. 5). The shape of the IB spectrum according to these calculations (generally referred to as KUB Theory) depends only slightly on the nature of the interaction and the degree of forbiddenness of the beta transition. However, the differences are sufficient to be detectable under favourable circumstances by a careful measurement utilizing a scintillation spectrometer. Most of the early work on the energy distribution and intensity covers only the low energy end of the spectrum and indicates agreement within the accuracy of the experiments with the theory. Goodrich and Payne 6)*** have extended the measurements on the energy distribution of IB from p32 up to .q00 keV. They found that the shape of the experimental spectrum throughout the measured region agreed well with the computed spectrum for an allowed beta transition and disagreed slightly but significantly with that for a forbidden beta transition. Subsequently reported work of Lid~n and Starfelt ~) on the IB spectrum of p32 in this energy range does not agree with these results. They find that the measured spectrum is less steep * ]?resent address: t h e U n i v e r s i t y of Miami, Coral Gables, Florida tf F o r a review of early e x p e r i m e n t s see ref.~). tt* T h i s p a p e r will be referred to as (GP). 322
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than the K U B spectrum. If these spectra are normalized at the low energy end, the experimental points lie above the theoretical ones at high energies. The deviation increases with energy and is about 70 % at 1 MeV. Mrs. LangevinJoliot s) has also reported measurements on p39 which disagree with both those of GP and of Lid6n and Starfelt. According to these measurements the number of photons observed at 153 keV is 150 % in excess of the theory while at 1 MeV the excess is 85 °/o, indicating that the spectrum falls off much more rapidly than the K U B spectrum. Recently Persson and Johannsson 9) have repeated measurements on p~9 in a coincidence experiment. Due to low counting rates the statistical error is very large. However, their results indicate general agreement with K U B theory. In the K U B calculations the effect of nuclear charge (usually called Coulomb effect) has been entirely neglected. A correction for this approximation has been proposed recently b y Nilsson 10), Lewis and Ford 11) and Spruch and Gold 19). In the case of Pa~ this correction is not very large. It increases the total number of photons b y about 5 % in the energy range 500--1000 keV, hence very accurate data are necessary to check these calculations. Another source of contribution to the continuous gamma radiation which has been discussed in the literature 13,14) arises from tile so-called detour transitions. The usual process of interest here is the one in which the parent nucleus undergoes a beta transition producing the daughter nucleus in .its ground state. The electron reaches its final state b y emitting a photon. This process can be represented b y the following expression: z NA -+ (z+a)Na+v+e * --+ ( z + l ) N a + v + e + y . In the detour transition the nucleus first emits a photon going to a virtual excited state~ then beta decays, or vice versa. We represent these transitions b y the following expression: zNA 7 zNA*+T "~ "~ tz+l)N ~ -}-e*+v 7 (z+l)Na+v+e+Y" In general the radiation arising from this nuclear effect will be weak compared to the IB radiation, since the nuclear dipole moment is small. This nuclear effect could certainly be present, but at least in allowed beta decay its contribution is expected to be negligible. For forbidden transitions, calculations of Lewis and Ford 15) indicate that the contribution is significant. The present investigation was undertaken primarily to obtain an improved measure of the IB spectral distribution against which the theoretical calculations including the Coulomb and detour effects might be compared. In view of the known low-energy-end agreement of the strength and distribution of the experimental spectra with K U B theory, it was considered desirable to design the experiment primarily to check the shape of the spectrum. This can be
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done more efficiently and precisely if the spectra to be compared are normalized at the low-energy end where the agreement is established. This eliminates the uncertainty in the determination of the absolute beta strength of the source. To obtain a reasonable counting rate towards the end point rather strong sources were used making a good determination of the strength of the beta source fairly difficult. The geometrical arrangement for the experiment has been somewhat improved and a large crystal utilized, enhancing the accuracy and reliability of the results by increasing the fraction of the photons totally absorbed in the crystal. It was also considered desirable to determine the spectral shape of IB, covering energies close to the end point from a first-forbidden beta emitter. The nucleus ygo was selected for this purpose because it has a high end point (2.26 MeV), short life (65 h) permitting high specific activity and is a pure beta emitter. It is classed as a unique first-forbidden transition (special case of selections rule AJ = 2, yes). Very precise measurements on the beta spectrum of ygo by Johnson et al. 16) have confirmed that between 0.5 MeV and the end point at 2.26 MeV no other group of beta rays is present. The results of the present experiment as well as those of previously reported measurements confirm the absence of monochromatic gamma rays. The internal conversion line and the positons arising from the 1.75 MeV transition of Zr 9° are much too weak to affect our measurements.
2. Experimental Details The spectrum was determined with a single-channel Jordan and Bell 1~) type scintillation spectrometer using a 7 cm long by 7 cm diameter cylindrical NaI(Th) crystal mounted directly on a DuMont 6363 photomultiplier. The source and detector geometry indicated in fig. 1 is basically the same as the one described in (GP). Due to the relatively low intensity of the IB, necessary precautions were taken to minimize the production of external bremsstrahlung (EB) in the source and the surrounding material, and the detector was adequately shielded to stop any scattered electrons and photons from striking the crystal. For a given source-to-crystal distance the total contribution from the EB produced in the beta stopper depends on its atomic number and its location. As the electrons are stopped completely in the low-Z absorber, the EB produced will be almost isotropic in the solid angle subtended by the beta stopper at the crystal. Under this assumption it can be shown that, for a lucite beta stopper and a source of 5 mm diameter located 30 cm above the crystal, the contribution to the counting rate from EB is minimum when the stopper is placed 25 cm above the crystal, and that this minimum value is about 2 ~o of the IB detected. The experimental arrangement was set up according to these calculations. The source and detector were isolated from any structure to a minimum distance of 1.5 m to reduce the EB contribution from the surroundings. With
INTERNAL BREMSSTRAHLUNG
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this arrangement the EB contribution of the recorded spectrum is principally from betas stopped in the source material and scattered in the source backing. To get an estimate of the EB contribution from the beta stopper, the spectrum was recorded using beta stoppers of tin, copper, aluminium and lucite. Extrapolation of the observed distribution to Z ---- 0 will eliminate the EB contribution from the beta stopper. Comparison of the integrated counts in the distribution for zero Z and for lucite beta stoppers indicates that the EB contribution ,----SOURCE
''
--(~ STOPPER r L U C I T E DISC LEAD COLLIMATER
- - - A L CYLINDER
'
/
__J Fig. 1. Scheme of the e x p e r i m e n t a l a r r a n g e m e n t for the m e a s u r e m e n t of IB.
from the latter is about 3 % of the recorded spectrum. This is in reasonable agreement with the estimated value of 2 % for the geometry of our experimental arrangement. To check the production of EB in the source material and its backing, a plastic film of surface density 2 mg/cm * was placed immediately above the source and attempts were made to detect an increase in the counting rate. This check was made at several energies. In another test the source was turned upside down so that the backing was above the source and measurements repeated. If the EB from the source backing are emitted with appreciable preference in the forward direction and in significant numbers, this should reduce the counting rate. Both these tests indicated that the change in counting rate was not detectable. Hence it was concluded t h a t the EB contribution from the source and backing was negligible.
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The linearity and long term stability of the amplifier and analyzer were examined carefully using a precision pulser and were found to be satisfactory. The spectrometer was calibrated using the monoenergetic gamma rays from Cr51 (323 keV), CsI~ (661 keV), Nb 95 (764 keV), Na 2~ (511, 1277 keV) and Zn 6s (1114 keV); and a careful check was maintained on the energy calibration. The p3, sources were prepared from solutions obtained from Oak Ridge National Laboratories. They were received as H~PO 4 in HC1 solution. Two different specific activities, one carrier-free and the other 0.025 mg/mCur was used. Sources of ygo were prepared from carrier-free material supplied by Abbott Laboratories at YC13 solution. Sources were prepared by evaporating these solutions slowly on a thin plastic film of 1.0 mg/cm * density mounted on a lucite ring of 10.0 cm outside diameter which was thus well outside of the collimation cone. Care was exercised to obtain a uniform spread and the extent of the source was strictly limited to a circular area of 5 mm diameter with the help of a small lucite ring. The data reported here have been obtained from three different sources for each isotope. The approximate beta strength of P~* sources used is (A) 2.1. (A') 3.9 and (B) 6.2 mCur while that of y~0 source is (A) 2.3, (A') 4.6, and (B), 7.2 mCur. To examine the purity of p32 and ygo small sources were prepared on LC600 films (100 mg/cm *) for the examination of the beta spectrum with the help of an anthracene crystal and a double focussing magnetic spectrometer t). No beta active impurity was detected. In these tests no conversion electrons were observed, indicating the absence of monoenergetic gamma rays. The smoothness of the experimental IB spectrum itself is a good check for the absence of any monoenergetic gammas-rays. As a further check for the purity, the sources were left for several half-lives and their beta and gamma activity re-examined. In the y~o sources careful checks of this type extended over a period of 17 half-lives indicated that Sr 9° contamination, if present, is less than 1 part in 107. Background was recorded before and after each run and subtracted from the observed distribution. Correction was made for absorption in the lucite beta stopper and in the 0.13 mm A1 foil covering the crystal. Data were also corrected for decay during the time measurements were performed. This correction was significant in the case of ygo due to its relatively short life but was entirely negligible for p32. Sufficient counts were recorded to insure a minimum counting statistics of 1.6 % even at the high energy end of the spectrum. By repeating the measurements several times and employing crystals of two different sizes (3.8 cm diameter, 2 cm long and 7 cm diameter, 7 cm long) the reproducibility and internal consistency of the data were checked. * We are indebted
t o D r . L . S. A u g u s t f o r h e l p i n t h e m a g n e t i c
spectrometer
measurement.
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3. Comparison with Theory The scintillation spectrometer enables one to determine the pulse-height distribution. In order to make a comparison with theory it is necessary either to convert the theoretical photon distribution into pulse-height distribution for a given crystal and geometry or on the other hand to derive the photon distribution from the observed pulse-height distribution. In the former method the distribution to be converted is known throughout the energy range and an extrapolation is not necessary. If the calculated pulse-height distribution derived from a particular theoretical photon spectrum is found to agree with the observations, one immediately knows the photon distribution detected in the experiment. However, if the calculated and observed pulse-height distributions do not agree, the observed photon distributions can be derived only from the percentage difference. Frequently this is not very satisfactory. A comparison between the results of different experiments can be more easily made if the observed pulse-height distribution is converted into photon distribution. We have used the method described in (GP) for the conversion of theoretical photon spectrum into pulse-height distribution. To convert the observed pulse-height distribution into photon distribution the following procedure was adopted. The observed pulse-height distribution was first extrapolated to the end point. Starting at the high energy end of the spectrum the energy scale was divided into intervals of 30 keV. It was assumed that the counts represented b y the area in the first interval were due to photons of energy equal to the mean energy of the interval detected in the photopeak. This assumption is justified as there are no photons present of energy greater than the end point of the spectrum. From the known values of total and peak efficiencies of the crystal for the geometry used, the number of counts arising from these photons due to Compton processes with incomplete energy absorption can be calculated with the approximation that this part of the crystal response curve has a uniform height from zero to the maximum energy for a Compton recoil electron. This height can be adjusted to include an area under the plateau equal to the number of calculated pulses. Wherever the rectangles overlapped the next interval the total common area was subtracted from the area of the interval and the remainder was taken to represent the number of counts in the photopeak due to photons of average energy of this interval. B y continuing this process the number of photons detected in the photopeak at the average energy of each interval is obtained. From this the photon distribution can be immediately deduced using the known value of the efficiency for detection in the photopeak. The resulting photon distribution was found to be quite insensitive to the extrapolation used towards the high energy end of the spectrum. This is
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expected as the number of photons in the IB spectrum falls off very steeply towards the end point. Changing the width of the interval from 30 keV to 50 keV in the above calculations did not change noticeably the resulting photon distribution. We have used the values of total and peak efficiency measured and calculated b y Bell zs). In these determinations the total absorption cross section for NaI is measured directly b y an anticoincidence arrangement. These measured values are then used to calculate the probability of absorption for a
oo
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o
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=
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I
I
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400 ENERGY
I 500 (keV)
I
I
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Fig. 2. Pulse-height spectrum of CsZS~(661 keV) gamma ray.
given set up, yielding the total efficiency. In a separate experiment the pulseheight spectrum obtained with the same set up is examined for several monochromatic gamma rays and the ratio of the pulses detected in the peak and the Compton plateau is determined and used to calculate the peak efficiency. This empirical method we believe is much superior and involves less uncertainty than calculating the efficiency from photoelectric and Compton cross sections. In calculations of this type one has to compute the probability of detection in the peak resulting from double, triple, etc., Compton processes. The geometrical conditions under which Bell's values of efficiencies are determined are the same as in our experiment except for the presence of the lead collimator. However, the collimator is not expected to affect these values. The only change it will produce in the pulse height spectrum of a monochromatic gamma ray
INTERNAL BREMSSTRAHLUNG
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is in the reduction of the backscatter. To check this further we have recorded the pulse-height spectra resulting from the monochromatic gamma rays from Cr sl (323 keV), Cs 137 (661 keV) and Zn 6~ (1116 keY) and determined the ratio of the pulses detected in the peak and the total number of pulses recorded. Comparison with Bell's values indicated an agreement within 3 °/o, which is satisfactory. The uncertainty in the values of efficiency according to Bell is 5 %. These spectra were also used to check the contribution to the counting rate from backscatter. The contribution was found to be negligible as expected. With the collimator the backscatter is primarily due to the photomultiplier itself. The pulse height spectrum of Cs137gamma ray as detected by our arrangement is given in fig. 2. To investigate the effect of the window width and the resolution of the spectrometer, experiments were performed with window widths of 5 and 15 keV and crystals of 8.5 and 13 % resolution. Comparison of these results indicated that the corrections due to these effects were much smaller than the uncertainty in the efficiencies, and were therefore negligible.
4. E x p e r i m e n t a l R e s u l t s and D i s c u s s i o n 4.1. T H E
pa2 I B S P E C T R U M
In fig. 3 we have shown the pulse-height distribution resulting from the calculated allowed IB spectrum of p3~ according to KUB theory, along with the experimental results. The observed and calculated distributions are normalized for 200 counts per sec at 153 keV per window width. The experimental points lie above the KUB spectrum, the difference increasing slowly with the energy. At 500 keV the difference is 4 % of the KUB value while at 1200 keV it is of the order of 15 %. The number of photons in the IB spectrum decreases very rapidly towards the high energy end of the spectrum necessitating the use of strong sources for the extension of measurements in this range. There is a possibility that the sum pulses resulting from the finite resolving time of electronics might distort the measured distribution at the high energy end where the number of real counts is very low. To check this we have measured the pulse-height distribution arising from two sources (A and B) differing in strength by a factor of 3, each with resolving times of 1 and 2 sec. Among the above four combinations one expects the sum pulse effect to be minimum in the case of the weak source (A) with 1 sec resolving time and maximum for the strong source (B) with 2 sec resolving time. Examination of the data in fig. 3 indicates that the four observed distributions do not differ noticeably from each other, hence, we conclude that the change in shape due to sum pulses is beyond the limit of detection. This is further supported by numerical estimates. If the number of true counts in the distribution at energy E 1 and E 2 is n 1 and n2, respectively, and the resolving time of the electronics is 3,
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2nln~z spurious pulses will be added to the distribution at an energy (El+E2). To calculate the sum pulse contribution at a given energy one has to add such contributions from all possible combinations of energies. This procedure will place an upper limit to the sum pulse contribution. The actual contribution will be somewhat less because of the finite rise time of the pulses. Using this procedure we have estimated that the deviation between the two extreme cases due to this effect is about 2 % at 1000 keV, well within the accuracy of the lO 3
~ ~ l
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to z
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8 10"1
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ENERGY (keY}
Fig. 3. P u l s e h e i g h t d i s t r i b u t i o n of P82IB. S t a n d a r d error f r o m c o u n t i n g s t a t i s t i c s is s m a l l e r t h a n t h e size of t h e points. T h e solid c u r v e is t h e d i s t r i b u t i o n for allowed b e t a t r a n s i t i o n according to K U B t h e o r y . T h e o b s e r v e d a n d calculated distrilJutions are n o r m a l i z e d to 200 c o u n t s a t 153 keV.
experiment. Comparison of the observed distribution resulting from different runs indicates that the data are reproducible within 2 %. The statistical error is much smaller than the size of the points. The uncertainty in the value of efficiency used is less than 5 %. From the error in reproducibility and the uncertainty in the efficiency we conclude that the present results are correct to within about 6 %. In fig. 4 we have plotted the photon distribution derived from the observed pulse-height distribution, the K U B spectrum and experimental results from (GP). Spectra are normalized at 153 keV for comparison. The results reported
INTERNAL BR]~MSSTRAHLUNG
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b y (GP) were obtained using a 3.8 cm diameter 2 cm long crystal, hence the correction factors are somewhat larger compared to the present experiment. The principal uncertainty in their experiment was in the values of efficiency which was of the order of 10 %. The present experiment is more reliable because of better values of efficiency available for the larger crystal and better counting statistics. In view of the accuracy of 10 ~o claimed b y them and the accuracy of 6 % for the present experiment the discrepancy between their data and the present data is not statistically significant. 900 f
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ENERGY (keY) F i g . 4. ps~ i n t e r n a l b r e m s s t r a h l u n g s p e c t r u m . T h e o b s e r v e d p h o t o n s p e c t r u m is a n a v e r a g e o f several measurements. The solid curve represents the spectrum according to KUB theory for a l l o w e d b e t a t r a n s i t i o n . T h e d a s h e d c u r v e is t h e C o u l o m b c o r r e c t e d s p e c t r u m a c c o r d i n g t o L e w i s and Ford. The results of Goodrich and Payne are also indicated. All spectra are normalized to 950 p h o t o n s p e r k e V a t 153 k e V .
In the same figure we have plotted the Coulomb corrected p3~ IB spectrum according to recent calculations of Lewis and Ford 11). These calculations indicate that at high energies the number of IB photons is increased when the Coulomb field of the nucleus is introduced as an additional perturbation in the K U B theory. For p32 at 1022 keV this excess is about 15 ~ and is about 15 and is about the same as the one observed in the present experiment. The very good agreement between our results and these calculations indicates that a
33 °
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first order Coulomb correction to KUB theory is adequate to describe tile Pa~ IB spectrum. Hence the nuclear radiation due to detour transitions from this isotope is negligible. Concerning the disagreement of these results with those of some of the previous experiments, we notice that the Lid~n and Starfelt measurements were made with a small crystal (1.5 cm × 1.5 cm) mounted on a 5 cm photomultiplier, and that their collimator was cylindrical, allowing gamma rays to strike the face of the multiplier. Both the larger amount of backscatter and the larger proportion of Compton pulses which result, make the corrections for the photon spectrum much larger than those of the present experiment. By aligning carefully the source, the crystal and the conical hole in the collimator, we have restricted the width of the beam to the size of the crystal. This minimizes scattering from the collimator and photomultiplier. An examination of fig. 2 confirms the absence of appreciable backscatter. The Langevin-Joliot results on the other had give a spectrum with a slope which is much steeper with relatively less photons at the high energies than is the case with the results reported here. Very recently Persson and Johansson 9) have reported a new determination of the pa~ IB spectrum. It was measured with an arrangement different from the usual one, using coincidences between the beta particle and the IB photon pulses. Only the IB pulses in coincidence with a beta ray pulse corresponding to a beta ray energy greater than 150 keV were recorded. Their results disagree with the results of Lid6n and Starfelt and Mrs. Langevin-Joliot and are in agreement with our experiment. 4.2. THE y*o IB SPECTRUM Preliminary results on ygo were reported previously 19). More data were obtained later which are included in this report. The distribution of yg0 IB is indicated in fig. 5. The results are the average of several measurements. The observed spectrum is less steep than the KUB spectrum for first forbidden transition with tensor interaction of AJ ---- 2, yes. The spectra are normalized at 153 keV. The experimental points start deviating appreciably around 300 keV. At 500, 1000, 1500 and 1900 keV, respectively, the deviation is 25, 55, 75 and 80 % of the KUB value. The spectrum modified by Lewis and Ford 11) taking the first order Coulomb correction into account, is also indicated in the figure for comparison. They claim that their method of calculation takes care of the Coulomb effect within 2 or 3 % for the case of yg0. It is clear from the figure that the contribution of the Coulomb effect is not sufficient to bring the theoretical spectrum into agreement with the observed spectrum. To explain this discrepancy Ford and Lewis 16) introduce the effect of detour transitions in which the nucleus first emits a photon and goes into a virtual excited state, then beta decays or vice versa. They find that the detour
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effect is significant only for forbidden transitions. The result of these calculations, indicated in the figure by the short dashed line, is in approximate agreement with the experimental results. We can get an upper limit for the possible number of nuclear gamma rays at 1750 keV from the 0 + level of Zr 9° as 2.6× 10-8 photons per beta particle, which lends support to the spin (0) and parity ( + ) assignment to the first excited state of Zr 9° by Ford 20). i05
1200
1300
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~ I04
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Fig. 5. y00 i n t e r n a l b r e m s s t r a h l u n g s p e c t r u m . T h e circles r e p r e s e n t t h e a v e r a g e o b s e r v e d distrib u t i o n . T h e s t a n d a r d d e v i a t i o n f r o m c o u n t i n g s t a t i s t i c s is 1.6 ~o; s m a l l e r t h a n t h e size of t h e circles. Solid c u r v e r e p r e s e n t s t h e s p e c t r u m according to K U B t h e o r y for first f o r b i d d e n b e t a t r a n s i tion. L o n g d a s h e d c u r v e is t h e C o u l o m b corrected s p e c t r u m a c c o r d i n g to Lewis a n d Ford. S h o r t d a s h e d c u r v e is t h e s p e c t r u m i n c l u d i n g t h e d e t o u r t r a n s i t i o n c a l c u l a t e d b y L e w i s a n d Ford. All s p e c t r a h a v e b e e n n o r m a l i z e d to 104 p h o t o n s p e r k e V a t 153 keV.
In conclusion we would like to remark that further investigation of IB from high Z nuclei and from forbidden beta transitions is desirable, to check the validity of the Coulomb effect calculation and the contribution of the detour effect in forbidden beta transitions. We are indebted to Professor J. S. Levinger for m a n y valuable discussions. One of us (M. A. H.) would like to thank Dr. B. Kurgunoglu and Dr. H. S. Robertson for m a n y useful suggestions.
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M. A. H A K E E M A N D M. GOODRICH
References 1) C. S. Wu, in Beta- and gamma- ray spectroscopy, ed. by K. Siegbahn (North-Holland Publ. Co., Amsterdam, 1955) 2) J. K. Knipp and G. E. Uhlenbeck, Physics 3 (1936) 425 3) F. Bloch, Phys. Rev. 50 (1936) 272 4) C. S. Wang Chang and D. L. Falkoff, Phys. Rev. 76 (1949) 76 5) L. Madansky, F. Lipps, P. Bolgiano and T. H. Berlin, Phys. Rev. 84 (1951) 596 6) M. Goodrich and W. B. Payne, Phys. Rev. 94 (1954) 405 7) K. Liden and N. Starfelt, Phys. Rev. 97 (1955) 419 8) H. Langevin-Joliot, thesis, University of Paris (1955) 9) B. Persson and $ven A. E. Johansson, Nuclear Physics 12 (1959) 432 10 S. B. Nilsson, Ark. Fys. 10 (1956) 467 11 R. R. Lewis and G. W. Ford, Phys. Rev. 107 (1957) 756 12 L. Spruch and W. Gold, P~ays. Rev. 1 1 3 (1959) 1060 13 C . Longmire, Phys. Rev. 75 (1949) 15 14 J. I-Iorowitz, J. Phys. et Radium 13 (1952) 429 15 R. R. Lewis and G, W. Ford, private communication (1956) 16 D. E. Johnson, R. G. Johnson and L. M. Langer, Phys. Rev. 98 (1955) 1517 17 W. H. Jordan and P. R. Bell, Nucleonics 5 (1949) 30; W, H. Jordan, Ann. Rev. Nuclear Sci. 1 (1952) 207 18 P. R. Bell and Oak Ridge Mathematical Panel, private communication (1954) 19 M. A. Hakeem and M. Goodrich, Bull. Am. Phys. Soc. 1 (1956) 264 20 K. W. Ford, Phys. Rev. 98 (1955) 1516
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INTERNAL B R E M S S T R A H L U N G FROM ps2 AND ygo M. A. H A K E E M t A N D M A X G O O D R I C H
Department o/ Physics and Astronomy, Louisiana State University Received 2 J u n e 1961 T h e i n t e r n a l b r e m s s t r a h l u n g s p e c t r a of t h e allowed b e t a e m i t t e r ]?s2 a n d t h e first forb i d d e n b e t a e m i t t e r yg0 h a v e been s t u d i e d w i t h a scintillation s p e c t r o m e t e r a n d c o m p a r e d w i t h available calculations. T h e e x p e r i m e n t a l s p e c t r u m of ]?s2 does n o t agree e x a c t l y w i t h K n i p p , U h l e n b e c k a n d Bloch's t h e o r y for allowed b e t a t r a n s i t i o n s . T h e d e v i a t i o n s are n o t very large b u t t h e y are significant a n d c a n be explained v e r y well b y t h e C o u l o m b corrections proposed b y Lewis a n d Ford. T h e observed s p e c t r u m of yg0 is in considerable d i s a g r e e m e n t w i t h t h e e x t e n s i o n of K n i p p , U h l e n b e c k a n d B l o c h ' s t h e o r y for first f o r b i d d e n b e t a t r a n s i t i o n s w i t h t e n s o r i n t e r a c t i o n s . T h e C o u l o m b correction in this case is q u i t e i n a d e q u a t e to a c c o u n t for t h e deviation. T h e o b s e r v e d p h o t o n excess m a y be arising f r o m d e t o u r t r a n s i t i o n s ; a n a s s u m p t i o n s u p p o r t e d b y calculations of Lewis a n d Ford.
Abstract:
1. Introduction A number of measurements on the internal bremsstrahlung (IB) accompanying beta decay have been reported 1)**. These measurements are usually compared with the theory originally given by Knipp and Uhlenbeck 2) and by Bloch 3) for allowed beta emitters and further developed by Chang and Falkoff 4) and Madansky et al. 5). The shape of the IB spectrum according to these calculations (generally referred to as KUB Theory) depends only slightly on the nature of the interaction and the degree of forbiddenness of the beta transition. However, the differences are sufficient to be detectable under favourable circumstances by a careful measurement utilizing a scintillation spectrometer. Most of the early work on the energy distribution and intensity covers only the low energy end of the spectrum and indicates agreement within the accuracy of the experiments with the theory. Goodrich and Payne 6)*** have extended the measurements on the energy distribution of IB from p32 up to .q00 keV. They found that the shape of the experimental spectrum throughout the measured region agreed well with the computed spectrum for an allowed beta transition and disagreed slightly but significantly with that for a forbidden beta transition. Subsequently reported work of Lid~n and Starfelt ~) on the IB spectrum of p32 in this energy range does not agree with these results. They find that the measured spectrum is less steep * ]?resent address: t h e U n i v e r s i t y of Miami, Coral Gables, Florida tf F o r a review of early e x p e r i m e n t s see ref.~). tt* T h i s p a p e r will be referred to as (GP). 322
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than the K U B spectrum. If these spectra are normalized at the low energy end, the experimental points lie above the theoretical ones at high energies. The deviation increases with energy and is about 70 % at 1 MeV. Mrs. LangevinJoliot s) has also reported measurements on p39 which disagree with both those of GP and of Lid6n and Starfelt. According to these measurements the number of photons observed at 153 keV is 150 % in excess of the theory while at 1 MeV the excess is 85 °/o, indicating that the spectrum falls off much more rapidly than the K U B spectrum. Recently Persson and Johannsson 9) have repeated measurements on p~9 in a coincidence experiment. Due to low counting rates the statistical error is very large. However, their results indicate general agreement with K U B theory. In the K U B calculations the effect of nuclear charge (usually called Coulomb effect) has been entirely neglected. A correction for this approximation has been proposed recently b y Nilsson 10), Lewis and Ford 11) and Spruch and Gold 19). In the case of Pa~ this correction is not very large. It increases the total number of photons b y about 5 % in the energy range 500--1000 keV, hence very accurate data are necessary to check these calculations. Another source of contribution to the continuous gamma radiation which has been discussed in the literature 13,14) arises from tile so-called detour transitions. The usual process of interest here is the one in which the parent nucleus undergoes a beta transition producing the daughter nucleus in .its ground state. The electron reaches its final state b y emitting a photon. This process can be represented b y the following expression: z NA -+ (z+a)Na+v+e * --+ ( z + l ) N a + v + e + y . In the detour transition the nucleus first emits a photon going to a virtual excited state~ then beta decays, or vice versa. We represent these transitions b y the following expression: zNA 7 zNA*+T "~ "~ tz+l)N ~ -}-e*+v 7 (z+l)Na+v+e+Y" In general the radiation arising from this nuclear effect will be weak compared to the IB radiation, since the nuclear dipole moment is small. This nuclear effect could certainly be present, but at least in allowed beta decay its contribution is expected to be negligible. For forbidden transitions, calculations of Lewis and Ford 15) indicate that the contribution is significant. The present investigation was undertaken primarily to obtain an improved measure of the IB spectral distribution against which the theoretical calculations including the Coulomb and detour effects might be compared. In view of the known low-energy-end agreement of the strength and distribution of the experimental spectra with K U B theory, it was considered desirable to design the experiment primarily to check the shape of the spectrum. This can be
3~4
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done more efficiently and precisely if the spectra to be compared are normalized at the low-energy end where the agreement is established. This eliminates the uncertainty in the determination of the absolute beta strength of the source. To obtain a reasonable counting rate towards the end point rather strong sources were used making a good determination of the strength of the beta source fairly difficult. The geometrical arrangement for the experiment has been somewhat improved and a large crystal utilized, enhancing the accuracy and reliability of the results by increasing the fraction of the photons totally absorbed in the crystal. It was also considered desirable to determine the spectral shape of IB, covering energies close to the end point from a first-forbidden beta emitter. The nucleus ygo was selected for this purpose because it has a high end point (2.26 MeV), short life (65 h) permitting high specific activity and is a pure beta emitter. It is classed as a unique first-forbidden transition (special case of selections rule AJ = 2, yes). Very precise measurements on the beta spectrum of ygo by Johnson et al. 16) have confirmed that between 0.5 MeV and the end point at 2.26 MeV no other group of beta rays is present. The results of the present experiment as well as those of previously reported measurements confirm the absence of monochromatic gamma rays. The internal conversion line and the positons arising from the 1.75 MeV transition of Zr 9° are much too weak to affect our measurements.
2. Experimental Details The spectrum was determined with a single-channel Jordan and Bell 1~) type scintillation spectrometer using a 7 cm long by 7 cm diameter cylindrical NaI(Th) crystal mounted directly on a DuMont 6363 photomultiplier. The source and detector geometry indicated in fig. 1 is basically the same as the one described in (GP). Due to the relatively low intensity of the IB, necessary precautions were taken to minimize the production of external bremsstrahlung (EB) in the source and the surrounding material, and the detector was adequately shielded to stop any scattered electrons and photons from striking the crystal. For a given source-to-crystal distance the total contribution from the EB produced in the beta stopper depends on its atomic number and its location. As the electrons are stopped completely in the low-Z absorber, the EB produced will be almost isotropic in the solid angle subtended by the beta stopper at the crystal. Under this assumption it can be shown that, for a lucite beta stopper and a source of 5 mm diameter located 30 cm above the crystal, the contribution to the counting rate from EB is minimum when the stopper is placed 25 cm above the crystal, and that this minimum value is about 2 ~o of the IB detected. The experimental arrangement was set up according to these calculations. The source and detector were isolated from any structure to a minimum distance of 1.5 m to reduce the EB contribution from the surroundings. With
INTERNAL BREMSSTRAHLUNG
~2~
this arrangement the EB contribution of the recorded spectrum is principally from betas stopped in the source material and scattered in the source backing. To get an estimate of the EB contribution from the beta stopper, the spectrum was recorded using beta stoppers of tin, copper, aluminium and lucite. Extrapolation of the observed distribution to Z ---- 0 will eliminate the EB contribution from the beta stopper. Comparison of the integrated counts in the distribution for zero Z and for lucite beta stoppers indicates that the EB contribution ,----SOURCE
''
--(~ STOPPER r L U C I T E DISC LEAD COLLIMATER
- - - A L CYLINDER
'
/
__J Fig. 1. Scheme of the e x p e r i m e n t a l a r r a n g e m e n t for the m e a s u r e m e n t of IB.
from the latter is about 3 % of the recorded spectrum. This is in reasonable agreement with the estimated value of 2 % for the geometry of our experimental arrangement. To check the production of EB in the source material and its backing, a plastic film of surface density 2 mg/cm * was placed immediately above the source and attempts were made to detect an increase in the counting rate. This check was made at several energies. In another test the source was turned upside down so that the backing was above the source and measurements repeated. If the EB from the source backing are emitted with appreciable preference in the forward direction and in significant numbers, this should reduce the counting rate. Both these tests indicated that the change in counting rate was not detectable. Hence it was concluded t h a t the EB contribution from the source and backing was negligible.
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M. A. HAKEEM AND M. GOODRICH
The linearity and long term stability of the amplifier and analyzer were examined carefully using a precision pulser and were found to be satisfactory. The spectrometer was calibrated using the monoenergetic gamma rays from Cr51 (323 keV), CsI~ (661 keV), Nb 95 (764 keV), Na 2~ (511, 1277 keV) and Zn 6s (1114 keV); and a careful check was maintained on the energy calibration. The p3, sources were prepared from solutions obtained from Oak Ridge National Laboratories. They were received as H~PO 4 in HC1 solution. Two different specific activities, one carrier-free and the other 0.025 mg/mCur was used. Sources of ygo were prepared from carrier-free material supplied by Abbott Laboratories at YC13 solution. Sources were prepared by evaporating these solutions slowly on a thin plastic film of 1.0 mg/cm * density mounted on a lucite ring of 10.0 cm outside diameter which was thus well outside of the collimation cone. Care was exercised to obtain a uniform spread and the extent of the source was strictly limited to a circular area of 5 mm diameter with the help of a small lucite ring. The data reported here have been obtained from three different sources for each isotope. The approximate beta strength of P~* sources used is (A) 2.1. (A') 3.9 and (B) 6.2 mCur while that of y~0 source is (A) 2.3, (A') 4.6, and (B), 7.2 mCur. To examine the purity of p32 and ygo small sources were prepared on LC600 films (100 mg/cm *) for the examination of the beta spectrum with the help of an anthracene crystal and a double focussing magnetic spectrometer t). No beta active impurity was detected. In these tests no conversion electrons were observed, indicating the absence of monoenergetic gamma rays. The smoothness of the experimental IB spectrum itself is a good check for the absence of any monoenergetic gammas-rays. As a further check for the purity, the sources were left for several half-lives and their beta and gamma activity re-examined. In the y~o sources careful checks of this type extended over a period of 17 half-lives indicated that Sr 9° contamination, if present, is less than 1 part in 107. Background was recorded before and after each run and subtracted from the observed distribution. Correction was made for absorption in the lucite beta stopper and in the 0.13 mm A1 foil covering the crystal. Data were also corrected for decay during the time measurements were performed. This correction was significant in the case of ygo due to its relatively short life but was entirely negligible for p32. Sufficient counts were recorded to insure a minimum counting statistics of 1.6 % even at the high energy end of the spectrum. By repeating the measurements several times and employing crystals of two different sizes (3.8 cm diameter, 2 cm long and 7 cm diameter, 7 cm long) the reproducibility and internal consistency of the data were checked. * We are indebted
t o D r . L . S. A u g u s t f o r h e l p i n t h e m a g n e t i c
spectrometer
measurement.
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3. Comparison with Theory The scintillation spectrometer enables one to determine the pulse-height distribution. In order to make a comparison with theory it is necessary either to convert the theoretical photon distribution into pulse-height distribution for a given crystal and geometry or on the other hand to derive the photon distribution from the observed pulse-height distribution. In the former method the distribution to be converted is known throughout the energy range and an extrapolation is not necessary. If the calculated pulse-height distribution derived from a particular theoretical photon spectrum is found to agree with the observations, one immediately knows the photon distribution detected in the experiment. However, if the calculated and observed pulse-height distributions do not agree, the observed photon distributions can be derived only from the percentage difference. Frequently this is not very satisfactory. A comparison between the results of different experiments can be more easily made if the observed pulse-height distribution is converted into photon distribution. We have used the method described in (GP) for the conversion of theoretical photon spectrum into pulse-height distribution. To convert the observed pulse-height distribution into photon distribution the following procedure was adopted. The observed pulse-height distribution was first extrapolated to the end point. Starting at the high energy end of the spectrum the energy scale was divided into intervals of 30 keV. It was assumed that the counts represented b y the area in the first interval were due to photons of energy equal to the mean energy of the interval detected in the photopeak. This assumption is justified as there are no photons present of energy greater than the end point of the spectrum. From the known values of total and peak efficiencies of the crystal for the geometry used, the number of counts arising from these photons due to Compton processes with incomplete energy absorption can be calculated with the approximation that this part of the crystal response curve has a uniform height from zero to the maximum energy for a Compton recoil electron. This height can be adjusted to include an area under the plateau equal to the number of calculated pulses. Wherever the rectangles overlapped the next interval the total common area was subtracted from the area of the interval and the remainder was taken to represent the number of counts in the photopeak due to photons of average energy of this interval. B y continuing this process the number of photons detected in the photopeak at the average energy of each interval is obtained. From this the photon distribution can be immediately deduced using the known value of the efficiency for detection in the photopeak. The resulting photon distribution was found to be quite insensitive to the extrapolation used towards the high energy end of the spectrum. This is
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expected as the number of photons in the IB spectrum falls off very steeply towards the end point. Changing the width of the interval from 30 keV to 50 keV in the above calculations did not change noticeably the resulting photon distribution. We have used the values of total and peak efficiency measured and calculated b y Bell zs). In these determinations the total absorption cross section for NaI is measured directly b y an anticoincidence arrangement. These measured values are then used to calculate the probability of absorption for a
oo
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102
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•
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t
i
I
o
o •
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=
0
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I
I
I
I
100
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300
400 ENERGY
I 500 (keV)
I
I
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Fig. 2. Pulse-height spectrum of CsZS~(661 keV) gamma ray.
given set up, yielding the total efficiency. In a separate experiment the pulseheight spectrum obtained with the same set up is examined for several monochromatic gamma rays and the ratio of the pulses detected in the peak and the Compton plateau is determined and used to calculate the peak efficiency. This empirical method we believe is much superior and involves less uncertainty than calculating the efficiency from photoelectric and Compton cross sections. In calculations of this type one has to compute the probability of detection in the peak resulting from double, triple, etc., Compton processes. The geometrical conditions under which Bell's values of efficiencies are determined are the same as in our experiment except for the presence of the lead collimator. However, the collimator is not expected to affect these values. The only change it will produce in the pulse height spectrum of a monochromatic gamma ray
INTERNAL BREMSSTRAHLUNG
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is in the reduction of the backscatter. To check this further we have recorded the pulse-height spectra resulting from the monochromatic gamma rays from Cr sl (323 keV), Cs 137 (661 keV) and Zn 6~ (1116 keY) and determined the ratio of the pulses detected in the peak and the total number of pulses recorded. Comparison with Bell's values indicated an agreement within 3 °/o, which is satisfactory. The uncertainty in the values of efficiency according to Bell is 5 %. These spectra were also used to check the contribution to the counting rate from backscatter. The contribution was found to be negligible as expected. With the collimator the backscatter is primarily due to the photomultiplier itself. The pulse height spectrum of Cs137gamma ray as detected by our arrangement is given in fig. 2. To investigate the effect of the window width and the resolution of the spectrometer, experiments were performed with window widths of 5 and 15 keV and crystals of 8.5 and 13 % resolution. Comparison of these results indicated that the corrections due to these effects were much smaller than the uncertainty in the efficiencies, and were therefore negligible.
4. E x p e r i m e n t a l R e s u l t s and D i s c u s s i o n 4.1. T H E
pa2 I B S P E C T R U M
In fig. 3 we have shown the pulse-height distribution resulting from the calculated allowed IB spectrum of p3~ according to KUB theory, along with the experimental results. The observed and calculated distributions are normalized for 200 counts per sec at 153 keV per window width. The experimental points lie above the KUB spectrum, the difference increasing slowly with the energy. At 500 keV the difference is 4 % of the KUB value while at 1200 keV it is of the order of 15 %. The number of photons in the IB spectrum decreases very rapidly towards the high energy end of the spectrum necessitating the use of strong sources for the extension of measurements in this range. There is a possibility that the sum pulses resulting from the finite resolving time of electronics might distort the measured distribution at the high energy end where the number of real counts is very low. To check this we have measured the pulse-height distribution arising from two sources (A and B) differing in strength by a factor of 3, each with resolving times of 1 and 2 sec. Among the above four combinations one expects the sum pulse effect to be minimum in the case of the weak source (A) with 1 sec resolving time and maximum for the strong source (B) with 2 sec resolving time. Examination of the data in fig. 3 indicates that the four observed distributions do not differ noticeably from each other, hence, we conclude that the change in shape due to sum pulses is beyond the limit of detection. This is further supported by numerical estimates. If the number of true counts in the distribution at energy E 1 and E 2 is n 1 and n2, respectively, and the resolving time of the electronics is 3,
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2nln~z spurious pulses will be added to the distribution at an energy (El+E2). To calculate the sum pulse contribution at a given energy one has to add such contributions from all possible combinations of energies. This procedure will place an upper limit to the sum pulse contribution. The actual contribution will be somewhat less because of the finite rise time of the pulses. Using this procedure we have estimated that the deviation between the two extreme cases due to this effect is about 2 % at 1000 keV, well within the accuracy of the lO 3
~ ~ l
I
I
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J
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I
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to z
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8 10"1
100
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ENERGY (keY}
Fig. 3. P u l s e h e i g h t d i s t r i b u t i o n of P82IB. S t a n d a r d error f r o m c o u n t i n g s t a t i s t i c s is s m a l l e r t h a n t h e size of t h e points. T h e solid c u r v e is t h e d i s t r i b u t i o n for allowed b e t a t r a n s i t i o n according to K U B t h e o r y . T h e o b s e r v e d a n d calculated distrilJutions are n o r m a l i z e d to 200 c o u n t s a t 153 keV.
experiment. Comparison of the observed distribution resulting from different runs indicates that the data are reproducible within 2 %. The statistical error is much smaller than the size of the points. The uncertainty in the value of efficiency used is less than 5 %. From the error in reproducibility and the uncertainty in the efficiency we conclude that the present results are correct to within about 6 %. In fig. 4 we have plotted the photon distribution derived from the observed pulse-height distribution, the K U B spectrum and experimental results from (GP). Spectra are normalized at 153 keV for comparison. The results reported
INTERNAL BR]~MSSTRAHLUNG
331
b y (GP) were obtained using a 3.8 cm diameter 2 cm long crystal, hence the correction factors are somewhat larger compared to the present experiment. The principal uncertainty in their experiment was in the values of efficiency which was of the order of 10 %. The present experiment is more reliable because of better values of efficiency available for the larger crystal and better counting statistics. In view of the accuracy of 10 ~o claimed b y them and the accuracy of 6 % for the present experiment the discrepancy between their data and the present data is not statistically significant. 900 f
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I 700
I 800
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ENERGY (keY) F i g . 4. ps~ i n t e r n a l b r e m s s t r a h l u n g s p e c t r u m . T h e o b s e r v e d p h o t o n s p e c t r u m is a n a v e r a g e o f several measurements. The solid curve represents the spectrum according to KUB theory for a l l o w e d b e t a t r a n s i t i o n . T h e d a s h e d c u r v e is t h e C o u l o m b c o r r e c t e d s p e c t r u m a c c o r d i n g t o L e w i s and Ford. The results of Goodrich and Payne are also indicated. All spectra are normalized to 950 p h o t o n s p e r k e V a t 153 k e V .
In the same figure we have plotted the Coulomb corrected p3~ IB spectrum according to recent calculations of Lewis and Ford 11). These calculations indicate that at high energies the number of IB photons is increased when the Coulomb field of the nucleus is introduced as an additional perturbation in the K U B theory. For p32 at 1022 keV this excess is about 15 ~ and is about 15 and is about the same as the one observed in the present experiment. The very good agreement between our results and these calculations indicates that a
33 °
M.A.
HAKEEM
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M. G O O D R I C H
first order Coulomb correction to KUB theory is adequate to describe tile Pa~ IB spectrum. Hence the nuclear radiation due to detour transitions from this isotope is negligible. Concerning the disagreement of these results with those of some of the previous experiments, we notice that the Lid~n and Starfelt measurements were made with a small crystal (1.5 cm × 1.5 cm) mounted on a 5 cm photomultiplier, and that their collimator was cylindrical, allowing gamma rays to strike the face of the multiplier. Both the larger amount of backscatter and the larger proportion of Compton pulses which result, make the corrections for the photon spectrum much larger than those of the present experiment. By aligning carefully the source, the crystal and the conical hole in the collimator, we have restricted the width of the beam to the size of the crystal. This minimizes scattering from the collimator and photomultiplier. An examination of fig. 2 confirms the absence of appreciable backscatter. The Langevin-Joliot results on the other had give a spectrum with a slope which is much steeper with relatively less photons at the high energies than is the case with the results reported here. Very recently Persson and Johansson 9) have reported a new determination of the pa~ IB spectrum. It was measured with an arrangement different from the usual one, using coincidences between the beta particle and the IB photon pulses. Only the IB pulses in coincidence with a beta ray pulse corresponding to a beta ray energy greater than 150 keV were recorded. Their results disagree with the results of Lid6n and Starfelt and Mrs. Langevin-Joliot and are in agreement with our experiment. 4.2. THE y*o IB SPECTRUM Preliminary results on ygo were reported previously 19). More data were obtained later which are included in this report. The distribution of yg0 IB is indicated in fig. 5. The results are the average of several measurements. The observed spectrum is less steep than the KUB spectrum for first forbidden transition with tensor interaction of AJ ---- 2, yes. The spectra are normalized at 153 keV. The experimental points start deviating appreciably around 300 keV. At 500, 1000, 1500 and 1900 keV, respectively, the deviation is 25, 55, 75 and 80 % of the KUB value. The spectrum modified by Lewis and Ford 11) taking the first order Coulomb correction into account, is also indicated in the figure for comparison. They claim that their method of calculation takes care of the Coulomb effect within 2 or 3 % for the case of yg0. It is clear from the figure that the contribution of the Coulomb effect is not sufficient to bring the theoretical spectrum into agreement with the observed spectrum. To explain this discrepancy Ford and Lewis 16) introduce the effect of detour transitions in which the nucleus first emits a photon and goes into a virtual excited state, then beta decays or vice versa. They find that the detour
INTERNAL
333
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effect is significant only for forbidden transitions. The result of these calculations, indicated in the figure by the short dashed line, is in approximate agreement with the experimental results. We can get an upper limit for the possible number of nuclear gamma rays at 1750 keV from the 0 + level of Zr 9° as 2.6× 10-8 photons per beta particle, which lends support to the spin (0) and parity ( + ) assignment to the first excited state of Zr 9° by Ford 20). i05
1200
1300
1400
1500
1600
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~ I04
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,
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Fig. 5. y00 i n t e r n a l b r e m s s t r a h l u n g s p e c t r u m . T h e circles r e p r e s e n t t h e a v e r a g e o b s e r v e d distrib u t i o n . T h e s t a n d a r d d e v i a t i o n f r o m c o u n t i n g s t a t i s t i c s is 1.6 ~o; s m a l l e r t h a n t h e size of t h e circles. Solid c u r v e r e p r e s e n t s t h e s p e c t r u m according to K U B t h e o r y for first f o r b i d d e n b e t a t r a n s i tion. L o n g d a s h e d c u r v e is t h e C o u l o m b corrected s p e c t r u m a c c o r d i n g to Lewis a n d Ford. S h o r t d a s h e d c u r v e is t h e s p e c t r u m i n c l u d i n g t h e d e t o u r t r a n s i t i o n c a l c u l a t e d b y L e w i s a n d Ford. All s p e c t r a h a v e b e e n n o r m a l i z e d to 104 p h o t o n s p e r k e V a t 153 keV.
In conclusion we would like to remark that further investigation of IB from high Z nuclei and from forbidden beta transitions is desirable, to check the validity of the Coulomb effect calculation and the contribution of the detour effect in forbidden beta transitions. We are indebted to Professor J. S. Levinger for m a n y valuable discussions. One of us (M. A. H.) would like to thank Dr. B. Kurgunoglu and Dr. H. S. Robertson for m a n y useful suggestions.
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M. A. H A K E E M A N D M. GOODRICH
References 1) C. S. Wu, in Beta- and gamma- ray spectroscopy, ed. by K. Siegbahn (North-Holland Publ. Co., Amsterdam, 1955) 2) J. K. Knipp and G. E. Uhlenbeck, Physics 3 (1936) 425 3) F. Bloch, Phys. Rev. 50 (1936) 272 4) C. S. Wang Chang and D. L. Falkoff, Phys. Rev. 76 (1949) 76 5) L. Madansky, F. Lipps, P. Bolgiano and T. H. Berlin, Phys. Rev. 84 (1951) 596 6) M. Goodrich and W. B. Payne, Phys. Rev. 94 (1954) 405 7) K. Liden and N. Starfelt, Phys. Rev. 97 (1955) 419 8) H. Langevin-Joliot, thesis, University of Paris (1955) 9) B. Persson and $ven A. E. Johansson, Nuclear Physics 12 (1959) 432 10 S. B. Nilsson, Ark. Fys. 10 (1956) 467 11 R. R. Lewis and G. W. Ford, Phys. Rev. 107 (1957) 756 12 L. Spruch and W. Gold, P~ays. Rev. 1 1 3 (1959) 1060 13 C . Longmire, Phys. Rev. 75 (1949) 15 14 J. I-Iorowitz, J. Phys. et Radium 13 (1952) 429 15 R. R. Lewis and G, W. Ford, private communication (1956) 16 D. E. Johnson, R. G. Johnson and L. M. Langer, Phys. Rev. 98 (1955) 1517 17 W. H. Jordan and P. R. Bell, Nucleonics 5 (1949) 30; W, H. Jordan, Ann. Rev. Nuclear Sci. 1 (1952) 207 18 P. R. Bell and Oak Ridge Mathematical Panel, private communication (1954) 19 M. A. Hakeem and M. Goodrich, Bull. Am. Phys. Soc. 1 (1956) 264 20 K. W. Ford, Phys. Rev. 98 (1955) 1516