Internal conversion studies of the 2+ → 0+ transitions in some deformed even nuclei

Nuclear Physics 80 (1064) 305---816; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written p e r m l ~ o n from the publisher

INTERNAL CONVERSION STUDIES OF T H E 2+ ~ 0+ TRANSITIONS I N S O M E D E F O R M E D EVEN N U C L E I B. V. THOSAR, M. C. JOSHI, R. P. SHARMA and K. G. PRASAD Tara Institute of Fundamental Research, Bombay-5, India

Received 30 August 1963 Almtraet: The K conversion coefficients of 2+ --* 0+ transitions in some deformed even nuclei have been determined with the help of ft.7, X.7 and 7"7 coincidence measurements. All possible uncertainties in these measurements have been minimised and properly evaluated. The aK values for 2+ --* 0+ transitions in Erlu, Yb1Te, Hf 176, W~", Os~u, Osm and D f ~ are found to be 1.67, 1.3l, 1.10, 0.55, 0.42, 0.34 and 1.52, respectively.These values are in agreement with the theoretical ones within an experimental error of about 6 ~o. Large deviations of the order of 15 to 20 ~o as reported by earlier workers are not observed.

1. Iatroductioa Several investigations have previously been made on the internal conversion coefficients o f the low-lying E2 transitions in various deformed even nuclei. Some of the results have shown considerable deviations from the theoretical ones. McGowan and Stelson :) in their measurements of K-shell conversion coefficients for a number of E2 transitions have pointed out that the experimental values of 0~K are appreciably larger than those calculated by Sliv and Band 2). To account for these observed discrepancies Subba Rao s) has tried to correlate • effip/0~eowith the deformation parameter. Very recently Bernstein 4) has also attempted to establish a correlation of ~c.p/~tbco with N / Z for 2 + -~ 0 + transitions. Recent experimental evidence does not seem to support these correlations. Theoretically also it has not been possible to explain these deviations, as the finite size effect which has been taken into account by Sliv and Band 2) and also by Rose 5) and the dynamic or penetration effect suggested by Church and Weneser e) do not appreciably change the value of E2 conversion coefficients. In the present work a systematic study of the K-internal conversion coefficients for the E2 transitions, resulting from the decay of the first rotational state in deformed even nuclei, has been carried out in those nucleides for which large deviations from the theoretical values have been reported. The nuclei studied are D y ~e°, Er 16~, Yb tT°, H f ~Te, W ~s6, Os lse and Os ~ss. The internal conversion coefficients have been determined mainly by beta-gamma coincidence, g a m m a - g a m m a coincidence and X-ray g a m m a coincidence methods using high transmission intermediate image betaray spectrometer and a 512-channel analyser. In the beta-gamma coincidence method the uncertainties due to bremsstrahlung, C o m p t o n contribution and any trace of 305

306

a . v . TaOS~t ct a/.

possible K-capture active impurity are eliminated while those due to scattering will slightly increase due to the surrounding pole piece. But they have been taken into account by the use of a shadow shield. 2. M e m m e w m s 2.1. SOURCE PREPARATION

Radioactive sources of Tb 16°, Ho lee, Tm iT°, Lu 17e, Re ls6 and Re 18s have been produced by (n, 7) reaction on spec pure or enriched samples by irradiating them in Apsara reactor at Trombay in a flux of 2 x 10x2 neutrons/cm2. sec. The Tb Is°, Ho xee, Tm t7° and Re lss sources have been chemically purified after irradiation by ion exchange method. These sources were deposited on a Mylar film of thickness 500 pg/cm2. An insulin drop was used to get the uniformity in the source. The diameter of the source in all cases was 2 mm and the thickness was not more than 200 /~g/cm2. 2.2. EXPERIMENTAL A R R A N G E M E N T FOR SINGLES SPECTRUM

The gamma-ray detector consisted of a 2.5 cmx 3.8 cm diameter NaI(TI) crystal coupled to a selected Dumont 6292 type photomultiplier tube with a resolution of 8.5~ for the 662 keV gamma-ray of Cs xs7. The source was placed at a distance of 10 cm in a well defined geometry and lead collimator lined with 3 mm thick perspex, cadmium and copper was used, The whole surface of the crystal was exposed to the SOUrce. 2.3. EXPERIMENTAL A R R A N G E M E N T F O R BETA-GAMMA COINCIDENCE

The high transmission Sieghahn-Slitis beta ray spectrometer 7) has been suitably modified for the study of beta-gamma coincidences. A separate pole piece on the source side has been used in which a 2.5 cm x 3.8cm diameter NaI(TI) crystal directly coupled to Dumont photomultiplier tube could be placed at a distance of 4 cm from the source, for the detection of gamma-rays. The effect of the magnetic field on the photomultiplier tube has been neutralised by compensating coils. The electrons in the spectrometer were focussed on a 6 mm diameter and 2 mm thick anthracene crystal coupled to the photomultiplier with the help of a logarithmic light guide. The beta pulses from this anthracene crystal and the gamma pulses from the NaI crystal were first amplified through three Hewlett Packard wide band amplifiers on each side in cascade and then fed to the usual fast-slow coincidence set up of Bell and Graham type. In this way the gamma spectrum in coincidence with a particular beta energy was scanned in the multichannel analyser. 2.4. A R R A N G E M E N T FOR G A M M A - G A M M A COINCIDENCES

The gamma-gamma and X-ray gamma coincidences were carried out with two scintillation spectrometers consisting of 7.5 cmx 7.5 cm diameter and 2.5 cm x 3.8 cm diameter NaI(TI) crystals. The coincidence arrangement was similar to that described

INTBRNAL C O ~ O N

STUDI]~

307

above. A smaller crystal was used for scanning the desired gamma region in the multichannel analyser. The detectors were kept at right angles and a 1.2 cm thick lead absorber covered with cadmium and copper was placed in between to prevent spurious coincidences due to Compton scattering. The coincidence resolving time used was 120 nsec and the coincidence efficiency was checked to be I00~o from 15 keV onwards, using the annihilation radiation from a N a 22 source. It was necessary to record the coincidence for a period extending from 200 min to 800 rain because in the beta-gamma coincidence method the coincidence counting rate was low. Also in the gamma-gamma coincidences the highest energy gamma-ray which has been fixed in the gate was very weak in intensity and a longer run for coincidence was necessary. The stability of the system was found to be satisfactory and shifts in photopeak positions were less than l ~o over a 24 h period. The true to chance ratio in all cases has been maintained to be above 30 : I. 2.5. ABSORPTION CORRECTION A 0.65 cm thick and 3.8 cm diameter perspex absorber was used for absorbing the beta particles of energy up to 1200 keY. In the case o f Re lss where the beta energy extends up to 2120 keV, a 0.95 cm thick perspex absorber was used. The absorption in perspex has been determined by taking the composition of perspex as CsHsO2. In the case of H e 166 the value of ~ has also been determined by using a standard aluminium absorber of suitable thickness. As this value was almost the same as that with perspex, this provided a check for the validity of the value of absorption coefficients used for perspex. The material in crystal package was taken to be alumiuium, neoprene rubber, polythylene and magnesium oxide as furnished by Harshaw Chemical Co. The absorption coefficients used for different materials for calculating the attenuation of various X-ray and gamma-ray energies are given in table 1. 2.6. ESCAPE PEAK DETERMINATION In those cases where the gamma-ray energy was less than 100 keV and the escape peak energy was very near the X-ray energy, suitably graded absorber consisting o f cadmium, molybdenum and copper was used to absorb the X-rays by a factor o f eight hundred relative to the corresponding gamma-ray. The contribution due to escape peak was thus experimentally determined. 2.7. DETECTION EFFICIENCY In all the cases the total areas under the gamma-ray spectrum and X-ray spectrum have been determined and the values o f total detectionef~ciency have been used. These values are given in table I. Tot take into account the scattering from the surroundings especially in the fl-7 coincidence method where the gamma-ray detector is inside the pole piece the detector was kept outside with minimum surrounding scattering material and the line shape of 141 keY transition in P r 14! ~ obtained. This distribution was also studied by using a shadow shield o f proper dimensions at a suitable distance to stop the direct rays. This correction was of the order of 8 ~ in the case o f Os ls¢ and

308

a. v . THO~iAR e t aL

Os xes and 3 ~ in the case of Er tee, Yb t~° and H f 17e and has been taken into account in the calculation. 2.8. THE ~K COEFFICIENT D E T E R M I N E D F R O M SINGLES G A M M A - R A Y SPECTRUM

The K conversion coefficient of the 80 keV transition (2 + - , 0 +) in Er lee has been determined from the singles gamma-ray spectrum. This case was suitable for this study because there is no electron capture branching and the high energy ga~-nma-rays are weak. Also the bramsstrahiung contribution can be estimated as the maximum beta energy is comparable to that of pure beta emitter p32. The gamma-ray spectrum was taken on a scintillation set-up described above. Beta particles were absorbed in a 960 rag/tin 2 aluminium absorber.

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Fig. 1. The singles gamma ray spectrum of Er ~x. The line shape for 80 keV transition as obtained by absorbing the X-rays is shown by the dotted line. Below are also shown (b) bremsstrahlung contribution, (¢) scattering contribution from the surrounding and (d) Compton distribution due to the high energy gamma-rays. All these contributions have been subtracted from the singles spectrum shown above.

INTBRNAL CONVBRBION S T U D ~

309

In order to correct for the bremsstrahlung produced by the intense beta transition to the ground and first excited state, a source o f P 3z of almost the same strength was prepared and the bremsstrahlung spectrum was taken under identical conditions of geometry. The Compton contribution due to the high-energy gamma-rays in the region of 80 keV gamma-ray and its X-ray was found by selective absorption of the 80 keV gamma-ray. The absorber was a suitably graded one consisting of tantalum, molybdenum, cadmium and copper. The higher energy gamma rays are weak in intensity their contribution being less than 1 ~o. Correction for scattering from the surroundings was made by using a shadow shield for the direct rays. This shield of proper dimensions consisting of the same material as the critical absorber mentioned above was placed below the source at a suitable distance to stop the direct rays reaching the crystal. Thus the contribution due to scattering from the surroundings in the region of 80 keV gamma-ray and 50 keV X-ray was found to be 2~o and 2.6~o, respectively. To account for the K-ionisation due to high energy beta particles scattered in the source itself the effect of source thickness was experimentally determined, by evaporating equal amounts of inactive Ho2Os dissolved in HCI on the prepared gamma ray source and the ratio of Nx/N 7 was determined after every addition of inactive material. This ratio was plotted against the source thickness and was extrapolated to zero thickness. The correction due to this self-scattering effect in the source thickness for a 1 mg/cm z thick source was < 2~o. The gamma ray spectrum of He 16~ in the region of 80 keV along with different corrections is shown in fig. 1. As the escape peak energy of the 80 keV gamma-ray is very near the X-ray energy the complete line shape of this gamma-ray has been obtained as described above. This line shape has been coincided with the singles spectrum and the intensity of the 80 keV photopeak and its escape peak was determined. The intensity of X-ray photopeak and escape peak was obtained after subtracting the 80 keV line shape. In this way N. and N 7 were determined and are given in table 1. The value of =K was determined in the usual way after correcting both X-ray and gamma-ray spectra for detector efficiency and for attenuation in beta absorber and crystal package. This value is given in table 2. 2.9. T H E

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COEFFICIENT DETERMINED FROM BETA-GAMMA COINCIDENCE

METHOD The K conversion coefficients for the 2 + -~ 0 + transitions in Er 1~, Yb 1~°, H f 17~, Os ls6 and Os lss have been determined by beta-gamma coincidence method described above. In case of Lu 176 there is active impurity due to Lu 177. Here the beta energy has been selected in such a w a y that Lu 177 contribution is eliminated. The contribution due to a large number of high energy gamma-rays present in the decay of Re tss has been avoided by selecting the beta energy above 1600 keV. In order to compare the value of ~E as obtained from the study of the singles gamma-rays spectrum with that from the beta-~mr~a coincidence spectrum, the 80 keV transition in Er 1~6 was stud-

310

n.v. mmmoe~tet

al.

ied in coincidence with 1110 keV beta-rays. In Yb '7° and H f 176 the magnetic spectrometer was set to focus electrons of energy 620 keV and 600 keV, respectively, so that the C o m p t o n contribution due to any possible high energy g a m m a is also completely eliminated in the coincidence spectrum. T o obtain the fine shape of 80,

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84 and 88.4 keV gamma-rays, the X-rays were absorbed as mentioned above and the coincident g a m m a spectrum was again recorded. In the case of Os ' s e and Os lss the line shape for 137 and 155 keV p r a y s is obtained by taking the spectrum of 142 keV 7-ray in Pr x4: and where the X-ray energy is also about 35 keV. In this way one gets the idea o f C o m p t o n distribution of 137 and 155 keV 8aroma rays in their respective X-ray regions. The total Nx and N 7 for each case as given in table 1 were calculated with the help of these line shapes and the value o f ~r was determined. The coincidence

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Fig. 3. The gamma-ray spectrum, o f Os 1" in coincidence with the 500 keV beta rays. The line shape o f 137 keV transition is shown by the dotted line. TAaLa 1 $ n m m ~ ' y o f experimental results Nudeides Er T M Yb ITs

Energy 0ceV)

Nx

80.57 1 2 8 2 1 8 84.23 12114

NT

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102094 11472

0.6154 0.6455

0.7687 0.7657

0.995 0.994

0.980 0.963

0.923 0.930

1.67 1.31

HInT* W~ Os tee

88.35 122 137

15023 3697 8694

16526 7221 20952

0.6634 0.7706 0.7776

0.7725 0.8261 0.8336

0.995 0.99 0.987

0.96 0.93 0.887

0.941 0.945 0.948

1.10 0.55 0.42

Os l u D y x'e

155 86.7

5238 19374

15701 15185

0.7323 0.7326

0.8041 0.8057

0.987 0.99

0.862 0.975

0.948 0.910

0.34 1.52

The value o f Ax has been given as the weighted m e a n o f attenuation for X , a n d X#. In the first three cases standard alum/n/tun absorber o f suitable thickness has been used for absorbing the beta particles, while perspex has been used in the remaln|~g cases.

312

e. V. T a O ~ t t e t a l .

spectra of H f 17e and Os 1s6 along with the line shapes are shown in figs. 2 and 3, respectively. The value of utc for each case is given in table 2. 2.10. THE gic COEFFICIENT DETERMINED METHODS

FROM X-7, A N D 7"Y COINCIDENCE

The K conversion coetticient for the 122 keV (2 + --, 0 +) transition in W 1s6 was determined by the X-~ coincidence method. Two percent of Re zs6 decays to the 122 keV first excited level of W ls6 by electron capture. Most of the transitions is by/~decay to Os lse ground state and 137 keV first excited state. The X-rays due to the 122 keV

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capture of orbital electrons were detected in a 7.5 cm x 7.5 cm diameter NaI(TI) crystal and the coincidence gamma spectrum was scanned. In this particular case in the gate spectrum one would get the contribution of X-rays due to conversion electrons and the Compton contribution of 122 and 137 keV gamma-rays. The detection of X-rays due to conversion electrons of W ~Se in the gate will simply double the coincidence counting rate in the X-ray region of the coincidence spectrum. To account for the Compton of 122 keV gamma-ray the gate was shifted beyond the X-ray peak and the coincidence spectrum was recorded. This has been further corrected by taking the ratio of the 122 keV Compton in the two regions, beyond the X-ray and below the X-ray peak, which have been taken in the gate. This ratio has been obtained by analys-

313

INTERNAL CONVERSION STUDIES

ing the singles spectrum with the help of 141 keV gamma ray line shape in Pr '41. The coincidence counts were collected for 800 rain. After analysis of the coincidence spectrum the total N~ and N 7 as given in table 1 were determined and the value of UK was calculated. This value of u~ is given in table 2. The coincidence spectrum along with the line shape is shown in fig. 4.

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Fig. 5. The gamma-ray spectrum of Dy lee in coincidence with the 1280 keV gamma-ray. The line shape for 86 keV transition is shown by the dotted line. In the inset are shown the particular transitions of interest.

The ~g for the 87 keV transition in Dy 1~° has been determined by taking the low energy gamma spectrum in coincidence with the highest energy gamma ray (1280 keV) feeding the first excited state. As this gamma-ray will only be in coincidence with the 87 keV transition the Compton contribution due to any other gamma ray will not be detected. This coincidence spectrum is shown in fig. 5. The line shape for 87 keV transition has been obtained by selective absorption of the X-rays. Here again the coincidence counts were collected for 800 rain. The total N~ and N 7 obtained after analysis of the coincidence spectrum are given in table 1. The ~K coefficient obtained from this measurement is given in table 2. 3.

~ion

The various values of~K for pure E2 transitions determined by earfier workers ~long ~ t h the present values are ~ven in table 2. The previous values de~ate considerably

314

B. V. TllO&An et al.

TAnt~ 2

K conversion coefficients of E2 (2 + --~ 0 +) transitions 80.57 keY t r a m i t i o n in ..Er~.." ~

Ref. 1) 11) 4) Present work

Method 7'-scintillation spectra 7'-scintillation spectra life time measurements ~-7' coincidence and singles spectrum 84.23 keV transition in veYb~ ~

in) 1) u) 14) Present work

(theoretical) -- 1.60

beta-gamma coincidence 7'-~intillation spectra IEC method 7'-scintillation spectra ~-7' coincidence

gx(expt)

~,x(expt)/g,~(theo)

1.85-;-0.13 1.76 1.676 1.67±0.07

1.16 1.10 1.05 1.04

(theoretical) ~ 1.33 1.69-1-0.02 1.65-t-0.12 1.57 1.34-I-0.08 1.31±0.08

1.27 1.24 1.18 1.01 0.98

88.35 keV transition in v4Hfl~t tT6 ~z (theoretical) ---- 1.08 1) Present work

~scintillation spectra fl-7' coincidence

1.324-0.11 1.10-4-0.06

1.22 1.02

122 keV transition in vtWxtl~ ~,r (theoretical) ~ 0.578 x) Present work

Coulomb excitation of nuclei X-ray gamma coincidence

0.82 0.55-1-0.03

1.42 0.95

137 keV transition in uOst~ " x (theoretical) m 0.428 x4) 14) ') Present work

beta=gamma coincidence double lens spectrometer electron*electron coincidence ~-7' coincidence

0.45-1-0.03 0.36 0.3984-0.028 0.42-I-0.03

1.051 0.84 0.93 0.98

155 keV transition in T4Oslx nxu ~ x (theoretical) = 0.33 14) Iv) Present work

beta.mtmma coincidence thin lens spectrometer fl-7 coincidence

0.40-1-0.05 0.29-/-0.03 0.34

1.21 0.97 1.03

86.7 keY transition in KDyt~ ~x (theoretical)~ 1.51 18) it) 0) Present work

absolute intensity measurement of e- and 7' 1.60 absolute intensity m e a s ~ t of e- and 7' 1.50-4-0.3 sum coincidence technique 1.54-I-0.06 7-7 coincidence 1.52-F-0.06

1.06 0.99 1.02 1.01

The theoretical veJues of ~,~ are taken from ref. I).

from the theoretical ones, but as the improved techniques are used and possible contribution of various uncertainties is taken into account the discrepancy between the theoretical and experimental values is very much reduced. Lu et al. s) have determined the total conversion coefficients in the case of Sm tsz,

INTERNAL CONVEIUION STUDIES

315

Gd ts4 and Dy 16° from the summing technique. The aK values as computed from these values of total ~ agree fairly well with the theoretical ones. Also El Nesr and Bashandy 9) from electron-electron coincidence measurements have derived the values o f 0(L f o r 2 + -+ 0 + transition in Er 166, Yb 1~° and Os ls~ which are in good agreement with those calculated by Rose ~). Recently Li and Schwarzschild 1o) have measured the life time of 4 +, 2 + states of the ground state rotational band for five (Dy ~ ° , Dy ~¢2, Er ~ss and H f Is°) even rare earth nuclei and have calculated the reduced transition probability ratio B(E2, 4 + - , 2 +)/B(E2, 2 + --*0 + ) using the theoretical values of conversion coefficients. They find good agreement with the ratio of ~ as predicted by the rotational model.

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MASS NUMgER Fig. 6. The ratio a . z p / ~ in different cases of interest as obtained from previous measurements is plotted against the mass number. The values obtained from the present measurements in seven cases a r e shown by solid triangles.

In fig. 6 the ratio ~ozp/~f.th.o has been plotted against the mass number. The value of • ~: for 2 + -~ 0 + transitions in Er 1~6, Yb 17°, H f t76, W ls~ and D y 1~° where large deviations were previously reported are now seen to be in agreement with the values calculated by Rose s) and $liv 2). This is also supported from the life time, sum coincidence and electron-electron coincidence measurements. It therefore appears that the earlier large deviations were probably due to some experimental causes rather than any new effects in nuclear structure. There may be small deviations ~ 5 ~o due to this effect but at the moment it is rather difficult to establish such deviation. Deviations less than 5~o cannot be detected by the present measurements. Hence any small dependence of~x on N/Z can only be investigated if the sources of error are minimised.

316

a.v. THC3aAItet al.

The authors wish to express their thanks to Mr. A. T. Rane and Mrs. Radha Menon for the chemical purification of different sources. Thanks are due also to Mr. E. A. S. Sarma for help in calculations. a e f m 1) F. K. Mc~3owan and P. H. Stebon, Phys. Rev. 107 (1957) 1674 2) L. A. Sliv and J. M. Band, Internal conversion ~lticients tables, Universityof Illinois, Report 55ICC K1 (1957) 3) B. N. Subba Rao, Nuovo Cim. 17 (1960) 189 4) E. M. Bernstein, Phys. Rev. Lett. 8 (1962) 100 5) M. E. Rose, Internal conversion coefl~ents (North-Holland Publ. Co., Amsterdam, 1958) 6) E. L. Church and J. Weneser, Ann. Rev. Nud. Sci. 10 (1960) 193 7) H. Slitis and K. Siegbahn, Ark. FYS. I (1950) 339 8) D. C. Lu and R. S. Dingus, Phys. Lett. 3 (1962) 44 9) M. S. E1 Nest and E. Bashandy, Physica 28 (1962) 1335 10) C. Li and A. Schwarzsc,hild, Phys. Rev. 129 (1963) 2664 11) I. Marklund, B. V. Nooijen and Z. Grabowski, Nuclear Physi~ 15 (1960) 533 12) A. Bisi, E. Germagnoli and L. Zappa, Nuovo Cim. 3 (1956) 1007 13) J. F. W. Jansen, S. Hultberg, P. F. A. Goudsmit and A. H. Wapstra, Nuclear Physics 38 (1962) 121 14) H. Houtermans, Z. Phys. 149 (1957) 215 15) M.W. Johns, C. C. McMullen, I. R. Williams and S. V. Nablo, Can. J. Phys. 34 (1956) 69 16) F.T. Porter, M. S. Freedman, T. B. Novey and F. Wagner Jr., Phys. Rev. 103 (1956) 921 17) V. R. Potnis, Phys. Rev. 104 (1956) 722 18) O. Nathan, Nuclear Physics 4 (1957) 125 19) M. A. Clark and J. W. Knowles, Bull. Am. Phys. Soc. 2 (1957) 231