The mixing of the gamma vibrational and ground state bands in 160Dy

Nuclear Physics A147 (1970) 527 --540; (~) North-Holland Publishing Co., Amsterdam

Not ~o be reproduced by photoprint or microfilmwithout written permission from the publisher

THE MIXING OF THE GAMMA VIBRATIONAL A N D G R O U N D S T A T E B A N D S I N Z6°Dy G. E. KELLER * and E. F. ZGANJAR Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana

Received 30 December 1969

Abstract: TheT-ray spectra accompanying the {?- decay of td°Tb to levels in 16°Dy has been studied using Ge(Li) detectors. Coincidence measurements were made in order to separate unresolved transitions. Five reduced E2 transition probability ratios for transitions between the gamma and ground state band were computed from the measured v-ray energies and intensities. The band mixing parameters deduced from each ratio are determined to be mutually inconsistent. The values, z2 × 103, are: 49.5i4.0, 18.7+2.8, 29.2~2.1, 30.5 ~4.7 and 55.8~5.6. A critical inconsistency with internal conversion data is pointed out. E [

RADIOACTIVITY id°Tb [from ~'gTb(n,v)]; measured Ey, I.,, ~7-coin; deduced l log ft, fl-branching. 16°Dy deduced levels, K, 3-, ~, cc, B(E2) ratios, b~md mixing parameters. I

1. Introduction The decay o f 16OTb has been thoroughly investigated 1-1 o); consequently the level scheme and the y-vibrational band (966 keV 2 +, 1049 keV 3 +, and 1156 keV 4 + levels) o f 16ODy are well established. Recent investigations 8-~ o) have been concerned with the determination o f the band-mixing parameter z2 which describes the coupling o f the 7-vibrational and the g r o u n d state band. The mixing parameter is introduced within the framework o f the phenomenological band-mixing model a a, 12) (non-adiabatic symmetric-rotor model) where the vibration-rotation interaction is treated as a pertt~rbation and the z z parameter is defined as a ratio o f unspecified matrix elements. The experimental measurement o f the mixing parameter is overdetermined since a value for z2 can be obtained for each ratio o f transition probabilities between the bands. This basic model a p p r o a c h is verified when the values are mutually consistent. A consistent set of z z values has been obtained for the nuclei t66Er [ref. 13)] and 168]~r [refs. 13-16)]. F o r the nuclei 152Sm and 154Gd ' the mixing o f the ~- and g r o u n d state bands has been described by a two-parameter analysis 17) which includes the second-order effect o f the mixing o f the ]3- and 7-bands. In a recent investigation 18) a consistent two-parameter description of the mixir(g of the ~- and g r o u n d state bands in 154Gd was not obtained when more precise data were used. F o r 16ODy' a consistent set o f mixing parameters has been obtained only by G u n t h e r et al. 1o). The results of refs. 8, 9) indicate that the :zg for the 682 and 765 keV interband transitions significant* Present address: Physics Department, West Georgia College, Carrollton, Georgia, USA. 527

:D 0 o

Fz

Ld Z 21 32 (.3

I0 4

i0 5

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10 7

...J~n__

~00

L

0

-

-

J

400

_

_

CHANNEL

500

~

I

600

:__ 1250.64 keV

215.65 keY

197.04 keV

700

~ . . . . .

A

800

I

337.:55 keY

309.56 keY

298.58 keV

Delector

900

5 9 2 . 4 9 keV

I000

D~Scm. 0,49 keV /Chennel

L.S.U.-I

Tb 160

Fig. l. The 0-450 key portion ofthe~-ray spectrmntaken with ~le 10 cm~ detector.

L

500

I

200

95.92 keY

86.80 ~eV

i

N 0

L~

z 0

\

.J b3 Z Z ,<

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J06 ~

1099

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---J 1299

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Fig. 2. The 450-900

q 1199

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"f"

1 1599

6 8 2 . 3 0 key

CHANNEL

l 1499

]

J~ 1699

I

1799

160

O=3cm.

L.S.U.- I

Tb

765.26 keV

L

k c V p o r t i m ] o f the y - r a y s p e c t r u m t a k e n w i t h t h e 10 c m s d e t e c t o r .

i 1399

r

879,35

1._ 1899

I 1999

0,49 keV/Channel

Defector

I

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2598

2498

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2698

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1271.87 keY

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2998

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1312.16keY

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SUM PEAK t 298+966 I

D=Scm.

L,S.U--I

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Fig. 3. The 900-1350 keV portion of the 7-ray spectrum taken with the 10 cm3 detector,

2298

96&16 keY

keVl

T'--

16°Dy BAND MIXING

531

ly differ from the theoretical czKfor pure E2 multipolarity. In the computation of the band-mixing parameters, the 682 and 765 keV photon intensities were assumed to be of pure E2 multipolarity. In an attempt to resolve the band-mixing discrepancies, the decay of 160Tb was reinvestigated with the emphasis placed on the precise determination of 7-ray intensities.

2. Experimental procedure The radioactive sources were prepared by thermal neutron irradiation of Tb203. N o source impurities were observed in the v-ray spectra presented in figs. 1-3. The 7-ray energies and intensities were determined from spectra taken with 2 cm 3 and 10 cm 3 Ge(Li) detectors. The photopeak efficiency calibrations for the Ge(Li) detectors and the non-linearity corrections for the spectrometers are described in ref. 16). The energies are measured relative to a set of high precision standards which also appears in ref. 16). The analysis of the spectra was accomplished using a computer routine 19). A set of V-V coincidence experiments was carried out to more accurately determine the relative intensities of the 962 and 966 keV interband transitions. The photopeaks from these transitions are not completely resolved in the singles spectrum, fig. 3, and a source of error in the measured intensity can result from the small asymmetry in the photopeaks. In the analysis of the singles spectra, the unresolved photopeaks are simultaneously fit by two Gaussian functions and the asymmetry of the 966 keV peak is included in the fit. In the Gaussian fitting, the peakpoints are weighted according to their height and as a result this asymmetry is included, for the most part, in the area of the less intense 962 keV peak. The singlet peaks are analysed by fitting the Gaussian to only those points above the F W H M in order to avoid the asymmetry and, more importantly, because the photopeak efficiencies were measured on that basis. In the first coincidence experiment the 87 keV transition was detected with a 7.6 x 7.6 cm NaI(T1) detector and the resulting signals were used to gate the analyser so as to simultaneously record the 879 and 962 keV transitions detected with the 2 cm 3 Ge(Li) detector. The coincident 7-spectrum was recorded at several angles since the 962-87 keV 3(2)2(2)0 and the 879-87 keV 2(2)2(2)0 correlations have non-zero A 4 .coefficients. In addition, the attenuation of the correlation across the 87 keV state must also be considered in making the correction for correlation effects. In the second coincidence experiment the 298 keV transition was used to gate the analyser to simultaneously record the 879 and 966 keV transitions detected with the 10 cna 3 Ge(Li) detector. The coincident 7-spectrum in this case was recorded only at 126 ° since for the 298-966 keV 2(1)2(2)0 and the 298-879 keV 2(1)2(2)2 correlations A4 = 0 and there is no attenuation across the 966 keY state.

3. Results The 7-ray energies and intensities o f the transitions observed in this investigation are listed in table 1. The quoted values, with the exception of the energy of the 962

532

G . E . KELLER A N D E.

1:. ZGANJAR

TABLE 1 The energies, relative y-ray intensities, K-shell conversion coefficients and transition intensities Energy

7-intensity

eK intensity a)

~K exp

~ theor b)

(keV)

(7-rays/100 decays)

( × 10 a)

( × 103)

( × 103)

86.798 93.92 197.036 215.648 230.641 298.579 309.564 337.347 392.494 486.165 682.298 765.260 872.12 879.350 962.285 966.158 1002.873 1069.113 1102.616 1115.122 1177.923 1199.896 1251.34 1271.873 1312.158

(10) (10) (14) (18) (68) (10) (44) (32) (23) (90) (54) (54) (28) (29) (37) ~) (36) (42) (87) (42) (42) (49) (46) (10) (46) (46)

13.9 0.036 5.11 3.87 0.061 26.7 0.81 0.34 1.35 0.095 0.532 1.91 0.282 29.7 9.91 25.2 1.00 0.112 0.555 1.50 15.5 2.46 0.095 7.73 2.97

(6) 22900 (2875) (6) 77 (19) (9) 838 (39) (9) 134 (7) (9) (7) 372 (21) (3) 11.3 (14) (3) (6) 10.4 (14) (15) (30)'~) 4.8 (14) (5) a) 11.9 (9) (39) a) (5) a) 98.1 (50) (50) r) 27.8 (20) (5) f) 68.4 (40) (7) 0.76 (14) (9) d) (30) (5) 1.49 (10) (4) 11.4 (6) (7) 1.78 (20) (9) (30) 4.86 (30) (12) 1.88 (10)

1650 2140 164 34 14.4 14.2

(220) (400) (2) (9) (18)

1610 2250 164 34

E2 M1 E2 E1

14.6 13.5

E1 E1 E1

7.7

(11)

7.7

8.9 6.2

(28) (5)

5.8 E2 4.5 E2

3.3 2.8 2.7 0.76

(2) (3) (2) (16)

3.4 2.8 2.7 1.0

0.99 0.74 0.73

(7) (4) (8)

0.88 E1 0.79 E1 0.77 E1

0.63 0.63

(5) (4)

0.68 E1 0.65 E1

E2 E2 E2 E1

Transition intensity ¢) (/100 decays) 75.06 0.13 6.35 4.02 0.06 27.15 0.82 0.34 1.36 0.10 0.54 1.92 0.28 29.82 9.94 25.28 1.00 0.11 0.56 1.50 15.51 2.46 0.10 7.74 2.97

(32) (2) (11) (9) (1) (71) (3) (3) (6) (2) (3) (5) (4) (50) (69) (50) (7) (1) (3) (5) (40) (7) (I) (30) (12)

a) The conversion electron intensities are from Ewan et al. 4) and are normalized to give the pure E2 conversion coefficient for the 197 keV transition. b) Theoretical conversion coefficients of I-Iager and Seltzer 2o). c) The eK of column 4 and theoretical L and M conversion coefficients 20) for the multipolarity indicated in column 5 were used in the calculations. For the other transitions the multipolarity was deduced from the decay scheme. d) These interband transitions have the following intensity ,uncertainties in the calculation of B(E2) ratios: 682:0.532±0.015 879:29.7 zk0.3 765:1.91 ±0.03 1069: 0.112z~0.008 872:0.282 i0.020. These values are calculated with a 3 ~ uncertainty in the relative efficiency since the energy range is only 400 keV. The uncertainties in the intensities of the 962 and 966 keV transitions are unchanged because of statistical considerations. ~) Energy determined from the difference in level energies. f) Intensity determined from coincidence experiments.

16°Dy BANDMIXING

533

keV transition, are weighted averages and the uncertainties (the values in parenthesis, applied to the least significant figure) are the larger of either the uncertainty in the weighted average or the rms deviation of the individual values from the weighted average. The energy quoted for the 962 keV transition is obtained from the difference in the corresponding level energies. The quoted energy uncertainties include contributions from the uncertainty in the calculated photopeak location, from the uncertainties in the energy standards, and from the quality of the calibration fit (energy versus non-linearity corrected peak location). TABLE 2 Comparison of crossover energies to the sums of cascade energies

Cascade v-rays ") 93.92 4 - 0 . 1 0 93.92 4 - 0 . 1 0 197.036±0.014 197.0364-0.014 86.7984-0.010 197.0364-0.014 230.6414-0,068 337,3474-0.032 215.6484-0.018 298.5794-0,010 197.0364-0,014 486.1654-0.090 93.92 4 - 0 . 1 0 309.5644-0,044 392.4944-0,023 197.0364-0.014

215.648+__0.018 298.5794-0.010 682.2984-0.054 765.260±0.054 879.3504-0.029 872.12 4-0.28 872.12 4 - 0 . 2 8 765.2604-0.054 962.2854-0.037 879.3504-0.029 1002.8734-0.042 765.2604-0.054 1177.9234-0.049 962.2854-0.037 879.3504-0.029 1115.1224-0.042

Cascade sum 309.5684-0.t02 392.4894-0.100 879.3344-0.056 962.2964-0.056 966.148±0.031 1069.156 =t=0.280 1102.7614-0.288 1102.6074-0.063 1177,9334-0.041 1177.929±0.031 1199.9064-0,044 1251.4254-0,105 1271.8434-0.111 1271.8494-0.057 1271.844:k0,037 1312.1584-0.044

Crossover 309.5644-0.044 392.4944-0.023 879.3504-0.029 962.2854-0.037 966.1584-0.036 1069.1134-0.087 1102.6164-0.042 1102.616.4-0.040 1177.9234-0.049 1177.923'--0.049 1199,8964-0,046 1251.344-0.10 1271.8734-0,040 1271.8734-0.040 1271.8734-0.040 1312.1584-0.046

AE]sigma b) --0.04 0.05 0.25 --0.16 0.21 --0.15 --0.50 0.12 --0.16 -0.10 --0.16 --.0.59 0.25 0.34 0.53 0.00

a) Energies in keV. b) The sigma referred to is ~/~sum2+acr~ 2. The 7-ray intensities are normalized relative to 29.7 units for the 879 keV transition and with this normalization the intensities are the number of y-rays emitted per 100 decays of 160Tb (assuming no ground state fl-feeding). The quoted uncertainties contain contributions from the uncertainty in the photopeak area determination and from the uncertainty in the efficiency calibration of the detectors which is 5 ~ over the energy range 60-2750 keV. The K-shell conversion electron intensities of Ewan et al. 4) are presented in column 3. These values, in conjunction with the y-intensities of column 2, yield the experimental aK listed in column 4. The theoretical al~ of Hager and Seltzer 2 o) for the indicated multipolarity are given in column 5. The total transition intensities are given in the last column. The agreement between the energies reported here and those of Ludington et al. 9) is excellent, especially for the low-energy ( < 400 keV) transitions which were measured on the University of Michigan curved crystal spectrometer. The validity of the

534

G. E. KELLER AND E. E. ZGAN,IAR

reported energies is attested to by the comparison of the energy of crossover transitions to the sum of the energies of the appropriate cascade 7-rays. These comparisons are made in table 2 and in no case is the difference in the energy sum and the crossover energy greater than 0.6 times the standard deviation of the comparison. There is also agreement between the intensities reported here and those of ref. 9); the disagreement arising only for the weak 93, 309, 872 and 1069 keV transitions. The intensity of the 872 keV transition, reported here, was determined by taking into account the exact shape of the 879 keV peak as determined from the shapes of the 834 and 898 keV photopeaks of 54Mn and 8Sy. The uncertainty in this case is derived from the interna! consistency of the determinations. The reported values give an intensity balance to within 0.3 % for the 87 keV level. The intensity balance for each level is displayed in table 3. The fi- branching percentage and logfi value reported by Nathan l) is assumed for the 87 keV level. For all other levels the logfi values are calculated using a ground state energy difference of 1840 keV [ref. 1)]. TABLE 3

T h e / 3 - b r a n c h i n g ratios and_ logJ~ values Level (keV)

I ~r

Population intensity

Depopulation intensity

% fi- feeding

Ep a)

logft

AI

Azc

87 284 966 1049 1156 1265 1287 1359 1386 1399 1535

2+ 4+ 2+ 3+ 4+ 232434-

74.90 (101) 5.89 (12) 28.51 (71) 5.29 (i1) 0.06 (1) 0.13 (2) 0 0 0 0 0

75,06 (324) 6.35 (11) 55.64 (72) 11.85 (70) 0.39 (4) 46.68 (82) 3.46 (10) 10.05 (31) 0.96 (5) 4.47 (13) 0.19 (2)

0.40 b) 0.46 (16) 27.13 (101) 6.56 (71) 0.33 (4) 46.55 (82) 3.46 (10) 10.05 (31) 0.96 (5) 4.47 (13) 0.19 (2)

1753 1556 874 791 684 575 553 481 454 441 305

11.9 11.8 8.9 9.5 10.5 8.2 9.1 8.5 9.4 8.7 9.5

I 1 1 0 1 1 0 1 1 0 1

yes yes yes yes yes no no no no no no

a) T h e g r o u n d state energy difference is a s s u m e d to be 1840 keV as given by N a t h a n 1). b) N a t h a n 1).

The K-shell conversion coefficients in column 4 of table 1 give a definitive indication of the transition multipolarity with the exception of the 682 and 765 keV transitions. The electron intensity for the 682 keV transition appears to be high by about one standard deviation since the next allowable multipole, M3, is not expected to compete with E2. Gunther et al. 1o) report a value for the 682 keV K-shell conversion electron intensity which is lower than the value of Ewan et al. 4) by about one standard deviation. "['he 765 keV transition may contain an M1 admixture but the electron intensity of Ewan et al. 4) is higher than the value of Gunther et al. 1 o) by 20 %. The electron intensities of Gunther et al. 1o) when combined with the photon intensities of this work give the following: ~K(682 k e V ) = (6.95_+0.63)x10-a; ~K(765 k e Y ) = (5.18 + 0.20) x 10-a. These values are still larger than the pure E2 theoretical values.

16’Dy

BAND

MIXING

OE’ZBS SE’BLB 9 1’996 92’99L

83'296 2 I ‘ZLB II’6901

F’60! bZ65

fl j-k+--Le’iLzI

I 9ei

I

536

G. E. KELLER AND E. F. ZGANJAR

The decay scheme in fig. 4 is consistent with the energy and intensity results of this investigation and the coincidence results of refs. s - 1 o). The decay scheme is essentially the same as that of Ludington et al. 9) and Gunther et al. ~o). The assignments of spins, parities and K quantum numbers for the positive parity levels are well established.

A NORMALIZED COMPTON SHAPE (ftorn 54Mn and 88y } • FROM 160Tb SPECTRUM 160Dy

682 keY 9xlO 4

8xlO 4

UNDERLYING COMP T ~

7xlO 4 J

2100

2120

2140

2160

CHANNEL

Fig. 5. The porCionof the ;J-rayspectrum around the 682 keV photopeak. The triangles represent the shape of the Compton edge as deterEainedfrom the Compton distributions produced by ~4Mn aud 88yo

The spin and parity assignments for the ~egative parity levels have been made by Gunther el al. 10) who interpreted the levels as belonging to two strongly mixed rotational bands with K = 1 and K = 2. These assignments are consistent with the results of this investigation. The K-assignments for the negative parity levels shown in fig. 4 are those values indicated by the comparison of B(E1) ratios, calculated from the results of this investigation, to adiabatic predictions.

537

16°Dy BAND MIXING

4. Discussion T h e results o f this i n v e s t i g a t i o n h a v e b e e n u s e d t o c o m p u t e r a t i o s o f r e d u c e d E 2 t r a n s i t i o n p r o b a b i l i t i e s f o r t r a n s i t i o n s b e t w e e n t h e 7 - v i b r a t i o n a l a n d g r o u n d state b a n d s . T h e s e B ( E 2 ) r a t i o s are c o m p a r e d in t a b l e 4 to t h e p r e d i c t i o n s o f t h e a d i a b a t i c s y m m e t r i c - r o t o r m o d e l 2~) ( c o l u m n 4). T h e c o r r e c t i o n f a c t o r s ( c o l u m n 5) w h i c h TABLE 4 Experimental B(E2) ratios and z2 values for transitions between the 7- and ground state bands IiKt -+ lrKr liK~ - + I f ' K r

E(I~ --lf) B(E2; IiKi -+ IfKf) Theory ~) F-(Ii--lr') B(E2; liKi - + Ir'Kr) (adiabatic)

0.5234-0.012

Correction factor

z2 ( × 103)

(1 --zz ] 2 \1 + 2 z z l

49.54-4.0

19.9

(1 +2z2~ 2 \1~2/

18.74-2.8

•3.9

[ l - - z 2 ~2 \1 +9z2 /

29.24-2.1

22 -+ 00 22 --~ 20

966 879

22--->20 22 -+ 40

879 68"--2

22 -+00 22 -> 40

966 682

8.21 4-0.28

32 --> 20 32 ~ 40

96_2_2 765

1.68 4-0.09

2.50

(1 --zz ~2 \1 + 6 z ~ l

30.5-4-4.7 --

42 -+20 42 -+ 40

106_~9 872

0.134~0.014

0.340

(1--5z2~ 2 \1 +2z2!

55.84-5.6

15.7

4-0.5

0.699

a) Calculated from the Clebsch-Gordan coelficients tabulated by Yamazaki 22). TABLE 5 Comparison of z2 values ( × 10 a) Gunther et al. l°)

Jaklevic et al. s)

Present work

53 ± 10

43.5 4-5.0

41 4-32

49.5 4-4.0

966 682

314- 7 a)

40.7:k5.0 a)

234-11

29.24-2.1

22 --> 20 22 ~ 40

879 682

204- 8

39.8 ~k6.6

144-17

18.7:k2.8

32 ~ 20 32 -+ 40

962 765

381-- 9

43.4:~3.5

454-36

30.5 q-4.9

42 --~ 20 42 --.'-40

1069 872

604-20

IiKi -+ IrKf Kili -+ Ir'K~

E(Ii --~ 1~) E(If -+ If')

22 ~ 00 22 -~ 20

966 879

22 -+ 00 22 ~ 40

weighted average

Ludington et al. 9)

55.84-5.6 41.9 ~: 3.5 b)

") These z2 values were calculated from the reported B(E2) ratios. b) The average does not contain the unreported z2 for the 2-+0/2-+4 ratio.

538

G. E. KELLER AND E. E. ZGANJAR

modify the adiabatic B(E2) ratios to include vibration-rotation coupling are from the non-adiabatic symmetric-rotor model 11,1z). The z z mixing parameter determined by equating the adiabatic B(E2) ratios to the experimenfal values are listed in column 6. The uncertainty in the z z values are the deviations caused by the uncertainties in the experimental B(E2) ratios. As is evident, a consistent set of z2 values has not been obtained. This result is in agreement with that of Ludington e t al. 9) where the corresponding z2 values show a similar trend. The zz values calculated from the data of Jaklevic e t al. ~) are widely varying and also show a trend similar to that of this work. In the recent investigation of Gunther et al. 1o) a consistent set of z2 values, with an average of (41.9+3.5)x 10 -a, was obtained. These comparisons are summarized in table 5. In view of the divergence of the z z values determined in this investigation and the consistency obtained by ref. lo), a re-examination of the measured quantities was made to determine possible error contributions to the B(E2) ratios. The determination of the 7-ray intensity of the 682, 765, 962 and 966 keV transitions involves some experimental difficulty. It can be seen in fig. 2 that the 682 and 765 keV photopeaks appear on the Compton edges of the 879, 962 and 966 keV transitions. Due to the low intensity of these peaks, an error in the estimate of the underlying Compton background could lead to an appreciably error in the area determination and consequently in the intensity. This error could be expected to be greater for the very weak 682 keV transition. A straight line estimate of the background under the peak is made in the computer analysis. In order to consider the exact shape of the Compton edge, the Compton distributions produced by the 834 keV transition in S4Mn and the 898 keV transition in 88y were used to artificially reproduce the shape of the Compton distribution of the 879 keV transition. The reference shapes were recorded at the same gain setting (keV/channel) as the 16OTb spectra, and were then gain-shifted and normalized so that a best fit point-bypoint correspondence with the Compton distribution adjacent to the 682 keV peak was achieved. The results of this procedure are displayed in fig. 5. The circular points are those obtained from one of the 16°Tb spectra and the triangles represent the reference Compton edge, gain shifted and normalized as described. The straight line shown is that which was used to estimate the underlying Compton in the photopeak analysis on the computer. The straight line estimate leads to a value for the area (intensity) which is 2 ~ larger than the value obtained from the reference shape. For the 765 keV transition, the uncertainty introduced by the straight line estimate of the Compton edge would be much smaller than for the 682 keV line since the 765 keV transition is more intense. The small intensity uncertainty, introduced by the background problem, cannot significantly affect the B(E2) ratios computed using the 682 and 765 keV 7-ray intensities. The intensities of the 962 and 966 keV 7-rays were determined from the coincidence experiments outlined in sect. 2. The photopeak of the 962 keV transition was not completely reso!ved from the photopeak of the 966 keV transition in the singles

16°Dy BAND MIXING

539

spectra (fig. 3). The coincidence experiments excluded one or the other of the 962 and 966 peaks and the intensity of each was determined relative to the intensity of the 879 keV transition. In the computation of B(E2) ratios, all interband transitions were assumed to be pure E2. However, it is possible for the 962, 879, 872 and 765 keV transitions to have M1 components. The assumption that the 962 and 879 keV transitions are pure E2 is consistent with the experimental conversion coefficients in table 1 and the directional correlation results of refs. 2, 3, 6- s, 23) which indicate that any M1 component is less than 2 %. There is no conversion electron information available for the 872 keV transition, but the eK of the 765 keV transition indicates an M1 component of TABLE 6 The comparison of the photon intensities of the interband transitions. The normalization is to the sum I~,(879) +Iy(962) +I7(966) Transition (keV)

Jraklevic et al. 8)

682 765 872 879 962 966 1069

0.515 (69) 1.78 (62) 30.2 7.9 26.7

(44) (20) (30)

Ludington et aL 9) 0.544 2.03 0.174 30.0 10.2 24.7 0.076

(50) (18) (35) (7) (15) (8)

Gunther et aL lo)

0.653 (47) 2.20 (7) 29.4 9.98 25.4

(5) (53) (5)

Present work 0.532 1.91 0.282 29.7 9.91 25.2 0.112

(15) (3) (20) (3) (69) (5) (8)

40+ 12 %. However, if the y-ray intensity of the 765 keV transition is reduced, the resulting z 2 value (fourth row, last column of table 4) becomes even smaller; and if it is reduced as much as 40 % z 2 becomes negative. It is interesting to note in this regard that the c~K for the 2 + --* 4 + 682 keV transition, ( 8 : 9 0 . 3 ) x 10 -3, is considerably higher than the theoretical E2 value of 5.8 x 10- 3. A 5 % M3 component is required to account for the high eK of the 682 keV transition. It seems more likely that there is an error in either the relative electron intensity or in the relative y-intensity. The interband 7-ray intensities reported here and those of refs. a-1 o) are compared in table 6. The normalization is to the sum I~(879) + I~(962) + I~(966). Considering only the 682 and 765 keV transitions, the present results lie between the results of refs. s, 9) with closer agreement to ref. 9). A weighted average of the results of refs. a, 9) yield 0.534_+0.040 and 2.01_+0.17 for the intensity of the 682 and 765 keV transitions respectively. This is in good agreement with the present results of 0.532_+0.015 and 1.91 __.0.03. The agreement of these results and those of ref. j o) is not as good, especially for the 682 keV transition, It appears that Gunther et al. 1o) 'obtained y-ray intensities for the 682 and 765 keV transitions by comparing the 682/879 and 765/879 K-shell electron intensities arid then using theoretical E2 conversion coefficients to compute the y-intensity relative to the y-intensity of the 879 keV transition. Gunther

540

G. E. KELLER AND E. F, ZGAN,IAR

et al. 10) quote ( 1 0 . 1 + 0 . 3 ) x 1 0 - 2 a n d (3.78_+0.26)x10 - 2 for the 765/879 a n d 682/879 K-shell electron intensity ratios. The c o r r e s p o n d i n g values o f E w a n et al. 4) are (12.1 _+ 1.1) × 10 - 2 a n d (4.9_+ 1.5) × 10 -2. Obviously the use o f these latter values w o u l d m a k e the d i s p a r i t y even worse. T h e results o f this investigation show t h a t the v a r i a t i o n in the b a n d mixing p a r a m eter is real. This is in a c c o r d with the results o f Jaklevic et al. s) a n d L u d i n g t o n et al. 9), b u t n o t with the set o f z 2 values r e p o r t e d by G u n t h e r et al. 1o). The source o f the disa g r e e m e n t with G u n t h e r et al. is the y-intensity o f the 682 a n d 765 keV transitions since the z2 d e t e r m i n e d f r o m the 966-879 keV intensity r a t i o (first r o w table 5) is agreed u p o n b y all. i t is possible, t h o u g h n o t likely, t h a t the ~r~ o f the 765 keV transition is higher t h a n the theoretical E2 value because o f a sizable M1 c o m p o n e n t . I t is h a r d l y likely, h o w ever, t h a t the 682 keV t r a n s i t i o n has a 5 % M3 c o m p o n e n t . H i g h r e s o l u t i o n electron s p e c t r o s c o p y a n d possibly C o m p t o n suppression y-spectroscopy s h o u l d be p e r f o r m e d in o r d e r to clarify these discrepancies. I t is n o t felt, however, t h a t such clarification will affect the conclusion, derived f r o m the results o f this investigation, t h a t the pert u r b a t i o n a l a p p r o a c h t o b a n d m i x i n g is n o t a p p l i c a b l e to the 16°Dy n u c l e u s . W e wish to t h a n k Mr. M a r k W a l t o n for his assistance with the c o m p u t e r p r o g r a m s .

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) !2) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23)

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