- Email: [email protected]
Nuclear orientation study of the decay of 171Lu
Nuclear Physics @ North-Holland
A440 (1985) 203-227 Publishing Company
NUCLEAR T.I.
ORIENTATION
KRACiKOVA,
STUDY
S. DAVAA,
OF THE DECAY
J. KVASIL,
M. FINGER
and
OF “‘Lu
J. KONicEK
Join? Institute for Nuclear Research, Dubna, USSR and W.D.
HAMILTON
Physics Division, University of Sussex, Brighton BNI 9QH, UK Received
16 November
1984
Abstract: The levels and -y-ray transitions in “‘Yb have been studied by radioactive decay of oriented “‘Lu. The orientation was produced using the hype&me field in ferromagnetic gadolinium to polarize an ensemble of “ILu nuclei at a temperature of 14 mK. The directional distribution of the y-rays was measured using high-resolution Ge(Li) detectors. Anisotropies of 30 y-rays in “‘Yb were measured. Multipole mixing ratios were deduced for most of the mixed y-ray transitions and unambiguous spin assignments were made for several levels. The energy and structure of the rotational band levels, reduced E2 and Ml transition probabilities and E2/ M 1 mixing ratios were calculated using the semi-microscopic quasiparticle-phonon with a Coriolis interaction. In general, good agreement is obtained between the theoretical tions and experimental results.
E
model predic-
RADIOACTIVITY “‘Lu [from Ta(p, X)]; measured y( 0), oriented nuclei. “‘y-b deduced levels, J, T, 6, y-multipolarities, B(A). Chemical, mass-separated target, Ge(Li) detectors. NUCLEAR STRUCTURE “‘Yb; calculated levels, J, n, B(A), 6. Quasiparticle-phonon model including Coridlis interaction.
1. Introduction The levels of “‘Yb
have been studied
extensively
from the decay of “‘Tm
and
“‘Lu and by the (d, p), (d, t), (d, d’), (p, t), ((Y, 3n), (3He, (Y) and (n, y) reactions I-*). The y-ray multipolarities have been deduced from internal-conversion coefficient measurements ‘72V4,5) ; directional correlations for four cascades have been measured by Sen and Bakhru 3). Low-temperature nuclear orientation of “‘Lu in a ZrFe, host has been investigated by Krane et al. 9). In their experiments, the “‘Lu activity was produced by irradiation of natural ytterbium. Significant disagreement is observed between the multipole mixing ratios obtained by Krane et al. and those deduced from the internal-conversion coefficients (ICC), of the low-energy y-rays. The most extensive decay schemes of “‘Lu have been proposed by Batsev and Bench-Osmolovskaya “) and Adam et al. 5). The transition and level energies listed in the latter have been used in the present work. 203
204
T.I.
Kracniova’ et al. / Nuclear orientation srudy
The “‘Yb levels have been identified with Nilsson configurations on the basis of the single-particle transfer-reaction studies of Burke et al. 6*7). Lindblad et al. “) observed the $+[633], $-[521], $-[512) and ?-[SOSj bands up to high-lying levels in the (ty, 3n) reaction. They paid particular attention theoreticaIIy to the positive-parity band. The rotational energies within this band, experimental E2/Ml mixing ratios and the cross sections obtained in transfer-reaction experiments were successfully explained within the non-adiabatic unified model with pairing and Coriolis interactions included. They found it necessary to reduce the Coriolis matrix elements for orbit& near the Fermi surface. In recent publications ‘o-‘3), we have reported investigations on the decays of ‘$‘Lu and ‘69L~ polarized at low temperatures in gadolinium hosts. The level structures of ‘67Yb and ‘69Yb were described within the semi-microscopic quasipartitle-phonon model of Soloviev ‘“) including Coriolis mixing 15),and in the present work we report on a similar investigation of the properties of “‘Yb.
2. Experimental details A radioactive source of 17’Lu (T,,* = 8.2 d) was produced by a spallation reaction on tantalum using the 10 GeV proton beam of the Dubna synchrophasotron. After chemical separation of the lutetium fraction, the “‘Lu isotope was selected by a mass-separator and implanted into pure (99.9%) gadolinium foil. This was melted in vacuum onto a tantalum foil which was then soldered to a copper foil using titanium-silver solder. The sample was finally formed into a disc of diameter 0.5 cm and was soldered to the refrigerator heat exchanger. The details of the lutetium-ingadolinium source preparation are described by Kracikovd et al. lo). The admixture of the ‘72Lu (T,,, = 6.7 d) activity in this source was less than OS%, while the admixtures of other Lu isotopes were considerably smaller. The sample was cooled using a top-loading ‘He:%e dilution refrigerator which operated at a base temperature of 14(2) mK. The sample was polarized with an external field of about 1 T. Data were recorded at 0” and 180” with respect to the orientation axis by two Ge(Li) detectors, both located 8.0 cm from the source. The y-rays with energy below 200 keV were recorded by a planar 200 mm’ x 7 mm X-ray detector with a resolution of 0.55 keV at 122 keV. A 53 cm3 coaxial detector with a resolution of 2.9 keV at 1332 keV was used to detect the y-rays with energy up to 1350 keV. Typical y-ray spectra measured with these detectors are shown in fig. 1. The y-ray spectra were analysed to give the areas of the y-ray peaks using the program SIMP 16). As may be seen from fig. 1, three peaks are multiplets of 17’Lu y-rays and X-rays of lead: these are 72.4y+72.81(,,, 75.OK,, +75.9y and 84.4KBj + 84.9K,, + 85.6 y-t- 87.3K,;. The areas of the 75.0, 75.9 and 85.6 keV peaks were evaluated by the program, whereas the area of the 72.4 keV peak was obtained by
205
T.1. KractIova’ et al. / Nuclear orientation study
subtracting the area of the 72.8 keV peak which was determined using the area of the 75.0 keV peak and the known intensity ratio of the 72.8 and 75.0 keV X-rays I’). 3. Data analysis The y-ray counting rates were analysed according to
W(e) = C
~~~Z)u~A~Q~p~ (cos 8) ,
(1)
Aeven
where the orientation coefficients B,(I) depend on the temperature and strength of the interaction between the orienting magnetic field and the nuclear magnetic moment, and the factors QA correct for the detector solid angle and PA are Legendre polynomials. The correlation coefficient is defined as A~=[F~(LLZ~Z~)+2SF~(LL’Z~Z~)+S2F~(L’L’Z~f~)](l+6*)-‘,
(2)
where the Fh are the angular-momentum-coupling factors, L’ = L + 1 and S is the amplitude ratio of the L + 1 to L multipole components in the transition. The y-ray mixing ratio S is defined in terms of emission matrix elements I’). The deorientation coefficients U, account for intermediate transitions: for y-radiation, they are given by U*(ZiZ~)=[U*(ZiZfL)+62U*(ZiZrL’)](1+S2))1~ If there is a low-energy highly-conveyed u
A
(z.z.e I fr
(3)
transition, the U, coefficient is written as
y~=(l+P)~*~ziz~L)+SZ(l+ar)U,(ziz~L’) ,
(l+p)+6*(1+1y)
’
(4)
where fy and p are total internal-conversion coefficients of the L+ 1 and L multipole components, respectively. The angular-momentum-coupling coefficients U, ( ZiZfL) and Fh are tabulated by Krane 19). The deo~entation coefficients U,, have been calculated on the basis of the decay scheme of Adam et al. 5, and all available data including the present results. For the low-energy transitions, we have used eq. (4) and theoretical ICC values of Band and Trzaskovskaya *‘) for the K, L and M shells and of Rose1 et al. “) for the N and 0 shells. The U, values obtained are given in table 1. The uncertainties quoted result from the uncertainties in the transition intensities and in mixing ratios. The decay level of “‘Yb including our results is shown in fig. 2. 4. Experimental 4.1. GAMMA-RAY
results
ANISOTROPIES
The measured y-ray anisotropies, 1 - W(O’) and 1 - W(180”), were corrected for the solid-angle factors Q2 and averaged. Initially we shall assume that the fourth-
T.I. Kracikovd et al. / Nuclear orientation study
206
6’761
NO
x
t--
m
13NNt’HI
t13d
m
SINnO
-=fz
m
7X Krucikovci et al. / Nuclear orientation study
OZZQ
O’LCS\
Z‘ZBZL
8LLS 9’867 -
:
0’866 S’S86 s
13NNVH3
ti3d SiNI
*o
208
T.I. Kracikovd et al. / Nuclear orientation study
209
TI. Kracikooa’ et al. f Nuclear orientation study TABLE 1 Deorientation coefficients for “‘Yb
levels
Level energy
Level energy
[keel
[kW
66.1 75.9 95.3 122.4 167.7 208.0
0.325 0.602 0.700 0.633 0.786 0.772
* * * f f i
0.032 0.005 0.002 0.021 0.002 0.026
230.6 246.6 259.1 317.3 449.6
0.707 f 0.025 0.675 f 0.062 0.878 zt 0.007 0.866*0.017 0.877 * 0.008
order orientation coefficient is negligibly small and base our analysis only on the B2U2A2 values. This assumption is subsequently justified. The anisotropies of 30 transitions
in “‘Yb
4.2. EVALUATION
obtained
OF THE
are listed in table 2.
B,(I)
COEFFICIENT
Two intense El transitions of 739.8 and 780.7 keV have been used to evaluate the initial-state orientation. These i-+ G’ and f- + 4’ transitions, respectively, were selected because they are known from conversion coefficient measurements 2,4*5)to contain vanishingly small M2 admixtures and because the A2 coefficient of the Al = 0 transition is considerably less sensitive to a given amount of M2/El mixing than is the Al = 1 transition. Moreover, the levels depopulating by these transitions TABLE 2
The measured
B,
55.7 66.7 72.4 75.9 85.6 91.4 109.3 194.9 498.8 517.8 627.0 631.0 667.4 689.3 712.6
anisotropies
of y-rays
B, 44
&A2 [%]
19110 6.6 f 2.3 4O.Oi 8.7 -3.7 f 1.o 39.9+3.8 39.4* 8.0 32.6 f 3.6 -24.6k7.4 19116 42.8 f 4.8 -29.2 i 2.2 -6.3 f 9.3 9.39 * 0.73 12.16*0.80 48.5 f 2.5
in “‘Yb
739.8 167.6 780.7 794.0 825.9 839.9 853.0 862.4 868.4 902.2 948.7 985.6 998.0 1209.8 1282.2
WI
-23.22 f 0.68 -4.3* 1.1 -25.5 1 * 0.54 -22.5 * 6.9 -31.0*9.0 57.1*2.2 16.31 1.3 13*10 -26.3 f 9.4 25.0+ 3.0 -12.6k5.6 16+ 16 34* 17 -6.7 + 9.0 -19.1*3.0
210
T.I. Kracikova’ et al. / Nuclear orientation study
are fed only by the B-decay. Averaging the corresponding values of B2(I) for these transitions, we obtained B2(I)= 0.636 f 0.015. It should be noted that this evaluation is independent of the fourth-order term since A, = 0 for an E 1 transition. On the basis of the known magnetic moment ]~(“‘Lu)l= 2.04 (10) n.m. [ref. ‘)I and the internal field B = 55 (6) T which we obtained by measurement of the anisotropy temperature dependences for the y-rays of ‘72LuGd, we would expect B2(I)= 0.8 f 0.2. The corresponding fourth-order coefficient is thus at most B4(I)0.15and since in nearly all the analysed transitions the U, coefficients of intermediate transitions are small or identical to zero, we are justified in neglecting the fourth-order contribution. The only exceptions are the 194.9, 7 12.6 and 825.9 keV transitions and they were corrected for the fourth-order term. Two low-lying levels in “‘Yb have long half-lives. One may expect therefore substantial perturbations of the directional distributions owing to changes in the relative populations of the magnetic substates arising from the interaction of the nuclear electromagnetic moments with the surrounding electromagnetic fields during the long half-lives of these levels. Thus substantial attenuations of the directional distributions may be expected for transitions which depopulate directly and indirectly the 95.3 keV level, T,,2 = 5.25 ms [ref. 2)], and probably the 122.4 keV level with T,,, = 265 ns [ref. ‘)I. The anisotropy of the low-energy 19.4 keV transition which only depopulates the 95.3 keV level was not recorded in our measurements. The 75.9 and 66.7 keV levels are strongly populated from the 95.3 keV level and also from the 122.4 keV level. Analysis of the anisotropies of the Ml + E2 66.7, the pure E2 75.9 and the M 1+ E2 55.7 keV transitions, using the above value of B2 and the calculated U2 coefficients, gave the attenuation factors G2(67 keV) = 0.32 f 0.12 ,
G2(76 keV) = 0.18 f 0.05 ,
for the 66.7, 75.9 and 122.4 keV levels, respectively.
G2(56 keV) = 1.Of 0.6.
In this analysis,
magnitudes
of
the mixing ratios of the 66.7 and 55.7 keV y-rays were evaluated from the ICC data, while the signs were determined in the present work. The deorientation coefficients for the M 1 + E2 9.15 and the El + M2 19.4 keV transitions, U, = 0.500* 0.006 and U2 = 0.867+ 0.007, were calculated using eq. (4) and the values of S2 = (3.4* 1.1) x 10e4 and 62 s 1.5 x 10e5, respectively, which were obtained from the results of the conversion electron measurements 22-24) re-analysed by Dzelepov 25). The half-life of the 122.4 keV level is much smaller than that of the 95.3 keV one and accordingly the external perturbation of the 122.4 keV state, if it exists at all, may be expected to be smaller. The large uncertainty in the 55.7 keV y-ray anisotropy does not allow us to make a final conclusion.
4.3. MIXING
RATIOS
The correlation coefficients A2 were evaluated using the measured B2 U,A, given in table 2 along with deduced B2 and calculated U2 values.
values of In several
T. I. Kracikovci et al. / Nuclear a~ie~~~iio~study
211
cases the A2 coefficients were determined independently of assumptions on B,(f) and lJ,(p, y) by comparison of an El transition anisotropy with the anisotropies of other transitions from the same level. Weighted average values of K-shell conversion coefficients QK have been determined from the experimental results given in refs. ‘-‘). Values of Is( were calculated from experimental conversion coefficients ffK and these were used to distinguish between possible solutions of eq. (2). The values of A2 and multipole
TABLE The correlation Level energy
I”
[keVl
’
66.7 122.4 167.7 208.0 259. I 317.3 835.1
coefficients
E,[keYl
G’
66.7 “f 55.7 72.4 85.6 91.4 109.3 194.9 517.8s) 627.0 b, 661.4 b, 712.6 ‘) 739.8
3
A, and the deduced
multipole
0.92 f 0.46 0.47 f 0.26 0.80*0.18 0.813*0.084 0.71 zto.14 0.592 f 0.068 -0.45*0.14 0.804 f 0.093 -0.549 + 0.044 0.177*0.015 0.9 1 I f 0.054 -0.458 f 0.017
902.2
0.600 * 0.073
935.2
767.6 839.9 868.4 498.8 631.0 689.3 780.7 825.9 853.0
-0.073 *0.019 0.97 1f 0.044 -0.47 f 0.17 0.33 f 0.27 -0.11*0.16 0.210*0.014 -0.420 f 0.015 -0.53*0.16 0.281*0.023
1024.6
1080.9 1093.3 1377.5
794.0 948.7 985.6 862.4 998.0 1209.8 t 282.2
b, b, b, ‘) b)
-0.44*0.13 -0.25 f 0. I 1 0.29 * 0.29 0.22*0.17 0.58 i 0.29 -0.13*0.18 -0.371 * 0.059
“) External perturbation of the 122.4 keV level was taken perturbed, we obtain a(67 keV) = -0.6fy:$ b, A, is deduced independently of B,(I) and U,(& y).
ratios Multipole mixing ratio
A*
902.2
944.3 948.3
mixing
into account.
-0.61:; -0.05 * 0.15 -0.31:;:;; -0.30? 0.07 06 -0.25 ?09 0.1I -0.16*0.04 0.01*0.13 0.54+:;(; 0.76’;:;; 0.016*0.010 -1.52*0.16 0.030 * 0.025 -0.06 * 0.05 -1.52+0.16 -0.477 f 0.025 -0.48’$$ 1.5?70s 0.1*0.2 2.o+‘-4 0.7 0.029 f 0.009 -0.033 f 0.024 0.09*0.16 0.011*0.012 1.1*0.4 { o.o*o.z 0.32 f 0.07 0.1*0.2 0.04 f 0.09 -0.16+“.‘6 021 -0.20’$; -0.08 f 0.07 If this level is not
T.1. Krackova’ et al. / Nuclear orientation study
212
TABLE The S-values
obtained deduced
4
in previous nuclear orientation and yy correlation studies and the /~?(a~)/ values from the experimental ICC data compared with the present results Multipole
E, [keYI
present
work
55.7 66.7 72.4 85.6 91.4 109.3 498.8 517.8
-0.05 * 0.15 -0.6 “f: ‘: -0.3 I”“, 1: -o.30’*.06 0.“7 -0.25 z;::‘: -0.16*0.04 0.1 rto.2 0.54:;;;
627.0
0.16 “’0.,9 ”
63 1.O 667.4
2.0” 4 O.O16ji4;.010
689.3
0.029 f 0.009
712.6 739.8 767.6 180.7
-1.52i0.16 0.030 * 0.025 -0.477 i 0.025 -0.033 f 0.024 1.1 Ito. { 0.010.2 -0.48 “-::“,; 0.011 r0.012
794.0 839.9 853.0 868.4
a
ratio
)
2.0”5O -0.,0:&6 -0.07 i 0.05 -0.22+;:;: “) -0.08 & 0.04 1.2?‘.7 07 1.3rto.3 { I.1 r;.:q 0.003 rt 0.014 0.015iO.016 0.146 i 0.004 d, -2.1 izo.4 0.02 IQ09 0.08 -0.34 i 0.08 -0.03 I 0.06 0.61 2tO.13 d, 0.43 “z.;: d) -0.5 1 z:.;: -0.029 i 0.014
isto
902.2
i
948.7 998.0 1282.2 “) Ref. 9), b, The magnitude
mixing
15
Transition
of &value
deduced
-0.06 i”d.05 -1.52*0.16 0.32 + 0.07 -0.16:;;: -0.08 i. 0.07
IS(ff,)l
Y
0.057 * 0,004 ‘) 0.696 * 0.013 ‘) 0.296 i: 0.006 ‘) 0.262*0.013’) 0.29 * 0.02 ‘) 0.20 * 0.03 0.38ztO.12 0.52 * 0.07 0.63*0.11 1.1*0.2 co.03 0.0s r;;: 1..541:0.08 El 0.56+E El 0.410.3 OSO* 0.06 SO.05 1.7:) OS 4 ~1.85’)
0.12:~::
0.5910.13 0.3 * 0.3 0.06 “O “’ U.“h
from the weighted averages of the y-ray and conversion electron
intensities available. ‘) Ref. 25). d, Re-analysed value of Sen and Bakhru 3). For the 794.0 keV transition measured in correlation with the 154.8 keV y-ray, two values of S were obtained depending on positive or negative values of (&(a,, 155 keV)/ =0.62*0.12 used in the anatysis.
ratios 6 giving the best agreement with the IS(cuK)I values are listed in table 3. Table 4 shows a comparison of our results with those of Krane el al. 9), with the results of Sen and Bakhru ‘) re-analysed by us, and with the values of 16(tuK)/. The A2 coefficient for the 66.7 keV transition was evaluated using the orientation coefficient corrected for the external perturbations of the 75.9 and 122.4 keV levels,
mixing
T.I. Kract’kovd et al. / Nuclear orientation study
213
i.e. Z3$(67 keV) = *
f3:(122)U,(y56)++ 56
where
B,*(76) Z-U ~9) , 56
9
Bf = B2lJ,G, and Z = Z, + Z, is total transition
9
intensity.
Large uncertainties
in the 55.7, 66.7 and 75.9 keV y-ray anisotopies result in the value of S(67 keV) = -0.6?7:: which agrees with 16(ak)j, but leaves an ambiguity in the sign. However, comparing our experimental value of A2(67 keV) = 0.92 f 0.46 with those calculated with negative and positive values of IS( ak)I = 0.696 * 0.013, A*(6(aK)< 0)= 0.986* 0.003 and A2(?I( aK)> 0)= -0.638 + 0.013, we conclude that mixing ratio of the Ml + E2 66.7 keV transition is S = -0.696*0.013. If we do not take account of the external perturbations, our value of A2 = 0.32 f 0.12 yields 6’ = 0.10 f 0.07 and 8* = -2.2 f 0.4 which disagree completely with the ICC result. It is seen from table 4 that our mixing ratios are in excellent agreement with the Is(a,)( values, but significant disagreement is observed with the results of Krane et al. ‘) particularly for the low-energy y-rays. It should be noted that Krane et al. have not observed the external perturbation of the long-lived levels in “‘Yb. Their anisotropies of .the 66.7 keV transition yield the values of A*(4 mK) = -0.64 f 0.33 and A2(20 mK) = - 1.86 * 0.43 which disagree with each other and with our result. These discrepancies may be explained by (i) the complexity of their source (by our estimation this contained a large admixture of about 50% of “*Lu, a substantial one of “‘Lu and some ‘73Lu impurity), and (ii) they were unable to resolve the very complex spectrum of ‘7’t’72+‘73t’77L~ in the low-energy range with their coaxial Ge(Li) detector. If we do not make the correction for the X-rays, our values of 6(72 keV) = -0.08 + 0.03 and a(86 keV) = -0.15 + 0.07 agree with those of Krane et al. 9), see table components
4. The
109.3, 627.0 and 712.6 keV y-rays
of the complex
the corresponding
&values
peaks containing are slightly
were also measured
the “*~“‘Lu y-rays;
different
therefore
as
probably
from our results.
After we re-analysed the data of Sen and Bakhru ‘) taking account of the fact that the 85.6 y-ray is not a pure Ml transition, their results (see table 4) agreed except for the value of 6(M2/El) for the with the present ones and with IS(a 4- + ?’ 689.3 keV transition. It seems that the 689- 164 keV cascade was not measured correctly by Sen and Bakhru since we obtained A*(689 keV) =0.017*0.007 from their result, while the corresponding theoretical is Aih= 0.288 for a pure El transition.
4.4. SPIN
value of the correlation
coefficient
ASSIGNMENTS
Spin assignments to excited states in odd-A nuclei are always a difficult task. Internal-conversion data, while indicating the multipolarity and type of radiation, usually allow a range of possible values for the spin of one state relative to that of the other, and the feeding and decay modes of the level must be used to restrict the choice. Directional-correlation experiments are also limited in odd-A nuclei
T.1. Kracikovd et al. / Nuclear orientarion study
214
since the number of unknown parameters describing the yy cascade usually exceeds the number of measured correlation coefficients and much additional information is required for a complete evaluation. On the other hand, nuclear orientation data involve only the A, coefficients and if one of the level spins is known then often both the multipolarity of the radiation and the other spin value may be obtained. It is true that the evaluation also depends on calculating the U, coefficients but, with a careful choice of the initial conditions for analysis, little ambiguity enters and even this may be subsequently removed by an iterative process until the complete data set has been evaluated. In this way one may make unique spin assignments which are directly based on measurements. 4.4,l. The 902.2 keV level, Ix = $-. This level decays only to the fP ground state by the Ml(+E2) transition 2-5). The large anisotropy of this 902.2 keV transition measured in the present work excludes spin i; for I = $ there is no orientation. Spin 2 is also impossible since the value of ASXP= 0.499 * 0.055 is inconsistent with Aih($+$ = -0.535 indicating that the 902.2 keV y-ray cannot be a pure E2 transition. Thus, we confirm the s- assignment proposed by Burke et al. “). 4.4.2. The 944.3 keV level, I” =$-. The decay scheme and transition multipolarities
indicate
transition
to the $- state yields a mixing
that this level should
be $- or $-. The anisotropy ratio S = 1.5’::: in agreement
of the 868.4 keV with jS( CY~)I=
1.7$:, if the level is assigned 5, while there is no solution of eq. (2) for a $- assignment. 4.4.3. The 1024.6 keV level, I” =f-. This level was assigned $- by Sen and Bakhru 3), while Batsev and Bench-Osmolovskaya “) and Adam et al. ‘) made a $assignment based on the Ml multipolarity of the weak 707.5 keV transition to the g- state. Sen and Bakhru have measured the directional correlation of the 794155 keV cascade. As their value of the a4 coefficient gives no additional information and the magnitude of Ii3(czK, 794 keV)I = 0.4* 0.3 agrees with any of the S-values obtained for the sP or s- assignment (I” = $-: 6 = -0.13 kO.04 and 6 = -0.20*0.02 for 6((r,, 155 keV) >O and ~0, respectively; I” =:-: see table 4), there is no possibility for making a choice. However, our result for I” =$-, 6(794 keV) = -0.53’:::& does not agree with that of Sen and Bakhru and the 3m assignment is preferable. Moreover, the anisotropy of the 948.7 keV transition yields 6 = 0.32 * 0.07 for a sor S=ll’:‘, if the level is assigned i-, while 6 = 0.18 * 0.09 or 6 = -2.6’::: assignment. The first value of 6 is in better agreement with IS((Y,J = 0.59kO.13 and spin s is also favoured. 4.4.4. The 1080.9 keVleve1, I” =4-. This level was assigned s-(3-) by Batsev and Bench-Osmolovskaya 4), while Adam et al. ‘) proposed a <- or E- assignment. The multipolarity of the 1005.0 keV transition to the gP state, Ml + (43 f 13)% E2, is not consistent with a z- assignment. Spin $ may also be ruled out as the observed anisotropy of the G-+ g’ 985.6 keV transition yields an admixture of M2 2 20%, which is unacceptably large. 4.4.5. The 1093.3 keV level, I” =F. The level was tentatively proposed Balalayev et al. 26) and supported by the yy- and ey-coincidence measurements
by 3,4).
T.f. Kracr’kova’et al. / N&ear orientation study
215
A 3’ or %’ assignment was suggested on the basis of the transition multipolarities “). Spin $ may be excluded since the anisotropy of the 862.4 keV y-ray is not consistent with the El transition: AzXP= 0.26 f 0.19, while Aih(z+ z) = -0.436. The spin-parities ofthe 167.7,208.0,259.1,317.3,835.1,935.2,948.3 and 1377.5 keV levels assigned previously are confirmed by the present results. The excellent agreement of our results with the ICC data shows that the assumptions made in evaluating the U, coefficients are good. 5. Comparison with theory 5.1. INTRODUCTION
has been shown recently “-‘3) that the semi-microscopic quasiparticle-phonon model of Soloviev 14), with a Coriolis interaction included I’), may be applied to a well-deformed odd-A nucleus with considerable success in describing a wide range of nuclear properties. Formally the model describes the nucleus in the adiabatic approximation and the hamiltonian can be thus divided into two parts representing the intrinsic motion of the nucleus and its rotation: It
ri = fii”t + ii,,, *
(5)
In the quasipa~icle-phonon model “*27) the intrinsic hamiltonian includes the hamiltonian of the axially-symmetric nuclear field described by a Woods-Saxon potential and residual (pairing and multipole-multipole) interactions. The eigenvalues Ek and eigenfunctions @p(K,) of fiiit are determined by solving the secular equation for the odd nucleus, so that @(KY) contain the single-quasiparticle and quasipa~i~Ie-plus-phonon components with amplitudes “*‘4) Ck and D$$, respectively. The parameters of I;i,, were chosen according to ref. 27). The rotational part of the hamiltonian (5) was taken as a quantum-mechanical rotor 28). In the case of axial symmetry of the average nuclear field, the rotation of the nucleus may be described by only one moment-of-inertia parameter. Different values of this parameter observed for various rotational bands in a given nucleus may be explained by non-adiabatic effects I’). The latter were included by Kvasil et al. 15) and the non-adiabaticity parameter used in the present calculations, B = 0.05 MeV-‘, is the same for ‘67*‘69Yb[refs. “*‘2)]. The eigenvalues of the total hamiltonian (S), &PF are determined by diagonalization basis of functions
= Ec*;M,
(6)
of the matrix for a given value of spin I in the
216
T.1. Kracikovd er al. 1 Nuclear orientation study
where DLK
are the Wigner
functions
and Z?,(n)
is the operator
of a rotation
of T
around the y-axis. The non-zero off-diagonal matrix elements arise from the Coriolis interaction which is included in the rotational part of the hamiltonian (5). The number
of the basis functions
(i.e. a dimension
of the matrix diagonalized)
is limited
by a final set of the states near the Fermi surface of a given nucleus. The following functions were included in the present calculation: $6601, $4001, $6511, $4021, $6421, $6331, 26241 and $5211, $5101, $5211, $5121, $5321, $5121, $5231, $5141, $5031, $5051. Using a double-diagonalization method “,‘5), we obtain the energies E’L of the rotational linear combinations
where b$ are In order to experimental various bands minimising
band levels, and the corresponding of the basis functions:
wave functions
qiM
are
the mixing coefficients. obtain better agreement between the calculated energies Elk and the values, an optimization of the moment-of-inertia parameters for the and the eigenvalues of the intrinsic hamiltonian was carried out by
The reduced transition probabilities were calculated using the standard formula of the adiabatic nuclear model including a Coriolis interaction [see refs. “,‘“)]. The multipole mixing ratio s(E2/Ml) is defined as the ratio of reduced matrix elements with the phase convention of Krane and Steffen “) (9) where
E, is the transition
5.2. RESULTS
energy
in MeV.
AND DISCUSSION
The experimental energies of the levels in 17’Yb and those calculated in the present work are compared in fig. 3 and in table 5, which also contains the calculated structure of these levels. Good agreement (usually within 2%) is obtained. between the calculated and experimental energies of the levels up to spin values of Z = p (see the ground-state rotational band and those based upon the $[512] and $6331 states). The effects of the Coriolis mixing may be seen from table 5 and fig. 4, which Z for some shows plots of the mixing coefficients b,Ik versus angular momentum rotational bands. Substantial Coriolis mixing is seen in some cases which results in a great change of the b$ coefficients. For the negative-parity bands, the $5101 state
11. Kracficova’
et al. / Nuclear
orientation
217
study
! I N
c
I : I
I :
! i
2 0)
I
N
N
;
l?
:I :I II a
i/law)
-AW3N3
?
NOllt’ll3X3
o
0
212
87 162 259 369 505
652 828
208
95 I68 259 369 501
648 826
I;-
f’ 4’ _:!+ &+ q+ 2 17+ f q+
130
122
f-
(1805)
0
66 80 224 249 477 492 817 863 1260 1286 1760 1780
0
of the experimental
67 76 231 247 487 509 832 860 1263 1293
Comparison
TABLE 5
633t 633r
633T 6331 633t 633f 633f
512f
512t
5211 5214 5211 5211 5211 5215 5211 5211 5211 S2ll 5211 5211 $214 5lOf+Q,,
94.8 51Ot+ Q22
642t 6421 642f 642t 642f 642f 642f
94.6
95.5 92.6 89.9 86.8 84.3 81.7 79.1
Qz2
52w+ ~~~ 52lT+ 022 52lT+Q,, 52~+Q,, 52lT+Q,, 52lt+Q,, 52l1+ Qzz 521t+~,, 521f+ Qzz 52lt+Q?? 52lt+
52lf+Q,, 521?+Q,,
95.8 95.8 95.6 95.4 95.3 95.3 94.6 94.8 93.8 86.6 92.7 93.5 88.0
Qz
1.8
14.5 16.2
2.2 4.8 7.2 10.0 12.0
3.4
3.4
5231+ Qzz
1.9
0.7 0.7
65jf+ Qzz 651t+Q,,
0.7
0.8 0.8 0.8 0.8 0.7
Qx
0.7
1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.2 1.2 1.1
1.2 1.2
651t+Q,, 65lt+Q,, 65lf+QX? 651t+Q,, 6511+Q,*
624f +
624r + QX,
5231+
52%+ Qzx =31+ Qzz SW+ Qn 5233. + Qn 5231+Qrz 5231+922 5231+Qx 5231+Qn 5233. + Qx 52%+ 422 SW+ Qzz
intensity
2.0 2.0 2.0 2.0 2.0 2.0 1.9 1.9 1.9 1.8 1.9
Component
[%I
0.1
5211
0.2
0.5 0.5 0.5 0.4 0.4 0.4 0.4
5214.
52ff+ QJ2 521t+QS2 5211+ Qj2 52l~+ ~~~ 52lf+Q,, 52l?+ Q32 521f+QJ2
512t 512f
0.1 0.2 0.1 0.1 0.4 0.3 0.2 8.0 0.3 0.1 3.2
651f 65lf
65lt 65lT 6511 651t
52lL+
52ll+Q,, Qzz
5211+Q:, 52ll+ QZZ
0.3 0.9
0.1 0.1 0.2 0.4
0.1
0.1
0.5 1.2
0.2 0.0 0.5 52lL+ Qz2 52li+ Qua 5211+Q,,
5211+ Qzz 5211+ Qz
0.1 0.1 0.2 0.2
respectively,
QZZ Q2z
52l1+ 52l1+
Qz2, QLOand Q32 correspond,
5121 512T 5127 512t 5121 512t 512f 5127 512T
and calculated energies and theoretical structure of the levels in “‘Yb (the symbols to the 2+y, O’p and 2- octupole vibrations of the even-even core)
V r: 2
F p1 3 B n, 2 % ;.
.“1 ?-
2
21+
958 1001 1056 1142 1251
(945) 995 1052 1144 1254
2iI f-
;s:f %-
(944) (1025) (1128)
935
(867)
984
1120
w93) 1407
3
;+ 3’ 8+ ,:+
T T13+
-1+ :+ I I7+ I9+ i3+ T
$f9-
s-
$-
2
876 955 1070 1106 1362
855 923 958 1103 1137
934
953 1153 1170
891 941 1022 1126
902 958 1025 1128
I-
;-
85Q 954
1013 1266 1452 1698
835 948
1004 1233 1434 1723
$-
23f T $ *7+ T
T
651t 651t 65it 651t 65lt
642t 642t 642t 642t 642t
624t
5234 5235 5233
Slot Slot S!Ot SiOt 510t
s21t s21t 521t 52lf
514J 5141
633t 633t 633t 633t
78.7 40.6 46.0 54.2 55.3
49.6 54.7 69.0 64.5 72.0
95.6
75.4 65.7 67.0
39.6 39.5 38.1 32.6 35.9
19.6 19.3 18.4 19.0
93.6 90.9
77.4 74.5 73.2 70.4
642t 642t 642t 6421‘
651t 651t 651t 65lt 651t
512t+Q,,
42.9 35.6 18.1 9.2
34.6 29.5 13.1 17.4 4.8
2.7
22.6 20.1 20.0
Qzs Qz2 Qzz
52lb 5211+ S215+
54.9 54.8 52.9 45.3 49.8
75.6 74.4 71.2 73.6
3.3 3.2
18.3 19.6 21.6 22.3
512t+Q,, 512t+Q,, 5l2t+ Qzz 512t+Q,, 5l2t+ Qz2
-li+Q,,
521&f 422 5211+ Qzz 52l1+ Qzz
51&+-Q,,
5121+ Qzz
642t 642t 642t 642t
1.2 3.6 4.8 8.4 8.7 4.5 5.1 6.0 6.1
633 t + Qzz 633 t + 422 633t+ 422 633t + 422 633t + Qn.
0.4
1.1 6.4 4.3
0.1 1.6 6.6 3.0
3.6 3.5 3.4 3.5
2.1 4.0
0.7 0.6 0.6 0.6
633t 6331 633t 633t
642t + Q22
512t+Q,, 512t+Q,, 512f + Qzz
5211+Qx
521J+ Qzz 5211+ Qa 5215+Q,,
Qx 6W+ 412 633f + 432 633t + Qsz 633t +
523$ 5233.
651t+Q22 651f+ Qzz 6Slt+ Qa
65lf+Q,, Qs2
Qzz 922 + Qzz + Qzz + Qtz + +
QZZ
65lf+Q,, 651t+ Qzo 651f+Q,, 651t+Qm 6Slt+Qm
633f 633t 633t 633 t 633t
65lt
slot 510f 5lOf
5l2i +
5W+Q,,
5l21+ 422 512&+ Qz2 5121+ Qz2
512t+ Qzz 512t+Q,,
512t+Q,,
512t+Q,,
521t+Qx 521t + Qa
52v+
521t+Q32
7.7 4.0 4.5 5.3 5.4
3.8 3.3 1.5 1.9 0.5
0.4
0.8 4.6 3.1
3.7 3.7 3.6 3.1 3.4
0.1 0.9 3.2 0.8
0.7 1.5
0.4 0.4 0.4 0.4
660t 660t 660f 660t 660f
660f 660t
6@t
660t 660f
642t
5144 5144
523J 5233. 523t
slot slot slot 510f
4x0 6W + Q30 633f +
65lt 651t 651f 651f
1.0 1.9 1.9 6.8 12.2
2.0 1.8 3.6 2.4 5.0
0.3
2.4 2.4
9.4 5.4
1.7
0.1 0.6 2.3 0.6
0.2 0.2
0.4 1.6 0.9 2.3
-
T.1. Kracikovci et al. / Nuclear orientation study
220 ‘.O
I ’
’ 3/2[6513
,____.____.___-____.-_--.----. 1.0
_ ---%
5/2[512]
t 0.5
-
0.0
!-
512 [6L2]
712 [633] 112 [660] 312 [651]
0.0
1.0 712 [633]
0.5
-_----_r,_-_,:::::::;
c
.-----
0.0 r 112 Fig. 4. Dependence
512
__,___ 912
1312
_ ___ .___ 1712
--.-I---.--------. 2112
2512
3,2[624] 2912
values of the mixing coefficients 6 $ on the angular momentum $-[SIO], $75121, $+[642], 1”[633] rotational bands in “‘Yb.
I
for the $+[651],
T.1. Kracikovd
et al. / Nuclear
orientation
221
study
TABLE 6 Experimental reduced E2 and Ml transition probabilities are compared The /3( uL.)~~~ were obtained from measured level half-lives Ii&[ Nn;Ali
f ;[521]
I&f
NnJ],
f $5211
f
$35121
B(E2) [e*.b’] exp theor
exp theor
$
exp theor
f &521]
exp theor
1 t
ev theor exp theor
1.23 f 0.09 1.18 0.88 f 0.09 1.11 0.25 f 0.09 0.32 (8.7 i0.9) x lO-6 3.2~10-~ (1.5kO.2) x~O-~ 8.2 x lO-4 (4.4kO.l) x 10-4 35 x lo-4
with the calculated
values.
I*‘) and S-values B(M1)
[&I
(0.80 f 0.05) x lo-’ 1.2 x lo-2
0.043 * 0.006 0.014
(1.00+0.08) x~O-~ 0.73 x 1o-4 (2.3 f 0.2) x lo-’ 31 x lo-5
is coupled to the %521] and $5231 states. The positive-parity states are perturbed due to strong coupling of the $6601 state with the $6511 and $6421 states. The calculated values of the E2 and Ml transition probabilities and their ratios are compared with the experimental results in tables 6 and 7. Average values of the transition intensities and multipole mixing ratios and the value of Q0=7.93 b [see ref. 2)] were used. Better agreement with experiment was obtained when the orbital and spin gyromagnetic ratios for the odd neutron were changed from the free-nucleon values: gl = 0.1, g, =0.9&r_., gR = Z/A = 0.41. The calculated and experimental values of 6(E2/Ml) are given in table 8; in general the agreement is good. The rotational bands in “’ Yb have been identified and analysed in previous work [see refs. 2,4*5-8)]and we confine the present discussion to several aspects connected with our results. The $5211 ground-state band, observed up to the 9 member in the (C-X, 3n) reaction *), has an irregular level spacing (see fig. 3). In ‘69Yb this irregularity is clearly reflected in the E2/Ml mixing ratios 12): the transitions connecting levels lying furthest apart have large E2 admixture (2 15%), while the close-lying levels are connected by nearly pure M 1 transitions (E2 =S 1% ). There are less data in “‘Yb; however the picture seems to be similar. The 3+ t 66.7 keV and s+ 5 154.8 keV transitions connecting widely spaced levels have within the limits of experimental errors large and approximately equal E2 admixtures, (32.6*0.8)% and (27.8* 7X)%, respectively, whereas the $+ 3 9.15 keV transition connecting the close-lying levels is nearly pure Ml with (0.034* 0.01 l)% E2 [ref. “)I. The agreement obtained between the experimental and theoretical values of transition probabilities and the magnitudes of 6(E2/Ml) is particularly good for this band. The sign of 6 within this band is only available for the 66.7 keV transition and was also calculated
TABLE I Experimental
reduced
E2 and MI transition
probability values
ratios are compared
B(oL;
K[N%Al,
I,- I,)/B(aL;
$5211
$5211
$5121
$5211
c+L
exp
theor
E2 E2 E2 E2
0.28*0.11 0.13 f ‘Z:$ 17.2 i 2.9 50*6 2.9 i 0.4 0.23 f 0.04 3.2+*.’ 1.5 16.7 f 8.5 0.6210.14 2.5 * 0.5 0.46*0.12 2.1 *0.3 0.73 ‘O0 23 s8 0.83*0.13 1.7*0.3 1.0?6OJ 0.6 +a.’ 0.3 3.1 T1.O 0.7
0.29 0.10 2.6 11 4.3 5.3 2.9 4.5 0.92 4.1 0.12 4.5 1.1 1.1 1.1 1.6 1.5 12
E2 $5 121
;[512]
$[514]
$[512]
($5211) >
I,+ 1;)
KJ NnJ], (r,+I‘)l(I,+G)
($5231)
with the calculated
{ Ml E2 E2 E2 { Ml E2 { Ml E2 { Ml E2 E2 E2 f Ml
f[521]
$6331
$6331
;[624]
3[633]
$[642]
;[633]
;[65 I]
$[633]
“) The value corresponds to the second levels (see table 5 and text).
possible
E2
~0.87
E2 E2
4.1* 1.3 24.7
I Ml E2 ( Ml E2 { Ml E2 { Ml E2 E2 Ml E2 E2 { Ml E2 { Ml E2 { Ml Ml Ml Ml E2 { Ml E2 { Ml E2 MI
0.45 ‘0OZI I29 2.1”40.9 1.3 ‘;I: 2.2:;: 0.8” 0.6 s l.1’2409 0.6? 0.5 Sl.3 S3.4
interpretation
1.5zto.5 4.7 ?.a 47 0.36 ?09 0.07 0.30 f 0.02 SO.034 0.012*0.004 SO.09 0.039 f 0.013 3.0+:.: 13::s 4.2?’ 17’:s: 1.s 1.2 ‘;:: f3”504 1.3$ 1.2 0.8 ‘;.; 1.1’2210 of the 1024.6 and
1.2 5.1 4.3 8.8 87 a { 0 76 ) I AJ* “) C:Z “) 1A.L “) {z,!=) {::: “) C:’ “) {I-: “) I:“,? 4.2 0.79 0.67 0.58 15 0.73 23 6.6 25 3.8 2.5 0.95 0.013 0.43 0.005 0.45 1127.7 keV
TABLE 8 The E2/Ml
multipole
mixing
ratios of the transitions
in “‘Yh
are compared E2/Ml
I&[ Nn:A],
4&INnJl,
E, Wfl
66.7 9.15 154.8 85.6 109.3 132.3 55.7 46.5 712.6 627.0 517.8 631.0 498.8 759.2 1255.1 1169.5 66.4 902.2 948.7 794.0 778.0 897.1 881.0 835.9 707.5 877.6 868.4 948.7 794.0 778.0 897.1 72.4 91.4 177.7 178.5 229.3 888.7 816.3 724.9 839.9 761.6 676.2 998.0 925.8 “) b, ‘) d,
with the calculated
mixing
ratio
ev
theor -0.50 -0.037 -0.39 -0.37 -0.35 -0.34 -0.16 0.20 -2.89 1.21 0.32 0.35 0.10 -4.42 -5.10 -0.43 0.58
-0.696*0.013 “) IO.018 f 0.0031 b) 10.62iO.121 ‘) -0.30’0,,~ -0.16+0.04 )1.2+:::1 b) -0.05*0.15 IO.165 *0.0221 b, -1.52*0.16 0.76” 0.19 I4 0.54+0,-:: 2.0+;,‘: 0.1*0.2 12.2+;;1 b) ~~1.0~ b) qo.91 b) 0.31 f 0.07 ‘) -0.06 * 0.05 -1.52*0.16 0.32*0.07 1.1*0.4 0.0 f 0.2 IO.7‘:.:I “) S IO.41b) S ]0.5( b)
2.13 0.021 0.044 0.047 0.059 0.034 0.27 -0.008 0.23 0.16 0.016
I2’PI b, -0b) S IO.31b) 1.5?’ 0,s 0.32kO.07 1.1*0.4 0.0*0.2 IO.7‘;::I b) S IO.41b) -0.31?‘3 o.,s -0.25 -to.” cl.*, -0.32 d, -0.28 d, -0.32 ‘) =-G Il.61 b, IO.6 * 0.71 b, -0s) -0.48 “-;:“o; -0.477 f 0.025 S IO.71b) -0 16:0.‘6 IO:66 2651
Magnitude is the ]S(a,)] value, the sign of which is determined These data are the magnitudes of S-values obtained from ICC. Ref. 2). Ref.‘).
-0.038 0.047 0.017 -0.23 -0.22 -0.21 -0.18 -0.21 -0.43 0.26 0.014 -0.16 -0.079 0.026 -0.31 0.48
b, in the present
work.
values
224
T. I. Kracikova’ et al. / Nuclear orientation study
correctly.
The proposed
structure
of this band
indicates
that the single-quasiparticle
is similar
component
to that found
is the major
in ‘69Yb and
one.
Coriolis mixing is important for the $6331 band and it grows rapidly, although slower than in ‘69Yb, with increasing spin value. The band levels depopulate by competing E2 and M 1 + E2 transitions and experimental mixing ratios are known for five of these Ml + E2 transitions. As in ‘69Yb, all these mixing ratios are negative and differ very little from each other and from the values obtained for the transitions in ‘69Yb. The theory describes this picture rather well, which may be clearly seen if we compare the experimental and theoretical values of 6 given in table 8. The mixing ratios of the last three - $! + 7, y+ 9 and f + $ - transitions were determined by Lindblad et al. “). A comparison of our proposed structure of the $6331 band levels with that of Lindblad et al. “) shows some differences: the amplitudes of the main $6331 and $[651] components change more rapidly in their case and a significant admixture of between 2% and 10% of the $6241 state is present when the spin changes calculations.
from 9 to 5. This contribution
is negligible
in our
The 902 and 1079 keV levels observed by Burke et al. “) in the (d, t) and (d, p) reactions were interpreted by them as the $ and $ members of the 35211 band. On the basis of the “‘Lu decay study, Batsev and Bench-0smolovskaya4) proposed that the 902.2, 958.2, 1024.6 and 1124.3 keV levels are respectively the z, 3, $ and 4 members of this band. Adam et al. ‘) have replaced the 1124.3 keV level by the 1127.7 keV level and proposed two possible interpretations: the first is the same as that of ref. 4), while the second considers that the 944.3, 1024.6 and 1127.7 keV levels are the s, s and s states of the $5231 band. The available data do not allow us to draw a conclusion. The experimental moment-of-inertia parameters for the levels of the 5[521] and $5231 bands in “‘Yb (see table 9) may be compared with those and are consistent with both interpretations, but it is clearly seen in ‘67~‘69~‘73~‘75Yb that the 1079 keV level cannot be the i state of the $5211 band. The precision of the mixing ratios of the transitions depopulating these levels is not high in most cases, but when it is sufficiently good and the sign of 6 is known, then the calculated magnitudes of 6 agree with the experimental ones within a factor of 2 and the signs agree in every case except for the 902.2 keV transition (see table 8). It is expected that the $5211 band is strongly coupled with the K = $ y-vibrational band based on the 25211 state. Burke et al. “) concluded that this admixture is not less than 50% in “‘Yb. Our calculated structure, shown in table 5, agrees with this experimental result. In the (d, p) reaction, Burke et al. “) observed five levels in “‘Yb with relative intensities which correspond to those of the members of the $[5 lo] bands in ‘73P’75Yb. However, the absolute intensities in “‘Yb were only about 60% of the values expected for this band. They explained this by the mixing between the $5101 band based on the single-particle state and the K =i y-vibrational band based on the $5 121 state. Our proposed structure of the 25101 band is consistent with the
11.34
A
“) Value was calculated
12.34 12.70
12.28
12.85
12.52
10.59
10.20 14.13 “)
{ 11.45 5.41 “)
1 9.49 11.26 “)
11.18
12.52
12.11
171krb
L69yb
12.42
12.57
12.20
17syb
9,2,LL,Z
4~2.~2
A T/2,11,2
A 5/2.9/2
A 11,2.13,2
A
A 7,?,9,2
As/~/z
A for the 35211 and $5231 hands
9
of the band (see text).
10.83 10.79
10.82
10.67
10.93
10.70
11.00
173yb
parameters
with the 1079 keV level as the 3 member
11.28
AS/W, A
T/2,11,2
11.48
9,2.11,2
A 3/&l/2
A
11.20
A,,,,,,,
7/49/2
11.88
A 3/u/2
167yb
35211 band
Moment-of-inertia
TABLE
11.14 10.98
11.18
10.84
11.15
11.13
11.24
167yb
35231 band
10.87
11.20
10.56
11.24
11.14
169yb
11.46
11.45
11.47
171yb
i
3 g.
3
S.
? b ?
!? P % a 2 .E ’
.Y .*
226
T.I. Kracfkovd
et al. / Nuclear orientation
result of Burke et al. and the calculated ones to within 2%.
experimental experimental
The 867 and 1118 keV levels were identified
study
level energies
as the 2 and y members
agree with the of the $6421
band ‘,‘). Batsev and Bench-Osmolovskaya “) observed the 984.0 keV level and interpreted it as the f member of this band. With this interpretation, the moment-ofinertia parameter AS,2,9,2 = 7.3 1 agrees with that of ‘69Yb, A5,2,9,2 = 7.26. The spin of the 1093.3 keV level was assigned uniquely in the present work as g, and we identified this level as the g member of the $[65 l] band. The 1093.3 keV level de-excites mainly to the 3’ and f’ levels of the $6331 band. The 834.1 f 0.4 keV transition, observed by Batsev and Bench-0smolovskaya4) to be equal in energy to the difference between the ;+$651] and y+$633] states, was not placed in their decay scheme. Adam et al. ‘) have also observed a transition, 834.5 + 0.4 keV, with similar relative intensity, but placed it as depopulating the 1080.9 keV level. If we assume that most of this transition intensity depopulates the 1093.3 keV level and all three depopulating transitions have pure E2 multipolarity, we obtain according to Alaga ratios are (0.78 f 0.04) : 1: (0.8 f rules 1998: Igz6 : I834 = 0.17 : 1 : 1.32. The experimental 0.4). Both
of the experimental
and
theoretical
ratios
agree
with
their
counter-
parts for similar transitions in ‘69Yb [ref. 29)], I,,, : I876: I,,, = 0.17 : 1: 1.28 and (G 1) : 1: (1.0 f 0.5). It seems that in both cases the agreement between the experimental and Alaga values is good for the two last transitions, while significant deviations are observed for the first 4’+ I’ transitions. This may be explained by the Coriolis interaction. Indeed, a strong Coriolis mixing is expected between pairs of the bands with K-values differing by unity. Our calculations for “‘Yb as well as for ‘69Yb confirm these expectations for both the $6421 and $6511 bands (see table 5 and fig. 4). Moreover, the calculated mixing ratios agree well with the experimental ones in magnitude
and sign for both bands.
6. Conclusions The nuclear
orientation
experiments
have been successful
in removing
previous
ambiguities and in obtaining an extensive set of spin of levels in “‘Yb. 29 b-values have been determined and they have confirmed and improved the ICC data. An important advantage of the directional-distribution experiments is that they are sensitive also to the sign of 6. Calculations based on the semi-microscopic quasiparticle-phonon model with Coriolis mixing included provide the energies of the rotational band levels, the reduced probabilities of E2 and M 1 transitions and the E2/Ml mixing ratios and their signs. Both positive- and negative-parity levels have been considered. The comparison between theory and experiment is, on the whole, successful. This approach has provided a more complete and detailed understanding of “‘Yb than previous work and extends the similar treatment of the lighter 167,‘69Ybisotopes.
T.I. Kracikovd et al. / Nuclear orientation study
221
In general it was not found necessary to reduce the Coriolis matrix elements in the calculations for any of these isotopes as had been done in previous theoretical studies.
References 1) D.J. Horen and B. Harmatz, Nucl. Data Sheets 11 (1974) 549 2) V.D. Vorobiev, T.M. Usypko and S.A. Shestopalova, Decay schemes of radioactive nuclei A = 171- 174 (Nauka, Leningrad, 1977) 3) P. Sen and H. Bakhru, 2. Phys. AZ81 (1977) 263 4) S. Batsev and N.A. Bench-Osmolovskaya, Izv. Akad. Nauk SSSR (ser. fiz.) 45 (1981) 697 5) J. Adam, V. Hnatowicz, V. Zvolska, J. Zvolsky, B. Kracik and M. FiSer, Izv. Akad. Nauk SSSR (ser. fiz.) 48 (1984) 318 6) D.G. Burke, B. Zeidman, B. Elbek, B. Herskind and M. Olesen, Mat. Fys. Medd. Dan. Vid. Selsk. 35, No. 2 (1966) 7) D.G. Burke, W.P. Alford and R.A:‘O’Neil, Nucl. Phys. A161 (1971) 129 8) Th. Lindblad, H. Ryde and D. Barneoud, Nucl. Phys. Al93 (1972) 155 9) K.S. Krane, C.E. Olsen, S.S. Rosenblum and W.A. Steyert, Phys. Rev. Cl3 (1976) 1295 10) T.I. Kracikova, M. Finger, S. Davaa, J. Dupak, V.N. Pavlov, N.A. Lebedev, W.D. Hamilton and C. &it, Czech. J. Phys. B31 (1981) 527 11) J. Kvasil, T.I. Kracikovl, M. Finger and B. Choriev, Czech. J. Phys. B31 (1981) 1376 12) S. Davaa, T.I. Kracikova, M. Finger, J. Kvasil, V.I. Fominykh and W.D. Hamilton, J. of Phys. G8 (1982) 1585 13) J. Kvasil, T.I. Kracikovl, S. Davaa, M. Finger and B. Choriev, Czech. J. Phys. B33 (1983) 626 14) V.G. Soloviev, Theory of complex nuclei (Pergamon, Oxford, 1976) 15) J. Kvasil, I.N. Mikhailov, R.Ch. Safarov and B. Choriev, Czech. J. Phys. B2ll (1978) 843 16) S.R. Avramov, E.V. Sosnovskaya and V.M. Tsupko-Sitnikov, Joint Institute for Nuclear Research, Dubna, JINR preprint RlO-9741 (1976) 17) C.M. Lederer and V.S. Shirley, Tables of isotopes, 7th ed. (Wiley, New York, 1978) 18) K.S. Krane and R.M. Steffen, Phys. Rev. C2 (1970) 724 19) K.S. Krane, At. Nucl. Data Tables All (1973) 350 20) I.M. Band and M.B. Trzaskovskaya, Tables of internal conversion coefficients on K, L and M shells, lOsZ< 104 (Leningrad, 1978) 21) F. Riisel, H.M. Fries, K. Alder and H.C. Pauli, At. Nucl. Data Tables 21 (1978) 291 22) G. Kaye, Nucl. Phys. 86 (1966) 241 23) K.P. Artamonova, E.P. Grigoriev, A.V. Zolotavin and V.O. Sergeev, Izv. Akad. Nauk SSSR (ser. fiz.) 39 (1975) 523 24) K.P. Artamonova, E.P. Grigoriev, A.V. Zolotavin and V.O. Sergeev, Izv. Akad. Nauk SSSR (ser. liz.) 39 (1975) 1773 25) B.S. Dzelepov, in The properties of deformed nuclei, Lectures of 10th USSR school on nuclear physics (Fan, Tashkent, 1983) pt. I, p. 3 26) V.A. Balalayev, B.S. Dzelepov, I.F. Uchevatkin and S.A. Shestopalova, Izv. Akad. Nauk SSSR (ser. fiz.) 35 (1971) 18 27) F.A. Gareev, S.P. Ivanova, V.G. Soloviev and S.I. Fedotov, Physics of elementary particles and atomic nuclei, Vol. 4 (Atomizdat, Moscow, 1973) pt. 2 28) A. Bohr and B.R. Mottelson, Nuclear structure II (Benjamin, New York, 1974) 29) V.A. Balalayev, B.S. Dzelepov and V.E. Ter-Nersesyants, (Nauka, Leningrad, 1978) p. 183
Isobaric
nuclei with mass number
A = 169
A440 (1985) 203-227 Publishing Company
NUCLEAR T.I.
ORIENTATION
KRACiKOVA,
STUDY
S. DAVAA,
OF THE DECAY
J. KVASIL,
M. FINGER
and
OF “‘Lu
J. KONicEK
Join? Institute for Nuclear Research, Dubna, USSR and W.D.
HAMILTON
Physics Division, University of Sussex, Brighton BNI 9QH, UK Received
16 November
1984
Abstract: The levels and -y-ray transitions in “‘Yb have been studied by radioactive decay of oriented “‘Lu. The orientation was produced using the hype&me field in ferromagnetic gadolinium to polarize an ensemble of “ILu nuclei at a temperature of 14 mK. The directional distribution of the y-rays was measured using high-resolution Ge(Li) detectors. Anisotropies of 30 y-rays in “‘Yb were measured. Multipole mixing ratios were deduced for most of the mixed y-ray transitions and unambiguous spin assignments were made for several levels. The energy and structure of the rotational band levels, reduced E2 and Ml transition probabilities and E2/ M 1 mixing ratios were calculated using the semi-microscopic quasiparticle-phonon with a Coriolis interaction. In general, good agreement is obtained between the theoretical tions and experimental results.
E
model predic-
RADIOACTIVITY “‘Lu [from Ta(p, X)]; measured y( 0), oriented nuclei. “‘y-b deduced levels, J, T, 6, y-multipolarities, B(A). Chemical, mass-separated target, Ge(Li) detectors. NUCLEAR STRUCTURE “‘Yb; calculated levels, J, n, B(A), 6. Quasiparticle-phonon model including Coridlis interaction.
1. Introduction The levels of “‘Yb
have been studied
extensively
from the decay of “‘Tm
and
“‘Lu and by the (d, p), (d, t), (d, d’), (p, t), ((Y, 3n), (3He, (Y) and (n, y) reactions I-*). The y-ray multipolarities have been deduced from internal-conversion coefficient measurements ‘72V4,5) ; directional correlations for four cascades have been measured by Sen and Bakhru 3). Low-temperature nuclear orientation of “‘Lu in a ZrFe, host has been investigated by Krane et al. 9). In their experiments, the “‘Lu activity was produced by irradiation of natural ytterbium. Significant disagreement is observed between the multipole mixing ratios obtained by Krane et al. and those deduced from the internal-conversion coefficients (ICC), of the low-energy y-rays. The most extensive decay schemes of “‘Lu have been proposed by Batsev and Bench-Osmolovskaya “) and Adam et al. 5). The transition and level energies listed in the latter have been used in the present work. 203
204
T.I.
Kracniova’ et al. / Nuclear orientation srudy
The “‘Yb levels have been identified with Nilsson configurations on the basis of the single-particle transfer-reaction studies of Burke et al. 6*7). Lindblad et al. “) observed the $+[633], $-[521], $-[512) and ?-[SOSj bands up to high-lying levels in the (ty, 3n) reaction. They paid particular attention theoreticaIIy to the positive-parity band. The rotational energies within this band, experimental E2/Ml mixing ratios and the cross sections obtained in transfer-reaction experiments were successfully explained within the non-adiabatic unified model with pairing and Coriolis interactions included. They found it necessary to reduce the Coriolis matrix elements for orbit& near the Fermi surface. In recent publications ‘o-‘3), we have reported investigations on the decays of ‘$‘Lu and ‘69L~ polarized at low temperatures in gadolinium hosts. The level structures of ‘67Yb and ‘69Yb were described within the semi-microscopic quasipartitle-phonon model of Soloviev ‘“) including Coriolis mixing 15),and in the present work we report on a similar investigation of the properties of “‘Yb.
2. Experimental details A radioactive source of 17’Lu (T,,* = 8.2 d) was produced by a spallation reaction on tantalum using the 10 GeV proton beam of the Dubna synchrophasotron. After chemical separation of the lutetium fraction, the “‘Lu isotope was selected by a mass-separator and implanted into pure (99.9%) gadolinium foil. This was melted in vacuum onto a tantalum foil which was then soldered to a copper foil using titanium-silver solder. The sample was finally formed into a disc of diameter 0.5 cm and was soldered to the refrigerator heat exchanger. The details of the lutetium-ingadolinium source preparation are described by Kracikovd et al. lo). The admixture of the ‘72Lu (T,,, = 6.7 d) activity in this source was less than OS%, while the admixtures of other Lu isotopes were considerably smaller. The sample was cooled using a top-loading ‘He:%e dilution refrigerator which operated at a base temperature of 14(2) mK. The sample was polarized with an external field of about 1 T. Data were recorded at 0” and 180” with respect to the orientation axis by two Ge(Li) detectors, both located 8.0 cm from the source. The y-rays with energy below 200 keV were recorded by a planar 200 mm’ x 7 mm X-ray detector with a resolution of 0.55 keV at 122 keV. A 53 cm3 coaxial detector with a resolution of 2.9 keV at 1332 keV was used to detect the y-rays with energy up to 1350 keV. Typical y-ray spectra measured with these detectors are shown in fig. 1. The y-ray spectra were analysed to give the areas of the y-ray peaks using the program SIMP 16). As may be seen from fig. 1, three peaks are multiplets of 17’Lu y-rays and X-rays of lead: these are 72.4y+72.81(,,, 75.OK,, +75.9y and 84.4KBj + 84.9K,, + 85.6 y-t- 87.3K,;. The areas of the 75.0, 75.9 and 85.6 keV peaks were evaluated by the program, whereas the area of the 72.4 keV peak was obtained by
205
T.1. KractIova’ et al. / Nuclear orientation study
subtracting the area of the 72.8 keV peak which was determined using the area of the 75.0 keV peak and the known intensity ratio of the 72.8 and 75.0 keV X-rays I’). 3. Data analysis The y-ray counting rates were analysed according to
W(e) = C
~~~Z)u~A~Q~p~ (cos 8) ,
(1)
Aeven
where the orientation coefficients B,(I) depend on the temperature and strength of the interaction between the orienting magnetic field and the nuclear magnetic moment, and the factors QA correct for the detector solid angle and PA are Legendre polynomials. The correlation coefficient is defined as A~=[F~(LLZ~Z~)+2SF~(LL’Z~Z~)+S2F~(L’L’Z~f~)](l+6*)-‘,
(2)
where the Fh are the angular-momentum-coupling factors, L’ = L + 1 and S is the amplitude ratio of the L + 1 to L multipole components in the transition. The y-ray mixing ratio S is defined in terms of emission matrix elements I’). The deorientation coefficients U, account for intermediate transitions: for y-radiation, they are given by U*(ZiZ~)=[U*(ZiZfL)+62U*(ZiZrL’)](1+S2))1~ If there is a low-energy highly-conveyed u
A
(z.z.e I fr
(3)
transition, the U, coefficient is written as
y~=(l+P)~*~ziz~L)+SZ(l+ar)U,(ziz~L’) ,
(l+p)+6*(1+1y)
’
(4)
where fy and p are total internal-conversion coefficients of the L+ 1 and L multipole components, respectively. The angular-momentum-coupling coefficients U, ( ZiZfL) and Fh are tabulated by Krane 19). The deo~entation coefficients U,, have been calculated on the basis of the decay scheme of Adam et al. 5, and all available data including the present results. For the low-energy transitions, we have used eq. (4) and theoretical ICC values of Band and Trzaskovskaya *‘) for the K, L and M shells and of Rose1 et al. “) for the N and 0 shells. The U, values obtained are given in table 1. The uncertainties quoted result from the uncertainties in the transition intensities and in mixing ratios. The decay level of “‘Yb including our results is shown in fig. 2. 4. Experimental 4.1. GAMMA-RAY
results
ANISOTROPIES
The measured y-ray anisotropies, 1 - W(O’) and 1 - W(180”), were corrected for the solid-angle factors Q2 and averaged. Initially we shall assume that the fourth-
T.I. Kracikovd et al. / Nuclear orientation study
206
6’761
NO
x
t--
m
13NNt’HI
t13d
m
SINnO
-=fz
m
7X Krucikovci et al. / Nuclear orientation study
OZZQ
O’LCS\
Z‘ZBZL
8LLS 9’867 -
:
0’866 S’S86 s
13NNVH3
ti3d SiNI
*o
208
T.I. Kracikovd et al. / Nuclear orientation study
209
TI. Kracikooa’ et al. f Nuclear orientation study TABLE 1 Deorientation coefficients for “‘Yb
levels
Level energy
Level energy
[keel
[kW
66.1 75.9 95.3 122.4 167.7 208.0
0.325 0.602 0.700 0.633 0.786 0.772
* * * f f i
0.032 0.005 0.002 0.021 0.002 0.026
230.6 246.6 259.1 317.3 449.6
0.707 f 0.025 0.675 f 0.062 0.878 zt 0.007 0.866*0.017 0.877 * 0.008
order orientation coefficient is negligibly small and base our analysis only on the B2U2A2 values. This assumption is subsequently justified. The anisotropies of 30 transitions
in “‘Yb
4.2. EVALUATION
obtained
OF THE
are listed in table 2.
B,(I)
COEFFICIENT
Two intense El transitions of 739.8 and 780.7 keV have been used to evaluate the initial-state orientation. These i-+ G’ and f- + 4’ transitions, respectively, were selected because they are known from conversion coefficient measurements 2,4*5)to contain vanishingly small M2 admixtures and because the A2 coefficient of the Al = 0 transition is considerably less sensitive to a given amount of M2/El mixing than is the Al = 1 transition. Moreover, the levels depopulating by these transitions TABLE 2
The measured
B,
55.7 66.7 72.4 75.9 85.6 91.4 109.3 194.9 498.8 517.8 627.0 631.0 667.4 689.3 712.6
anisotropies
of y-rays
B, 44
&A2 [%]
19110 6.6 f 2.3 4O.Oi 8.7 -3.7 f 1.o 39.9+3.8 39.4* 8.0 32.6 f 3.6 -24.6k7.4 19116 42.8 f 4.8 -29.2 i 2.2 -6.3 f 9.3 9.39 * 0.73 12.16*0.80 48.5 f 2.5
in “‘Yb
739.8 167.6 780.7 794.0 825.9 839.9 853.0 862.4 868.4 902.2 948.7 985.6 998.0 1209.8 1282.2
WI
-23.22 f 0.68 -4.3* 1.1 -25.5 1 * 0.54 -22.5 * 6.9 -31.0*9.0 57.1*2.2 16.31 1.3 13*10 -26.3 f 9.4 25.0+ 3.0 -12.6k5.6 16+ 16 34* 17 -6.7 + 9.0 -19.1*3.0
210
T.I. Kracikova’ et al. / Nuclear orientation study
are fed only by the B-decay. Averaging the corresponding values of B2(I) for these transitions, we obtained B2(I)= 0.636 f 0.015. It should be noted that this evaluation is independent of the fourth-order term since A, = 0 for an E 1 transition. On the basis of the known magnetic moment ]~(“‘Lu)l= 2.04 (10) n.m. [ref. ‘)I and the internal field B = 55 (6) T which we obtained by measurement of the anisotropy temperature dependences for the y-rays of ‘72LuGd, we would expect B2(I)= 0.8 f 0.2. The corresponding fourth-order coefficient is thus at most B4(I)0.15and since in nearly all the analysed transitions the U, coefficients of intermediate transitions are small or identical to zero, we are justified in neglecting the fourth-order contribution. The only exceptions are the 194.9, 7 12.6 and 825.9 keV transitions and they were corrected for the fourth-order term. Two low-lying levels in “‘Yb have long half-lives. One may expect therefore substantial perturbations of the directional distributions owing to changes in the relative populations of the magnetic substates arising from the interaction of the nuclear electromagnetic moments with the surrounding electromagnetic fields during the long half-lives of these levels. Thus substantial attenuations of the directional distributions may be expected for transitions which depopulate directly and indirectly the 95.3 keV level, T,,2 = 5.25 ms [ref. 2)], and probably the 122.4 keV level with T,,, = 265 ns [ref. ‘)I. The anisotropy of the low-energy 19.4 keV transition which only depopulates the 95.3 keV level was not recorded in our measurements. The 75.9 and 66.7 keV levels are strongly populated from the 95.3 keV level and also from the 122.4 keV level. Analysis of the anisotropies of the Ml + E2 66.7, the pure E2 75.9 and the M 1+ E2 55.7 keV transitions, using the above value of B2 and the calculated U2 coefficients, gave the attenuation factors G2(67 keV) = 0.32 f 0.12 ,
G2(76 keV) = 0.18 f 0.05 ,
for the 66.7, 75.9 and 122.4 keV levels, respectively.
G2(56 keV) = 1.Of 0.6.
In this analysis,
magnitudes
of
the mixing ratios of the 66.7 and 55.7 keV y-rays were evaluated from the ICC data, while the signs were determined in the present work. The deorientation coefficients for the M 1 + E2 9.15 and the El + M2 19.4 keV transitions, U, = 0.500* 0.006 and U2 = 0.867+ 0.007, were calculated using eq. (4) and the values of S2 = (3.4* 1.1) x 10e4 and 62 s 1.5 x 10e5, respectively, which were obtained from the results of the conversion electron measurements 22-24) re-analysed by Dzelepov 25). The half-life of the 122.4 keV level is much smaller than that of the 95.3 keV one and accordingly the external perturbation of the 122.4 keV state, if it exists at all, may be expected to be smaller. The large uncertainty in the 55.7 keV y-ray anisotropy does not allow us to make a final conclusion.
4.3. MIXING
RATIOS
The correlation coefficients A2 were evaluated using the measured B2 U,A, given in table 2 along with deduced B2 and calculated U2 values.
values of In several
T. I. Kracikovci et al. / Nuclear a~ie~~~iio~study
211
cases the A2 coefficients were determined independently of assumptions on B,(f) and lJ,(p, y) by comparison of an El transition anisotropy with the anisotropies of other transitions from the same level. Weighted average values of K-shell conversion coefficients QK have been determined from the experimental results given in refs. ‘-‘). Values of Is( were calculated from experimental conversion coefficients ffK and these were used to distinguish between possible solutions of eq. (2). The values of A2 and multipole
TABLE The correlation Level energy
I”
[keVl
’
66.7 122.4 167.7 208.0 259. I 317.3 835.1
coefficients
E,[keYl
G’
66.7 “f 55.7 72.4 85.6 91.4 109.3 194.9 517.8s) 627.0 b, 661.4 b, 712.6 ‘) 739.8
3
A, and the deduced
multipole
0.92 f 0.46 0.47 f 0.26 0.80*0.18 0.813*0.084 0.71 zto.14 0.592 f 0.068 -0.45*0.14 0.804 f 0.093 -0.549 + 0.044 0.177*0.015 0.9 1 I f 0.054 -0.458 f 0.017
902.2
0.600 * 0.073
935.2
767.6 839.9 868.4 498.8 631.0 689.3 780.7 825.9 853.0
-0.073 *0.019 0.97 1f 0.044 -0.47 f 0.17 0.33 f 0.27 -0.11*0.16 0.210*0.014 -0.420 f 0.015 -0.53*0.16 0.281*0.023
1024.6
1080.9 1093.3 1377.5
794.0 948.7 985.6 862.4 998.0 1209.8 t 282.2
b, b, b, ‘) b)
-0.44*0.13 -0.25 f 0. I 1 0.29 * 0.29 0.22*0.17 0.58 i 0.29 -0.13*0.18 -0.371 * 0.059
“) External perturbation of the 122.4 keV level was taken perturbed, we obtain a(67 keV) = -0.6fy:$ b, A, is deduced independently of B,(I) and U,(& y).
ratios Multipole mixing ratio
A*
902.2
944.3 948.3
mixing
into account.
-0.61:; -0.05 * 0.15 -0.31:;:;; -0.30? 0.07 06 -0.25 ?09 0.1I -0.16*0.04 0.01*0.13 0.54+:;(; 0.76’;:;; 0.016*0.010 -1.52*0.16 0.030 * 0.025 -0.06 * 0.05 -1.52+0.16 -0.477 f 0.025 -0.48’$$ 1.5?70s 0.1*0.2 2.o+‘-4 0.7 0.029 f 0.009 -0.033 f 0.024 0.09*0.16 0.011*0.012 1.1*0.4 { o.o*o.z 0.32 f 0.07 0.1*0.2 0.04 f 0.09 -0.16+“.‘6 021 -0.20’$; -0.08 f 0.07 If this level is not
T.1. Krackova’ et al. / Nuclear orientation study
212
TABLE The S-values
obtained deduced
4
in previous nuclear orientation and yy correlation studies and the /~?(a~)/ values from the experimental ICC data compared with the present results Multipole
E, [keYI
present
work
55.7 66.7 72.4 85.6 91.4 109.3 498.8 517.8
-0.05 * 0.15 -0.6 “f: ‘: -0.3 I”“, 1: -o.30’*.06 0.“7 -0.25 z;::‘: -0.16*0.04 0.1 rto.2 0.54:;;;
627.0
0.16 “’0.,9 ”
63 1.O 667.4
2.0” 4 O.O16ji4;.010
689.3
0.029 f 0.009
712.6 739.8 767.6 180.7
-1.52i0.16 0.030 * 0.025 -0.477 i 0.025 -0.033 f 0.024 1.1 Ito. { 0.010.2 -0.48 “-::“,; 0.011 r0.012
794.0 839.9 853.0 868.4
a
ratio
)
2.0”5O -0.,0:&6 -0.07 i 0.05 -0.22+;:;: “) -0.08 & 0.04 1.2?‘.7 07 1.3rto.3 { I.1 r;.:q 0.003 rt 0.014 0.015iO.016 0.146 i 0.004 d, -2.1 izo.4 0.02 IQ09 0.08 -0.34 i 0.08 -0.03 I 0.06 0.61 2tO.13 d, 0.43 “z.;: d) -0.5 1 z:.;: -0.029 i 0.014
isto
902.2
i
948.7 998.0 1282.2 “) Ref. 9), b, The magnitude
mixing
15
Transition
of &value
deduced
-0.06 i”d.05 -1.52*0.16 0.32 + 0.07 -0.16:;;: -0.08 i. 0.07
IS(ff,)l
Y
0.057 * 0,004 ‘) 0.696 * 0.013 ‘) 0.296 i: 0.006 ‘) 0.262*0.013’) 0.29 * 0.02 ‘) 0.20 * 0.03 0.38ztO.12 0.52 * 0.07 0.63*0.11 1.1*0.2 co.03 0.0s r;;: 1..541:0.08 El 0.56+E El 0.410.3 OSO* 0.06 SO.05 1.7:) OS 4 ~1.85’)
0.12:~::
0.5910.13 0.3 * 0.3 0.06 “O “’ U.“h
from the weighted averages of the y-ray and conversion electron
intensities available. ‘) Ref. 25). d, Re-analysed value of Sen and Bakhru 3). For the 794.0 keV transition measured in correlation with the 154.8 keV y-ray, two values of S were obtained depending on positive or negative values of (&(a,, 155 keV)/ =0.62*0.12 used in the anatysis.
ratios 6 giving the best agreement with the IS(cuK)I values are listed in table 3. Table 4 shows a comparison of our results with those of Krane el al. 9), with the results of Sen and Bakhru ‘) re-analysed by us, and with the values of 16(tuK)/. The A2 coefficient for the 66.7 keV transition was evaluated using the orientation coefficient corrected for the external perturbations of the 75.9 and 122.4 keV levels,
mixing
T.I. Kract’kovd et al. / Nuclear orientation study
213
i.e. Z3$(67 keV) = *
f3:(122)U,(y56)++ 56
where
B,*(76) Z-U ~9) , 56
9
Bf = B2lJ,G, and Z = Z, + Z, is total transition
9
intensity.
Large uncertainties
in the 55.7, 66.7 and 75.9 keV y-ray anisotopies result in the value of S(67 keV) = -0.6?7:: which agrees with 16(ak)j, but leaves an ambiguity in the sign. However, comparing our experimental value of A2(67 keV) = 0.92 f 0.46 with those calculated with negative and positive values of IS( ak)I = 0.696 * 0.013, A*(6(aK)< 0)= 0.986* 0.003 and A2(?I( aK)> 0)= -0.638 + 0.013, we conclude that mixing ratio of the Ml + E2 66.7 keV transition is S = -0.696*0.013. If we do not take account of the external perturbations, our value of A2 = 0.32 f 0.12 yields 6’ = 0.10 f 0.07 and 8* = -2.2 f 0.4 which disagree completely with the ICC result. It is seen from table 4 that our mixing ratios are in excellent agreement with the Is(a,)( values, but significant disagreement is observed with the results of Krane et al. ‘) particularly for the low-energy y-rays. It should be noted that Krane et al. have not observed the external perturbation of the long-lived levels in “‘Yb. Their anisotropies of .the 66.7 keV transition yield the values of A*(4 mK) = -0.64 f 0.33 and A2(20 mK) = - 1.86 * 0.43 which disagree with each other and with our result. These discrepancies may be explained by (i) the complexity of their source (by our estimation this contained a large admixture of about 50% of “*Lu, a substantial one of “‘Lu and some ‘73Lu impurity), and (ii) they were unable to resolve the very complex spectrum of ‘7’t’72+‘73t’77L~ in the low-energy range with their coaxial Ge(Li) detector. If we do not make the correction for the X-rays, our values of 6(72 keV) = -0.08 + 0.03 and a(86 keV) = -0.15 + 0.07 agree with those of Krane et al. 9), see table components
4. The
109.3, 627.0 and 712.6 keV y-rays
of the complex
the corresponding
&values
peaks containing are slightly
were also measured
the “*~“‘Lu y-rays;
different
therefore
as
probably
from our results.
After we re-analysed the data of Sen and Bakhru ‘) taking account of the fact that the 85.6 y-ray is not a pure Ml transition, their results (see table 4) agreed except for the value of 6(M2/El) for the with the present ones and with IS(a 4- + ?’ 689.3 keV transition. It seems that the 689- 164 keV cascade was not measured correctly by Sen and Bakhru since we obtained A*(689 keV) =0.017*0.007 from their result, while the corresponding theoretical is Aih= 0.288 for a pure El transition.
4.4. SPIN
value of the correlation
coefficient
ASSIGNMENTS
Spin assignments to excited states in odd-A nuclei are always a difficult task. Internal-conversion data, while indicating the multipolarity and type of radiation, usually allow a range of possible values for the spin of one state relative to that of the other, and the feeding and decay modes of the level must be used to restrict the choice. Directional-correlation experiments are also limited in odd-A nuclei
T.1. Kracikovd et al. / Nuclear orientarion study
214
since the number of unknown parameters describing the yy cascade usually exceeds the number of measured correlation coefficients and much additional information is required for a complete evaluation. On the other hand, nuclear orientation data involve only the A, coefficients and if one of the level spins is known then often both the multipolarity of the radiation and the other spin value may be obtained. It is true that the evaluation also depends on calculating the U, coefficients but, with a careful choice of the initial conditions for analysis, little ambiguity enters and even this may be subsequently removed by an iterative process until the complete data set has been evaluated. In this way one may make unique spin assignments which are directly based on measurements. 4.4,l. The 902.2 keV level, Ix = $-. This level decays only to the fP ground state by the Ml(+E2) transition 2-5). The large anisotropy of this 902.2 keV transition measured in the present work excludes spin i; for I = $ there is no orientation. Spin 2 is also impossible since the value of ASXP= 0.499 * 0.055 is inconsistent with Aih($+$ = -0.535 indicating that the 902.2 keV y-ray cannot be a pure E2 transition. Thus, we confirm the s- assignment proposed by Burke et al. “). 4.4.2. The 944.3 keV level, I” =$-. The decay scheme and transition multipolarities
indicate
transition
to the $- state yields a mixing
that this level should
be $- or $-. The anisotropy ratio S = 1.5’::: in agreement
of the 868.4 keV with jS( CY~)I=
1.7$:, if the level is assigned 5, while there is no solution of eq. (2) for a $- assignment. 4.4.3. The 1024.6 keV level, I” =f-. This level was assigned $- by Sen and Bakhru 3), while Batsev and Bench-Osmolovskaya “) and Adam et al. ‘) made a $assignment based on the Ml multipolarity of the weak 707.5 keV transition to the g- state. Sen and Bakhru have measured the directional correlation of the 794155 keV cascade. As their value of the a4 coefficient gives no additional information and the magnitude of Ii3(czK, 794 keV)I = 0.4* 0.3 agrees with any of the S-values obtained for the sP or s- assignment (I” = $-: 6 = -0.13 kO.04 and 6 = -0.20*0.02 for 6((r,, 155 keV) >O and ~0, respectively; I” =:-: see table 4), there is no possibility for making a choice. However, our result for I” =$-, 6(794 keV) = -0.53’:::& does not agree with that of Sen and Bakhru and the 3m assignment is preferable. Moreover, the anisotropy of the 948.7 keV transition yields 6 = 0.32 * 0.07 for a sor S=ll’:‘, if the level is assigned i-, while 6 = 0.18 * 0.09 or 6 = -2.6’::: assignment. The first value of 6 is in better agreement with IS((Y,J = 0.59kO.13 and spin s is also favoured. 4.4.4. The 1080.9 keVleve1, I” =4-. This level was assigned s-(3-) by Batsev and Bench-Osmolovskaya 4), while Adam et al. ‘) proposed a <- or E- assignment. The multipolarity of the 1005.0 keV transition to the gP state, Ml + (43 f 13)% E2, is not consistent with a z- assignment. Spin $ may also be ruled out as the observed anisotropy of the G-+ g’ 985.6 keV transition yields an admixture of M2 2 20%, which is unacceptably large. 4.4.5. The 1093.3 keV level, I” =F. The level was tentatively proposed Balalayev et al. 26) and supported by the yy- and ey-coincidence measurements
by 3,4).
T.f. Kracr’kova’et al. / N&ear orientation study
215
A 3’ or %’ assignment was suggested on the basis of the transition multipolarities “). Spin $ may be excluded since the anisotropy of the 862.4 keV y-ray is not consistent with the El transition: AzXP= 0.26 f 0.19, while Aih(z+ z) = -0.436. The spin-parities ofthe 167.7,208.0,259.1,317.3,835.1,935.2,948.3 and 1377.5 keV levels assigned previously are confirmed by the present results. The excellent agreement of our results with the ICC data shows that the assumptions made in evaluating the U, coefficients are good. 5. Comparison with theory 5.1. INTRODUCTION
has been shown recently “-‘3) that the semi-microscopic quasiparticle-phonon model of Soloviev 14), with a Coriolis interaction included I’), may be applied to a well-deformed odd-A nucleus with considerable success in describing a wide range of nuclear properties. Formally the model describes the nucleus in the adiabatic approximation and the hamiltonian can be thus divided into two parts representing the intrinsic motion of the nucleus and its rotation: It
ri = fii”t + ii,,, *
(5)
In the quasipa~icle-phonon model “*27) the intrinsic hamiltonian includes the hamiltonian of the axially-symmetric nuclear field described by a Woods-Saxon potential and residual (pairing and multipole-multipole) interactions. The eigenvalues Ek and eigenfunctions @p(K,) of fiiit are determined by solving the secular equation for the odd nucleus, so that @(KY) contain the single-quasiparticle and quasipa~i~Ie-plus-phonon components with amplitudes “*‘4) Ck and D$$, respectively. The parameters of I;i,, were chosen according to ref. 27). The rotational part of the hamiltonian (5) was taken as a quantum-mechanical rotor 28). In the case of axial symmetry of the average nuclear field, the rotation of the nucleus may be described by only one moment-of-inertia parameter. Different values of this parameter observed for various rotational bands in a given nucleus may be explained by non-adiabatic effects I’). The latter were included by Kvasil et al. 15) and the non-adiabaticity parameter used in the present calculations, B = 0.05 MeV-‘, is the same for ‘67*‘69Yb[refs. “*‘2)]. The eigenvalues of the total hamiltonian (S), &PF are determined by diagonalization basis of functions
= Ec*;M,
(6)
of the matrix for a given value of spin I in the
216
T.1. Kracikovd er al. 1 Nuclear orientation study
where DLK
are the Wigner
functions
and Z?,(n)
is the operator
of a rotation
of T
around the y-axis. The non-zero off-diagonal matrix elements arise from the Coriolis interaction which is included in the rotational part of the hamiltonian (5). The number
of the basis functions
(i.e. a dimension
of the matrix diagonalized)
is limited
by a final set of the states near the Fermi surface of a given nucleus. The following functions were included in the present calculation: $6601, $4001, $6511, $4021, $6421, $6331, 26241 and $5211, $5101, $5211, $5121, $5321, $5121, $5231, $5141, $5031, $5051. Using a double-diagonalization method “,‘5), we obtain the energies E’L of the rotational linear combinations
where b$ are In order to experimental various bands minimising
band levels, and the corresponding of the basis functions:
wave functions
qiM
are
the mixing coefficients. obtain better agreement between the calculated energies Elk and the values, an optimization of the moment-of-inertia parameters for the and the eigenvalues of the intrinsic hamiltonian was carried out by
The reduced transition probabilities were calculated using the standard formula of the adiabatic nuclear model including a Coriolis interaction [see refs. “,‘“)]. The multipole mixing ratio s(E2/Ml) is defined as the ratio of reduced matrix elements with the phase convention of Krane and Steffen “) (9) where
E, is the transition
5.2. RESULTS
energy
in MeV.
AND DISCUSSION
The experimental energies of the levels in 17’Yb and those calculated in the present work are compared in fig. 3 and in table 5, which also contains the calculated structure of these levels. Good agreement (usually within 2%) is obtained. between the calculated and experimental energies of the levels up to spin values of Z = p (see the ground-state rotational band and those based upon the $[512] and $6331 states). The effects of the Coriolis mixing may be seen from table 5 and fig. 4, which Z for some shows plots of the mixing coefficients b,Ik versus angular momentum rotational bands. Substantial Coriolis mixing is seen in some cases which results in a great change of the b$ coefficients. For the negative-parity bands, the $5101 state
11. Kracficova’
et al. / Nuclear
orientation
217
study
! I N
c
I : I
I :
! i
2 0)
I
N
N
;
l?
:I :I II a
i/law)
-AW3N3
?
NOllt’ll3X3
o
0
212
87 162 259 369 505
652 828
208
95 I68 259 369 501
648 826
I;-
f’ 4’ _:!+ &+ q+ 2 17+ f q+
130
122
f-
(1805)
0
66 80 224 249 477 492 817 863 1260 1286 1760 1780
0
of the experimental
67 76 231 247 487 509 832 860 1263 1293
Comparison
TABLE 5
633t 633r
633T 6331 633t 633f 633f
512f
512t
5211 5214 5211 5211 5211 5215 5211 5211 5211 S2ll 5211 5211 $214 5lOf+Q,,
94.8 51Ot+ Q22
642t 6421 642f 642t 642f 642f 642f
94.6
95.5 92.6 89.9 86.8 84.3 81.7 79.1
Qz2
52w+ ~~~ 52lT+ 022 52lT+Q,, 52~+Q,, 52lT+Q,, 52lt+Q,, 52l1+ Qzz 521t+~,, 521f+ Qzz 52lt+Q?? 52lt+
52lf+Q,, 521?+Q,,
95.8 95.8 95.6 95.4 95.3 95.3 94.6 94.8 93.8 86.6 92.7 93.5 88.0
Qz
1.8
14.5 16.2
2.2 4.8 7.2 10.0 12.0
3.4
3.4
5231+ Qzz
1.9
0.7 0.7
65jf+ Qzz 651t+Q,,
0.7
0.8 0.8 0.8 0.8 0.7
Qx
0.7
1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.2 1.2 1.1
1.2 1.2
651t+Q,, 65lt+Q,, 65lf+QX? 651t+Q,, 6511+Q,*
624f +
624r + QX,
5231+
52%+ Qzx =31+ Qzz SW+ Qn 5233. + Qn 5231+Qrz 5231+922 5231+Qx 5231+Qn 5233. + Qx 52%+ 422 SW+ Qzz
intensity
2.0 2.0 2.0 2.0 2.0 2.0 1.9 1.9 1.9 1.8 1.9
Component
[%I
0.1
5211
0.2
0.5 0.5 0.5 0.4 0.4 0.4 0.4
5214.
52ff+ QJ2 521t+QS2 5211+ Qj2 52l~+ ~~~ 52lf+Q,, 52l?+ Q32 521f+QJ2
512t 512f
0.1 0.2 0.1 0.1 0.4 0.3 0.2 8.0 0.3 0.1 3.2
651f 65lf
65lt 65lT 6511 651t
52lL+
52ll+Q,, Qzz
5211+Q:, 52ll+ QZZ
0.3 0.9
0.1 0.1 0.2 0.4
0.1
0.1
0.5 1.2
0.2 0.0 0.5 52lL+ Qz2 52li+ Qua 5211+Q,,
5211+ Qzz 5211+ Qz
0.1 0.1 0.2 0.2
respectively,
QZZ Q2z
52l1+ 52l1+
Qz2, QLOand Q32 correspond,
5121 512T 5127 512t 5121 512t 512f 5127 512T
and calculated energies and theoretical structure of the levels in “‘Yb (the symbols to the 2+y, O’p and 2- octupole vibrations of the even-even core)
V r: 2
F p1 3 B n, 2 % ;.
.“1 ?-
2
21+
958 1001 1056 1142 1251
(945) 995 1052 1144 1254
2iI f-
;s:f %-
(944) (1025) (1128)
935
(867)
984
1120
w93) 1407
3
;+ 3’ 8+ ,:+
T T13+
-1+ :+ I I7+ I9+ i3+ T
$f9-
s-
$-
2
876 955 1070 1106 1362
855 923 958 1103 1137
934
953 1153 1170
891 941 1022 1126
902 958 1025 1128
I-
;-
85Q 954
1013 1266 1452 1698
835 948
1004 1233 1434 1723
$-
23f T $ *7+ T
T
651t 651t 65it 651t 65lt
642t 642t 642t 642t 642t
624t
5234 5235 5233
Slot Slot S!Ot SiOt 510t
s21t s21t 521t 52lf
514J 5141
633t 633t 633t 633t
78.7 40.6 46.0 54.2 55.3
49.6 54.7 69.0 64.5 72.0
95.6
75.4 65.7 67.0
39.6 39.5 38.1 32.6 35.9
19.6 19.3 18.4 19.0
93.6 90.9
77.4 74.5 73.2 70.4
642t 642t 642t 6421‘
651t 651t 651t 65lt 651t
512t+Q,,
42.9 35.6 18.1 9.2
34.6 29.5 13.1 17.4 4.8
2.7
22.6 20.1 20.0
Qzs Qz2 Qzz
52lb 5211+ S215+
54.9 54.8 52.9 45.3 49.8
75.6 74.4 71.2 73.6
3.3 3.2
18.3 19.6 21.6 22.3
512t+Q,, 512t+Q,, 5l2t+ Qzz 512t+Q,, 5l2t+ Qz2
-li+Q,,
521&f 422 5211+ Qzz 52l1+ Qzz
51&+-Q,,
5121+ Qzz
642t 642t 642t 642t
1.2 3.6 4.8 8.4 8.7 4.5 5.1 6.0 6.1
633 t + Qzz 633 t + 422 633t+ 422 633t + 422 633t + Qn.
0.4
1.1 6.4 4.3
0.1 1.6 6.6 3.0
3.6 3.5 3.4 3.5
2.1 4.0
0.7 0.6 0.6 0.6
633t 6331 633t 633t
642t + Q22
512t+Q,, 512t+Q,, 512f + Qzz
5211+Qx
521J+ Qzz 5211+ Qa 5215+Q,,
Qx 6W+ 412 633f + 432 633t + Qsz 633t +
523$ 5233.
651t+Q22 651f+ Qzz 6Slt+ Qa
65lf+Q,, Qs2
Qzz 922 + Qzz + Qzz + Qtz + +
QZZ
65lf+Q,, 651t+ Qzo 651f+Q,, 651t+Qm 6Slt+Qm
633f 633t 633t 633 t 633t
65lt
slot 510f 5lOf
5l2i +
5W+Q,,
5l21+ 422 512&+ Qz2 5121+ Qz2
512t+ Qzz 512t+Q,,
512t+Q,,
512t+Q,,
521t+Qx 521t + Qa
52v+
521t+Q32
7.7 4.0 4.5 5.3 5.4
3.8 3.3 1.5 1.9 0.5
0.4
0.8 4.6 3.1
3.7 3.7 3.6 3.1 3.4
0.1 0.9 3.2 0.8
0.7 1.5
0.4 0.4 0.4 0.4
660t 660t 660f 660t 660f
660f 660t
6@t
660t 660f
642t
5144 5144
523J 5233. 523t
slot slot slot 510f
4x0 6W + Q30 633f +
65lt 651t 651f 651f
1.0 1.9 1.9 6.8 12.2
2.0 1.8 3.6 2.4 5.0
0.3
2.4 2.4
9.4 5.4
1.7
0.1 0.6 2.3 0.6
0.2 0.2
0.4 1.6 0.9 2.3
-
T.1. Kracikovci et al. / Nuclear orientation study
220 ‘.O
I ’
’ 3/2[6513
,____.____.___-____.-_--.----. 1.0
_ ---%
5/2[512]
t 0.5
-
0.0
!-
512 [6L2]
712 [633] 112 [660] 312 [651]
0.0
1.0 712 [633]
0.5
-_----_r,_-_,:::::::;
c
.-----
0.0 r 112 Fig. 4. Dependence
512
__,___ 912
1312
_ ___ .___ 1712
--.-I---.--------. 2112
2512
3,2[624] 2912
values of the mixing coefficients 6 $ on the angular momentum $-[SIO], $75121, $+[642], 1”[633] rotational bands in “‘Yb.
I
for the $+[651],
T.1. Kracikovd
et al. / Nuclear
orientation
221
study
TABLE 6 Experimental reduced E2 and Ml transition probabilities are compared The /3( uL.)~~~ were obtained from measured level half-lives Ii&[ Nn;Ali
f ;[521]
I&f
NnJ],
f $5211
f
$35121
B(E2) [e*.b’] exp theor
exp theor
$
exp theor
f &521]
exp theor
1 t
ev theor exp theor
1.23 f 0.09 1.18 0.88 f 0.09 1.11 0.25 f 0.09 0.32 (8.7 i0.9) x lO-6 3.2~10-~ (1.5kO.2) x~O-~ 8.2 x lO-4 (4.4kO.l) x 10-4 35 x lo-4
with the calculated
values.
I*‘) and S-values B(M1)
[&I
(0.80 f 0.05) x lo-’ 1.2 x lo-2
0.043 * 0.006 0.014
(1.00+0.08) x~O-~ 0.73 x 1o-4 (2.3 f 0.2) x lo-’ 31 x lo-5
is coupled to the %521] and $5231 states. The positive-parity states are perturbed due to strong coupling of the $6601 state with the $6511 and $6421 states. The calculated values of the E2 and Ml transition probabilities and their ratios are compared with the experimental results in tables 6 and 7. Average values of the transition intensities and multipole mixing ratios and the value of Q0=7.93 b [see ref. 2)] were used. Better agreement with experiment was obtained when the orbital and spin gyromagnetic ratios for the odd neutron were changed from the free-nucleon values: gl = 0.1, g, =0.9&r_., gR = Z/A = 0.41. The calculated and experimental values of 6(E2/Ml) are given in table 8; in general the agreement is good. The rotational bands in “’ Yb have been identified and analysed in previous work [see refs. 2,4*5-8)]and we confine the present discussion to several aspects connected with our results. The $5211 ground-state band, observed up to the 9 member in the (C-X, 3n) reaction *), has an irregular level spacing (see fig. 3). In ‘69Yb this irregularity is clearly reflected in the E2/Ml mixing ratios 12): the transitions connecting levels lying furthest apart have large E2 admixture (2 15%), while the close-lying levels are connected by nearly pure M 1 transitions (E2 =S 1% ). There are less data in “‘Yb; however the picture seems to be similar. The 3+ t 66.7 keV and s+ 5 154.8 keV transitions connecting widely spaced levels have within the limits of experimental errors large and approximately equal E2 admixtures, (32.6*0.8)% and (27.8* 7X)%, respectively, whereas the $+ 3 9.15 keV transition connecting the close-lying levels is nearly pure Ml with (0.034* 0.01 l)% E2 [ref. “)I. The agreement obtained between the experimental and theoretical values of transition probabilities and the magnitudes of 6(E2/Ml) is particularly good for this band. The sign of 6 within this band is only available for the 66.7 keV transition and was also calculated
TABLE I Experimental
reduced
E2 and MI transition
probability values
ratios are compared
B(oL;
K[N%Al,
I,- I,)/B(aL;
$5211
$5211
$5121
$5211
c+L
exp
theor
E2 E2 E2 E2
0.28*0.11 0.13 f ‘Z:$ 17.2 i 2.9 50*6 2.9 i 0.4 0.23 f 0.04 3.2+*.’ 1.5 16.7 f 8.5 0.6210.14 2.5 * 0.5 0.46*0.12 2.1 *0.3 0.73 ‘O0 23 s8 0.83*0.13 1.7*0.3 1.0?6OJ 0.6 +a.’ 0.3 3.1 T1.O 0.7
0.29 0.10 2.6 11 4.3 5.3 2.9 4.5 0.92 4.1 0.12 4.5 1.1 1.1 1.1 1.6 1.5 12
E2 $5 121
;[512]
$[514]
$[512]
($5211) >
I,+ 1;)
KJ NnJ], (r,+I‘)l(I,+G)
($5231)
with the calculated
{ Ml E2 E2 E2 { Ml E2 { Ml E2 { Ml E2 E2 E2 f Ml
f[521]
$6331
$6331
;[624]
3[633]
$[642]
;[633]
;[65 I]
$[633]
“) The value corresponds to the second levels (see table 5 and text).
possible
E2
~0.87
E2 E2
4.1* 1.3 24.7
I Ml E2 ( Ml E2 { Ml E2 { Ml E2 E2 Ml E2 E2 { Ml E2 { Ml E2 { Ml Ml Ml Ml E2 { Ml E2 { Ml E2 MI
0.45 ‘0OZI I29 2.1”40.9 1.3 ‘;I: 2.2:;: 0.8” 0.6 s l.1’2409 0.6? 0.5 Sl.3 S3.4
interpretation
1.5zto.5 4.7 ?.a 47 0.36 ?09 0.07 0.30 f 0.02 SO.034 0.012*0.004 SO.09 0.039 f 0.013 3.0+:.: 13::s 4.2?’ 17’:s: 1.s 1.2 ‘;:: f3”504 1.3$ 1.2 0.8 ‘;.; 1.1’2210 of the 1024.6 and
1.2 5.1 4.3 8.8 87 a { 0 76 ) I AJ* “) C:Z “) 1A.L “) {z,!=) {::: “) C:’ “) {I-: “) I:“,? 4.2 0.79 0.67 0.58 15 0.73 23 6.6 25 3.8 2.5 0.95 0.013 0.43 0.005 0.45 1127.7 keV
TABLE 8 The E2/Ml
multipole
mixing
ratios of the transitions
in “‘Yh
are compared E2/Ml
I&[ Nn:A],
4&INnJl,
E, Wfl
66.7 9.15 154.8 85.6 109.3 132.3 55.7 46.5 712.6 627.0 517.8 631.0 498.8 759.2 1255.1 1169.5 66.4 902.2 948.7 794.0 778.0 897.1 881.0 835.9 707.5 877.6 868.4 948.7 794.0 778.0 897.1 72.4 91.4 177.7 178.5 229.3 888.7 816.3 724.9 839.9 761.6 676.2 998.0 925.8 “) b, ‘) d,
with the calculated
mixing
ratio
ev
theor -0.50 -0.037 -0.39 -0.37 -0.35 -0.34 -0.16 0.20 -2.89 1.21 0.32 0.35 0.10 -4.42 -5.10 -0.43 0.58
-0.696*0.013 “) IO.018 f 0.0031 b) 10.62iO.121 ‘) -0.30’0,,~ -0.16+0.04 )1.2+:::1 b) -0.05*0.15 IO.165 *0.0221 b, -1.52*0.16 0.76” 0.19 I4 0.54+0,-:: 2.0+;,‘: 0.1*0.2 12.2+;;1 b) ~~1.0~ b) qo.91 b) 0.31 f 0.07 ‘) -0.06 * 0.05 -1.52*0.16 0.32*0.07 1.1*0.4 0.0 f 0.2 IO.7‘:.:I “) S IO.41b) S ]0.5( b)
2.13 0.021 0.044 0.047 0.059 0.034 0.27 -0.008 0.23 0.16 0.016
I2’PI b, -0b) S IO.31b) 1.5?’ 0,s 0.32kO.07 1.1*0.4 0.0*0.2 IO.7‘;::I b) S IO.41b) -0.31?‘3 o.,s -0.25 -to.” cl.*, -0.32 d, -0.28 d, -0.32 ‘) =-G Il.61 b, IO.6 * 0.71 b, -0s) -0.48 “-;:“o; -0.477 f 0.025 S IO.71b) -0 16:0.‘6 IO:66 2651
Magnitude is the ]S(a,)] value, the sign of which is determined These data are the magnitudes of S-values obtained from ICC. Ref. 2). Ref.‘).
-0.038 0.047 0.017 -0.23 -0.22 -0.21 -0.18 -0.21 -0.43 0.26 0.014 -0.16 -0.079 0.026 -0.31 0.48
b, in the present
work.
values
224
T. I. Kracikova’ et al. / Nuclear orientation study
correctly.
The proposed
structure
of this band
indicates
that the single-quasiparticle
is similar
component
to that found
is the major
in ‘69Yb and
one.
Coriolis mixing is important for the $6331 band and it grows rapidly, although slower than in ‘69Yb, with increasing spin value. The band levels depopulate by competing E2 and M 1 + E2 transitions and experimental mixing ratios are known for five of these Ml + E2 transitions. As in ‘69Yb, all these mixing ratios are negative and differ very little from each other and from the values obtained for the transitions in ‘69Yb. The theory describes this picture rather well, which may be clearly seen if we compare the experimental and theoretical values of 6 given in table 8. The mixing ratios of the last three - $! + 7, y+ 9 and f + $ - transitions were determined by Lindblad et al. “). A comparison of our proposed structure of the $6331 band levels with that of Lindblad et al. “) shows some differences: the amplitudes of the main $6331 and $[651] components change more rapidly in their case and a significant admixture of between 2% and 10% of the $6241 state is present when the spin changes calculations.
from 9 to 5. This contribution
is negligible
in our
The 902 and 1079 keV levels observed by Burke et al. “) in the (d, t) and (d, p) reactions were interpreted by them as the $ and $ members of the 35211 band. On the basis of the “‘Lu decay study, Batsev and Bench-0smolovskaya4) proposed that the 902.2, 958.2, 1024.6 and 1124.3 keV levels are respectively the z, 3, $ and 4 members of this band. Adam et al. ‘) have replaced the 1124.3 keV level by the 1127.7 keV level and proposed two possible interpretations: the first is the same as that of ref. 4), while the second considers that the 944.3, 1024.6 and 1127.7 keV levels are the s, s and s states of the $5231 band. The available data do not allow us to draw a conclusion. The experimental moment-of-inertia parameters for the levels of the 5[521] and $5231 bands in “‘Yb (see table 9) may be compared with those and are consistent with both interpretations, but it is clearly seen in ‘67~‘69~‘73~‘75Yb that the 1079 keV level cannot be the i state of the $5211 band. The precision of the mixing ratios of the transitions depopulating these levels is not high in most cases, but when it is sufficiently good and the sign of 6 is known, then the calculated magnitudes of 6 agree with the experimental ones within a factor of 2 and the signs agree in every case except for the 902.2 keV transition (see table 8). It is expected that the $5211 band is strongly coupled with the K = $ y-vibrational band based on the 25211 state. Burke et al. “) concluded that this admixture is not less than 50% in “‘Yb. Our calculated structure, shown in table 5, agrees with this experimental result. In the (d, p) reaction, Burke et al. “) observed five levels in “‘Yb with relative intensities which correspond to those of the members of the $[5 lo] bands in ‘73P’75Yb. However, the absolute intensities in “‘Yb were only about 60% of the values expected for this band. They explained this by the mixing between the $5101 band based on the single-particle state and the K =i y-vibrational band based on the $5 121 state. Our proposed structure of the 25101 band is consistent with the
11.34
A
“) Value was calculated
12.34 12.70
12.28
12.85
12.52
10.59
10.20 14.13 “)
{ 11.45 5.41 “)
1 9.49 11.26 “)
11.18
12.52
12.11
171krb
L69yb
12.42
12.57
12.20
17syb
9,2,LL,Z
4~2.~2
A T/2,11,2
A 5/2.9/2
A 11,2.13,2
A
A 7,?,9,2
As/~/z
A for the 35211 and $5231 hands
9
of the band (see text).
10.83 10.79
10.82
10.67
10.93
10.70
11.00
173yb
parameters
with the 1079 keV level as the 3 member
11.28
AS/W, A
T/2,11,2
11.48
9,2.11,2
A 3/&l/2
A
11.20
A,,,,,,,
7/49/2
11.88
A 3/u/2
167yb
35211 band
Moment-of-inertia
TABLE
11.14 10.98
11.18
10.84
11.15
11.13
11.24
167yb
35231 band
10.87
11.20
10.56
11.24
11.14
169yb
11.46
11.45
11.47
171yb
i
3 g.
3
S.
? b ?
!? P % a 2 .E ’
.Y .*
226
T.I. Kracfkovd
et al. / Nuclear orientation
result of Burke et al. and the calculated ones to within 2%.
experimental experimental
The 867 and 1118 keV levels were identified
study
level energies
as the 2 and y members
agree with the of the $6421
band ‘,‘). Batsev and Bench-Osmolovskaya “) observed the 984.0 keV level and interpreted it as the f member of this band. With this interpretation, the moment-ofinertia parameter AS,2,9,2 = 7.3 1 agrees with that of ‘69Yb, A5,2,9,2 = 7.26. The spin of the 1093.3 keV level was assigned uniquely in the present work as g, and we identified this level as the g member of the $[65 l] band. The 1093.3 keV level de-excites mainly to the 3’ and f’ levels of the $6331 band. The 834.1 f 0.4 keV transition, observed by Batsev and Bench-0smolovskaya4) to be equal in energy to the difference between the ;+$651] and y+$633] states, was not placed in their decay scheme. Adam et al. ‘) have also observed a transition, 834.5 + 0.4 keV, with similar relative intensity, but placed it as depopulating the 1080.9 keV level. If we assume that most of this transition intensity depopulates the 1093.3 keV level and all three depopulating transitions have pure E2 multipolarity, we obtain according to Alaga ratios are (0.78 f 0.04) : 1: (0.8 f rules 1998: Igz6 : I834 = 0.17 : 1 : 1.32. The experimental 0.4). Both
of the experimental
and
theoretical
ratios
agree
with
their
counter-
parts for similar transitions in ‘69Yb [ref. 29)], I,,, : I876: I,,, = 0.17 : 1: 1.28 and (G 1) : 1: (1.0 f 0.5). It seems that in both cases the agreement between the experimental and Alaga values is good for the two last transitions, while significant deviations are observed for the first 4’+ I’ transitions. This may be explained by the Coriolis interaction. Indeed, a strong Coriolis mixing is expected between pairs of the bands with K-values differing by unity. Our calculations for “‘Yb as well as for ‘69Yb confirm these expectations for both the $6421 and $6511 bands (see table 5 and fig. 4). Moreover, the calculated mixing ratios agree well with the experimental ones in magnitude
and sign for both bands.
6. Conclusions The nuclear
orientation
experiments
have been successful
in removing
previous
ambiguities and in obtaining an extensive set of spin of levels in “‘Yb. 29 b-values have been determined and they have confirmed and improved the ICC data. An important advantage of the directional-distribution experiments is that they are sensitive also to the sign of 6. Calculations based on the semi-microscopic quasiparticle-phonon model with Coriolis mixing included provide the energies of the rotational band levels, the reduced probabilities of E2 and M 1 transitions and the E2/Ml mixing ratios and their signs. Both positive- and negative-parity levels have been considered. The comparison between theory and experiment is, on the whole, successful. This approach has provided a more complete and detailed understanding of “‘Yb than previous work and extends the similar treatment of the lighter 167,‘69Ybisotopes.
T.I. Kracikovd et al. / Nuclear orientation study
221
In general it was not found necessary to reduce the Coriolis matrix elements in the calculations for any of these isotopes as had been done in previous theoretical studies.
References 1) D.J. Horen and B. Harmatz, Nucl. Data Sheets 11 (1974) 549 2) V.D. Vorobiev, T.M. Usypko and S.A. Shestopalova, Decay schemes of radioactive nuclei A = 171- 174 (Nauka, Leningrad, 1977) 3) P. Sen and H. Bakhru, 2. Phys. AZ81 (1977) 263 4) S. Batsev and N.A. Bench-Osmolovskaya, Izv. Akad. Nauk SSSR (ser. fiz.) 45 (1981) 697 5) J. Adam, V. Hnatowicz, V. Zvolska, J. Zvolsky, B. Kracik and M. FiSer, Izv. Akad. Nauk SSSR (ser. fiz.) 48 (1984) 318 6) D.G. Burke, B. Zeidman, B. Elbek, B. Herskind and M. Olesen, Mat. Fys. Medd. Dan. Vid. Selsk. 35, No. 2 (1966) 7) D.G. Burke, W.P. Alford and R.A:‘O’Neil, Nucl. Phys. A161 (1971) 129 8) Th. Lindblad, H. Ryde and D. Barneoud, Nucl. Phys. Al93 (1972) 155 9) K.S. Krane, C.E. Olsen, S.S. Rosenblum and W.A. Steyert, Phys. Rev. Cl3 (1976) 1295 10) T.I. Kracikova, M. Finger, S. Davaa, J. Dupak, V.N. Pavlov, N.A. Lebedev, W.D. Hamilton and C. &it, Czech. J. Phys. B31 (1981) 527 11) J. Kvasil, T.I. Kracikovl, M. Finger and B. Choriev, Czech. J. Phys. B31 (1981) 1376 12) S. Davaa, T.I. Kracikova, M. Finger, J. Kvasil, V.I. Fominykh and W.D. Hamilton, J. of Phys. G8 (1982) 1585 13) J. Kvasil, T.I. Kracikovl, S. Davaa, M. Finger and B. Choriev, Czech. J. Phys. B33 (1983) 626 14) V.G. Soloviev, Theory of complex nuclei (Pergamon, Oxford, 1976) 15) J. Kvasil, I.N. Mikhailov, R.Ch. Safarov and B. Choriev, Czech. J. Phys. B2ll (1978) 843 16) S.R. Avramov, E.V. Sosnovskaya and V.M. Tsupko-Sitnikov, Joint Institute for Nuclear Research, Dubna, JINR preprint RlO-9741 (1976) 17) C.M. Lederer and V.S. Shirley, Tables of isotopes, 7th ed. (Wiley, New York, 1978) 18) K.S. Krane and R.M. Steffen, Phys. Rev. C2 (1970) 724 19) K.S. Krane, At. Nucl. Data Tables All (1973) 350 20) I.M. Band and M.B. Trzaskovskaya, Tables of internal conversion coefficients on K, L and M shells, lOsZ< 104 (Leningrad, 1978) 21) F. Riisel, H.M. Fries, K. Alder and H.C. Pauli, At. Nucl. Data Tables 21 (1978) 291 22) G. Kaye, Nucl. Phys. 86 (1966) 241 23) K.P. Artamonova, E.P. Grigoriev, A.V. Zolotavin and V.O. Sergeev, Izv. Akad. Nauk SSSR (ser. fiz.) 39 (1975) 523 24) K.P. Artamonova, E.P. Grigoriev, A.V. Zolotavin and V.O. Sergeev, Izv. Akad. Nauk SSSR (ser. liz.) 39 (1975) 1773 25) B.S. Dzelepov, in The properties of deformed nuclei, Lectures of 10th USSR school on nuclear physics (Fan, Tashkent, 1983) pt. I, p. 3 26) V.A. Balalayev, B.S. Dzelepov, I.F. Uchevatkin and S.A. Shestopalova, Izv. Akad. Nauk SSSR (ser. fiz.) 35 (1971) 18 27) F.A. Gareev, S.P. Ivanova, V.G. Soloviev and S.I. Fedotov, Physics of elementary particles and atomic nuclei, Vol. 4 (Atomizdat, Moscow, 1973) pt. 2 28) A. Bohr and B.R. Mottelson, Nuclear structure II (Benjamin, New York, 1974) 29) V.A. Balalayev, B.S. Dzelepov and V.E. Ter-Nersesyants, (Nauka, Leningrad, 1978) p. 183
Isobaric
nuclei with mass number
A = 169