- Email: [email protected]
Angular-correlation study of the level scheme of 193Ir
Nuclear Physics A426 (1984) 20-36 ~) North-Holland Publishing Company
A N G U L A R - C O R R E L A T I O N S T U D Y O F T H E L E V E L S C H E M E OF 19air H. H. GHALEB and K. S. KRANE
Department of Physics, Oregon State University, Corvallis, Oregon 97331, USA
Received 2 February 1984 Abstract: The decay of 193Os to 1931r has been studied by 77 angular correlations. Inconsistencies between previous angular correlations, internal conversion coefficients, and nuclear orientation angular distributions have been satisfactorily resolved by the present results. These data are used to derive a set of E2/M1 multipole mixing ratios of the transitions between low-lying states. The resulting electromagnetic transition moments are compared with calculations based on the Nilsson model with Coriolis mixing and on the interacting boson-fermion model. E I
RADIOACTIVITY 193Os [from Os(n,y)]; measured ?y(0). '93Ir deduced 6(E2/M1).
I
1. I n t r o d u c t i o n
The electromagnetic properties of the low-lying states of odd-mass nuclei are calculable from a variety o f models, from extreme single-particle models to those involving the coupling of the single-particle degrees of freedom to multiparticle and collective excitations. In order to judge the success of such calculations, it is necessary to have the most complete set of experimental values of the static and transitional electromagnetic moments. Unfortunately a reasonably complete and precise set of such data (static moments, branching ratios, lifetimes, internal conversion coefficients, E2/M1 multipole mixing ratios) is available for only very few nuclei. In a previous publication 1) concerning the levels of 191Ir, the available spectroscopic data were combined with precise E2/M1 multipole mixing ratios from angulardistribution and angular-correlation experiments, and it was shown how the deduced E2 and M 1 moments could be used to differentiate a m o n g the competing theories. The present work describes a similar analysis of the levels of 193Ir. When this work was begun, the previous data available for 193Ir did not form a mutually consistent set. It was necessary to remeasure several of the 7? angular correlations, the results of which are reported in the present work. In the process of comparing those results with previous nuclear orientation (n.o.) angular distributions, a small but systematic error in the latter was discovered. The n.o. data are reanalyzed, and it is shown that the present angular correlation data and the reanalyzed nuclear orientation data, along with the other previous 20
H. H. Ghaleb, K. S. Krane / 1931r
21
spectroscopic data, give a consistent set of. multipole matrix elements. The remarkable agreement between the corresponding 191Ir and Jgalr multipole moments is discussed, and it is concluded that the model used previously to describe t91Ir serves equally well to describe ~galr.
2. The 19305 decay scheme The radioactive decay of 193Os to '931r was previously studied by Berg et al. 2) and by Price and Johns 3). The decay scheme is shown in fig. 1. The available spectroscopic data have been recently summarized by Shirley 4), and table 1 shows a summary of the electromagnetic properties of some of the low-lying even-parity levels. For most of the transitions listed in table 1, the E2 admixtures are not determined with sufficient precision to permit meaningful comparisons withtheory. In order to improve that situation, several ~;), angular-correlation measurements have been reported 5-a). In many cases these data lead to improved values of the E2/M1 multipole mixing ratios, but there are remaining unresolved discrepancies and inconsistencies in the data. A further improvement in the knowledge of the electromagnetic transition moments resulted from measurement of the 7-ray 31.5 h
,93
'
\
3 / 2 - 3/2 [512]
760SI17 ' ~ I ~ -
0.03
8.6
0.3
8.2
0.5 0.1
8.0 8.8
874
¢~
r4o '
712 ~
~5/23/2
--
e.ON ~ q" iO ,~1"'q" i,";
0.1
I0.0
0.7 2.4
8.3 7.8
8
0.02
7.5 8.7 10.4
0.05
I0.1
2.0 12
8.6 7.9
leo 139 80
19
7.8 7.5
o
0.8
( 3 / 2 +, 5/2 + ) r o e d ed ,~ ~- - ;.N ,~ ~,.~ ~ OJ ~ g~ON
559
I
356 \ 299
. . . . . ]
I~(%}
Io~
ft
3/2 ÷ I/2 [4H]
II IIIII I!111 -
I
l'iiiiii fill illi , ° wo
.
54
3/2"
I
460 362
.
I I I II I I I
• II II
I I!
I I
I
I
.
.
+
E (keV)
m
-
III
/_3/2~-
~-5/2+ •),--,,,'2I12 +
1/2 [400]
I II3,2-3,2t4o2
I'K [ Nnz A] 193. 77Lr116
Fig. 1. Decay scheme of 193Os to 1931r.
22
H. H. Ghaleb, K. S. Krane / xgalr
TABLE 1 Electromagnetic transitions from 1931r levels Level E (keV)
Mean life (ns)
73 139
8.79 (22) 0.1150 (3)
180
0.085 (10)
358
0.029 (4)
362
0.052 (10)
460
0.016 (3)
557
0.049 (11)
559
0.0015 (2)
712
0.022 (20)
E:,
y-intensity
~0 E2
(keV) 73 66 139 41 107 180 219 358 182 289 362 99 280 322 387 460 97 377 418 484 557 420 559 155 252 532 573 712
82.0 ( 1 2 )
27.8(10)
108.0 (5)
9.1 (8)
16.1 (8) 4.6 (5) 0.22 (5) 0.25 (8) 4.9 (5) 3.6 (3) 7.5 (6) 0.42 ~6~ 31.5 116) 32.3 (16) 31.9 (16) 100 (5) 2.5 (2) 1.8 12~ 1.38(14) 4.3 (3) 33 (3) 4.2 (3) 12.3 (12) 0.76(11 ) 5.5 (4) 2.10(15) O.49 (5) O.39 (6)
1.7 (4) 20 (8) 100 15 (13) 100 < 8 < < < 17 4
10 8 10 (7) ~2)
100 < 12 < 4 < 8 < 20 < 24
a n g u l a r d i s t r i b u t i o n s f o l l o w i n g l o w - t e m p e r a t u r e nuclear o r i e n t a t i o n g). T h e analyses o f the a n g u l a r - d i s t r i b u t i o n a n d a n g u l a r - c o r r e l a t i o n d a t a suffer from similar difficulties-there is a lack of a sufficient n u m b e r of transitions of pure m u l t i p o l a r i t y in parallel o r in coincidence with the transitions of m i x e d M1 + E 2 m u l t i p o l a r i t y . F o r example, in the a n g u l a r - d i s t r i b u t i o n analysis, four mixed transitions (280, 322, 387, 460 keV) d e p o p u l a t e the 460 keV level, a n d an a c c u r a t e k n o w l e d g e of the m u l t i p o l e mixing ratio of any one w o u l d p e r m i t analysis of the o t h e r three. T h e 322-139 keV a n g u l a r c o r r e l a t i o n has been previously m e a s u r e d 5-8), and its analysis could in principle yield 6(322), which c o u l d in turn serve for analysis of the other transitions, but the results of the previous a n g u l a r - c o r r e l a t i o n w o r k are not in g o o d m u t u a l a g r e e m e n t ; in fact, the r e m e a s u r e m e n t of this correlation, which is critical for the analysis of the previous a n g u l a r - d i s t r i b u t i o n work, was the p r i m a r y m o t i v a t i o n for the present work. O u r results indicate t h a t the previous results are systematically incorrect, a n d thus
H. H. Ghaleb, K. S. Krane / 1931r
23
many of the decay parameters deduced previously 9) based on this correlation are incorrect. As we show below, the 322-139 keV angular correlation has an unusually large anisotropy, and thus even small admixtures of other correlations are liable to have a substantial effect; previous angular correlation work using NaI detectors may show effects of interfering cascades, while the present work using Ge(Li) detectors is relatively free of such interference.
3. Experimental details 3.1. SAMPLE PREPARATION Radioactive samples of 193Os were prepared by neutron activation of Os metal powder in natural isotopic abundance. Samples in the range of 10-100 mg were irradiated for approximately one hour in a thermal neutron flux of 1013 n/cm2/s, resulting in activities in the range of 100 pCi. The accompanying longerTlived 191Os activity did not interfere with the measurement, since it gives only a single 7-ray of energy 129 keV. Each sample was measured for approximately one half-life, and the present results represent data from more than 50 individual samples. The samples were used in the original chemical form, since the short lifetimes of the levels make it unlikely that extranuclear perturbations can attenuate the correlations. [Even the longest-lived level at 139 keV shows an attenuation of only about 10~o in a magnetized ferromagnetic alloy 5).] Since the present results show a larqer anisotropy for the 322-139 keV correlation than previous work using liquid s'6) or crystalline salt v) environments, the assumption of negligible attenuation of the present results seems justified. 3.2. APPARATUS The angular correlations were measured using a Ge(Li)-Ge(Li) system in two different modes. (A sample 7-ray spectrum is shown in fig. 2.) The first mode was a conventional one in which single channel analyzer (SCA) windows were set on each detector and coincidence counts were accumulated at up to 9 angles between 90 ° and 270 °. Four cascades could be simultaneously measured in this mode lo). In the second mode, a complete coincidence spectrum gated by a SCA window on one detector was routed into one of four quadrants of a multichannel analyzer (MCA) for four different positions of the movable detector. In this latter mode, corrections for effects on the measured correlations from coincident Compton backgrounds could be made directly. As discussed in a previous publication 11), angular correlations can be subject to systematic errors in cases in which an intense cross-over transition competes with the cascade under investigation. In the case of the 193Os decay, the intense 460 keV transition can Compton-scatter from one detector to another, and in the process
24
H. H. Ghaleb, K. S. Krane I
I
139 129 .:. 107 ~.,.
1931r
I
I
180
-. " "
280 r.
+
: ""
182
219
252
~'--"~"~" <"~"/"'~,,.,'-.,~,""k,,,,,___,,'
t-
/
:522
',;'-,,,-",
587
/ :'
362
:":
r.,
"--.-.~....:~..,.:~
:". 4 6 0 ••
418
557
+
g 0
-
420
'
-...,., j...~
.
'. ~,.-.:',.:~
+
(-559
...
":'r':.V.,.~:S=....;:" !-... 5". ;'~* \':.~,'.,..~..':-..,,/~".
6"
" ::/::-';~'~:::<:'/:':'!:'<:'::*'5
L
i
I
200
500
700
800
,
[
i
400 900 Channel
I
500
,
I
,__
600
1000 Number
Fig. 2. 7-spectrum of the 193Os decay.
energies can be deposited that simulate 280-180 keV coincidences. In particular, when the angle between the two detectors is 0 = 90 ° (in which case the Compton scattering angle is about q~ = 135°), the scattered photon has energy E' = 181 keV, while 279 keV is left with the first detector. Lead shields used in the present study block the path of the scattered p h o t o n and eliminate this problem at that particular position. However, when 0 > 120° (4~ > 150°), it is not possible for lead shields to eliminate this effect without also blocking direct radiation from the source, and in fact the present results for the 280-180 keV correlation showed anomalously large coincidence counting rates when 0 --- 120°. (Such counting rates must be spurious, because only a large A44 term in the correlation could give such an increase in the counting rate near 120 °, but an an A44 term is forbidden for the 280-180 keV correlation with its spin-~ intermediate state.) For 135° < 0 < 180°, the scattered photon has energy E' = 164 to 168 keV, and no interference is to be expected when using Ge(Li) detectors, but the poorer energy resolutions of NaI detectors may result in contributions from these Compton coincidences. This effect would tend to increase the counting rates near 180°, contributing a positive anisotropy to the measured correlation. Indeed, the previously reported 7.8) 280180 keV correlations both show a positive anisotropy, while the present results show a negative anisotropy. The positive anisotropy does n o t give a solution for the 280 and 180 keV mixing ratios consistent with the conversion data and with other measured correlations, as discussed in the previous A = 193 compilation 12). The presently reported negative anisotropy, on the other hand, is entirely consistent with previous spectroscopic results.
H. H. Ghaleb, K. S. Krane / tgalr
25
3.3. DATA ANALYSIS The coincidence counting rates~ corrected for background and accidental coincidences, were fit to the usual angular-correlation function W(O) = 1 + Q 2 2 A e 2 P 2 ( c o s O)+Q,,4A,,,,P4(cos 0),
(1)
where Qkk are the geometrical factors that correct for finite detector solid angle and where the angular correlation coefficients Akk are Akk = Bk(y l)UkAk(y2).
(2)
The coefficients Bk(~;1) and Ak(Y2) depend on the y-ray multipole mixing ratios of the transitions under study ; the U k correct for the effects of unobserved radiations intermediate between ?~ and Y2. The dependence of these coefficients on the y-ray mixing ratios is discussed in ref. lo). For comparison with the angular-correlation data, the n.o. angular distributions are written W(O) = 1 + Q2a2P2(cos 0),
(3)
a 2 = B 2 ( T ) U 2 A e ( y ).
(4)
where
The orientation parameter B E ( T ) depends on the orientation of the parent state; U2 and A 2 have the same meaning as in eq. (2).
4. Results
The angular-correlation coefficients measured in the present work are compared with those measured in previous work in table 2. Several differences with previous work are notable: (i) the present 322-139 keV anisotropy is larger than that reported in previous work, as was discussed above in sect. 2; (ii) the present 280180 keV anisotropy has the opposite sign compared with those previously reported, as discussed above in subsect. 3.2. Before attempting to compare the present angular-correlation results with those obtained previously from low-temperature nuclear orientation g), a careful review of the latter was made. This review was in part prompted by the new results presently reported for the 322-139 keV correlation, which invalidated the previous analysis for many of the mixing ratios. In re-examining the data from the previous n.o. experiment, it was discovered that a systematic anisotropy amounting to I-2 ~,,,
H. H. Ghaleb, K. S. Krane / 19Sir
26
TABLE 2 Angular correlations in the decay of 1'~3Os Cascade
A 22
A44
Refl
322 139
0.602(14) 0.555 (5) 0.575(12) 0.338(36) 0.676 (8) 0.113{13) 0.137(15) -0.132 (91 -0.139(12) -0.13 (1) - 0.111 (27) -0.098 (9) -0.090(11) -0.199 (7~ -0.187 (7) - 0.420(24) -0.380(29) -0.112 (9) -0.093(10) -0.221(15) -0.210(18) - 0.362(30) - 0.480(40) - 0.477149) -0.152(23) -0.159(27) + 0.206(35 ) +0.225(41)
- 0.024~ 16) 0.006 (7) 0.045(20) - 0.001 16) -0.005(12) 0.052(41 ) -0.029(18)
s) ") ~) s) PW~t 7) s) PW PW ~') 8) PW PW ~') 8) PW PW 7) 8) PW PW 7) PW PW PW PW PW PW
280-180
280-107
420-139
252-460
252-387
252-322 252-280
-0.017(15t 0.02 (3) 0.024(31 ) -0.028(13) 0.02 (2) -0.013(10~ -0.075(44) -0.067(58) +0.055(14) -0.028(27) - 0.022(58) 0.000(55) +0.008(41) -0.042(47)
a) Present work.
was present in those transitions that were expected to show a vanishing anisotropy (K X-rays, 511 keV annihilation radiation, 193Ir transitions from spin-½ levels). The cause of this small and spurious but systematic effect is not known, but it was present in several transitions in both the low-energy and high-energy portions of the spectrum. (Even a spectral line originating from a test pulser fed into the detector preamp showed the effect.) It was therefore decided to correct the anisotropies of all of the 19Sir transitions by an amount determined from the average measured anisotropy of the 7-rays that were expected to show vanishing anisotropies. This correction factor amounts to + 0 . 0 1 8 _ 0 . 0 0 2 , and the corrected angular distributions are shown in table 3. The consistency between the angular-distribution and angular-correlation data can be examined by comparing cases in which several transitions depopulate the same level. Considering first the 460 keV level, since the A22 from the angular
H. H. Ghaleb, K. S. Krane / 19Slr
27
TABLE 3 Corrected results from angular distribution experiment [results from ref. 9) corrected for spurious systematic anisotropy] ~,-ray
a2
";-ray
a2
107 139 155 180 182 219 235 252 280 289
0.056(10) 0.215 (2) 0.006(20) 0.088 (5) 0.019 (5) -0.033 (3) 0.172 (9) -0.099 (3) - 0 . 0 5 0 (2) -0.119 (4)
299 322 362 377 + 379 387 418+420 441 460 532 557+559
- 0.029 14) 0.058 (2) 0.196 (2) 0.009[ 12) 0.129 (2) -0.077 (3) -0.135 (6) 0.065 (2) -0.333 (8} 0.022 (2)
correlation and the a2 from the angular distribution are both proportional to A2()'), we expect the ratios
A22(252-280) : A2z(252-322) : A2z(252-387) : A22(252-460), az(280):a2(322) : az(387) : a2(460) to be identical. The experimental values are, respectively, -0.93+0.17:0.69__+0.11 : 2.17+0.20:1.00___0.07 from table 2, and - 0.77 + 0.03 : 0.89 + 0.03 : 1.98 _ 0.03 : 1.00 + 0.03 from table 3. The agreement between these two sets of ratios is excellent. For the transitions from the 180 keV level, the ratios A22(280- 107) : A22(280- 180), az(107) • a2(180) can be compared. These give, respectively, 0.74 _ 0.07 • 1.00 __+0.07, 0.64+__0.11:1.00+0.06. Again the ratios are in good agreement; in particular, the sign of the 280-180 keV anisotropy is consistent with the sign of the 280-107 keV anisotropy.
28
H. H. Ghaleb, K. S. Krane / 1931r
In all of the reported angular correlations, both transitions are of mixed multipolarity; thus the correlations cannot be independently analyzed for the multipole mixing ratios of both transitions. It is necessary to begin the analysis with a transition of known multipolarity, for which the 139 keV 7-ray can be chosen since its multipolarity has been precisely determined from L-subshell conversion ratios: 16[ = 0.353+_0.021 from Berg et al.Z); 161 = 0.316+_0.015 from Price and Johns 3). The sign of 6 has been determined to be negative from angulardistribution measurements following nuclear orientation 9) and also following Coulomb excitation 13). We therefore take 6(139) = - 0 . 3 2 9 + 0 . 0 1 2 which corresponds to A2(139 ) = +0.882+0.013, A4(139)= +0.069+0.004. The presently measured 322-139 correlation, together with the above deduced value of 6(139), can then be analyzed to give 6(322) = +0.234+0.010. Following the same procedure as ref. 1), the angular distributions of the transitions depopulating the 460 keV level can be analyzed by comparison with the 322 keV angular distribution, according to the relationship
a2(}')
A2(7)
--
a2(322) A2(322)
(5)
which gives for the mixing ratios 6(280) = -0.049+0.012, 6(387) = - 0.24-+ 0.04, 6(460) = - 0.64 + 0.03. These four deduced mixing ratios are in good agreement with the internal conversion results summarized in table 1. With the above deduced value for 6(280), the 280-180 keV and 280-107 keV correlations can be analyzed, with the results 6(107) = +0.16_+0.01, 6(180) = -0.48__.0.02. The internal conversion results 2, 3) give, respectively, 0.14 + 0.01 and 0.59 + 0.10 for the magnitudes of the mixing ratios and are again in excellent agreement with the angular-correlation results.
H. H. Ghaleb, K. S. Krane / 1931r
29
The four cascades involving the 252 keV radiation can be analyzed using the deduced values of the mixing ratios of the four transitions depopulating the 460 keV level, 252-280:
6(252) = -0.16_+0.08,
252-322:
6(252) =
252-387:
6(252) = -0.12_+0.04,
252-460:
6(252) = -0.08_+0.02,
0.00_+0.04,
which give the average value 6(252) = - 0.079_+ 0.020. This value of 6(252) then permits the n.o. data for the angular distributions of the 155 and 532 keV transitions to be analyzed by comparison with the 252 keV angular distribution, yielding 6(155) = +0.26_+0.03, 6(532)
=
-L'f~AR+O'32 ~
~.-r~--O.l
6.
With this value of 6(532) the expected 532-107 keV correlation is A22 = +0.052, in agreement with the measured values A22 = 0.089_+0.030 [ref.°)], A22 = 0.058_+0.018 [ref. 8)]. The present results for the combined (418+420)-139 keV correlation show a larger anisotropy than the results of previous work. Correcting for the 25~o contribution from the pure-E2 418 keV transition, the resulting 420-139 keV correlation gives 6(420) = + 0.030_+ 0.041. This value of 6(420) can then be used to analyze the n.o. data for 6(559) by comparing the angular distributions of the 420 and 559 keV transitions. The result is 6(559) = +0.007+0.031. Finally, the corrected n.o. angular distributions of the 362 and 182 keV transitions can be analyzed in comparison with the angular distribution of the pure-E2 289 keV transition which also depopulates the 362 keV level. The resulting coefficients are A2(362) = +0.881(31) and A2(182) = +0.085(22) and the
30
H. H. Ghaleb, K. S. Krane / tgalr
corresponding mixing ratios are 6(362) = - 0 . 3 2 8 + 0 . 0 2 8 , 6(182) = +0.149-1-0.011. Based on this analysis, the expected 182-.107 keV angular correlation is A22 = - 0 . 0 1 6 ; t h e measured value 6) is Azz = -0.40(8), which does not agree with the value expected on the basis of the angular-distribution data. The re-evaluation and re-analysis of the n.o. data lead to improved value of the ~gaos orientation parameter and the deorientation coefficients of the //-decays. Again assuming the 142 keV transition to be at most 20~o E2, as in ref. 9), the 219 and 299 keV angular distributions give B 2 = 0 . 4 0 + 0 . 0 5 , including a 10~/o correction for the effects of nonalignment of the local and applied fields ~4). The deduced magnetic m o m e n t is q#[.= 0.78___0.07 PN, in better agreement with the systematics of other 3-[512] states in this region than was the original value of 1.30 + 0.19/~N deduced in ref. 9). The A I = 1 first-forbidden fl-decays (those leading to the 5+ final states at 139, 362, and 559 keV) can be mixtures of j~ = 1 and 2 radiations; the jp = 2 contribution is usually of small intensity and is often neglected ((-approximation). Previously g) we found substantial (50~,) contributions from the ja = 2 terms. With the modified analysis described above, theja = 2 contributions to the three decays are, respectively, (12+ 10)~o, (15__9)~, and (18+8)~,~. These values are more consistent with the expected small contribution ofja = 2 decays~ The fl-decays to the 3+ final states (180,460, and 712 keV) can be mixtures ofja = 0, 1, and 2. The decays to the 180 and 712 keV levels show virtually pure Jt~ = 0 decays (U 2 = 1.1+__0.1 and 0.90+_0.11, respectively), while the decay to 460 keV has U2 = 0.45+__0.05 and thus, neglecting the j~ = 2 contribution, the decay is (31 +6)~,jp = 0 and (69+6)~,,jp = 1.
5. Discussion The multipole mixing ratios deduced in the present work are summarized and compared with the analogous 1911r transitions in table 4. The agreement between the two sets is quite remarkable, in magnitude as well as in phase. [This agreement even extends to the transitions from the (3)3 level in 189ir' ref. 15).] The good agreement suggests that the model used previously ~) to describe the levels of 191Ir may be applicable to 193Ir as well. The previous calculations considered the 191Ir states according to the Nilsson model with Coriolis coupling. The states at 0, 139, and 358 keV can be interpreted as the three lowest members of a rotational band based on the 3+1-402] Nilsson state. If such an interpretation is valid, the electromagnetic properties of those states can be calculated from three intrinsic pa.rameters: OR, gr, and Qo. With gR = Z/A = 0.40, g r - g ~ = -0.52, and
H. H. Ghaleb, K. S. Krane [ 'gait
31
TABLE 4 Comparison of 19~Ir and '93Ir 3,-ray multipole mixing ratios ,9tlr E:, (½), ._. (3), (3), --" (3), (3)2 ~ (½h (3)2 ~ (3), (3)2 --* (3)2 (3)2 ~ (3), (3)3 ~ (3)2 (3)3 --~ (3)2 (3)3 --* (3), (3)3~(½) I (3)3--,-(3) t (3)3 -" (3)~ (3)3 --" (3), (3), __. (½)z (3)4 3 (~)3 (~)4 (3)2 (3),, -" (3),
1931r 6
82 129 97 179 172 351 188 360 409 456 539
0.839(17) -0.403 (4) +0.141 19) -0.75 (3) +0.072 (6) -0.30 (2) +0.10 (3) +0.023 (9) +0.184 (6) -0.32 (4) -0.68 (2)
E~.
6
73 139 107 180 182 362 99 280 322 387 460 420 559 155 252 532 573
-0.558 (5) -0.329(12) +0.16 (1) -0.48 (2) +0.149(11) -0.328(28) -0.049(12) +0.234(10) -0.24 (4) -0.64 (3) +0.030(41) +0.007(31) +0.26 (3) -0.079(20) i.a--n v . 4~ v _+o .°'32 16 +0.03 (2)
Qo = 3.7 b, the calculated properties are compared with the experimental values in table 5. The good agreement suggests that the model may serve as a reasonable basis for a calculation of the properties of the levels. Also shown in table 5 is a similar analysis of the ½+[400] band, consisting of the states at 73, 180 and 362 keV. For these states also the agreement between theory and experiment is good. The transitions connecting the 3+[402] and ½+[400] bands should be related in intensity by ratios of Clebsch-Gordan coefficients, and thus we expect B(M1,362) : B(M1,180) : B(M1, 73) = 0.067:0.40 : 1, whereas the experimental ratios are 0,71(9) :0.68(10) :1. These ratios can be improved if we consider the direct mixing of the two bands resulting from Coriolis coupling. Fitting the experimental M1 matrix elements to two parameters (a single intrinsic M1 transition strength, m~l = (Ktlm(M1)JKi), and the Coriolis mixing parameter a) gives the results shown in table 6 for rnM1 = +0.023, a = - 0 . 0 8 4 ; . the corresponding values for 191Ir were mM~ = +0.020, a = - 0 . 0 6 5 . Using the same techniques for the E2 matrix elements, and keeping the mixing parameter fixed at -0.084, the interband E2
H. H. Ghaleb, K. S. Krane /
32
1931r
TABLE 5
Electromagnetic properties of the 3+[402] and ½+[400] bands of 1931r Band
Property
Theory
Experiment
2'+[402]
B(E2, 2--* 3) B(M 1, 3 ~ 3) B(E2,-~3) B(M 1, ~ --, -~) B(E2, ~ --, 3) 6(~ ~ 3) 6(~ --, 2) /~(3) g(3) Q(3)
0.47 e2-b ~ 0.039/~2 0.29 e 2 . b 2 0.052 #2 0.20 e 2. b z -0.40 -0.43 +0.132/~N +0.67 ~ +0.74 b
0.445 (44) e2.b 2 0.0493 (4)/ar~ +o282e 2 • b 2 0.36_Ct 0.068 [27) g~ 0.237 (26) e 2. b 2 - 0 . 3 2 9 (12) - 1 0 "4 ~"~+°'14~ - 0 . 0 8 / +0.1591 (6) /~N +0.53 (9) /1N +0.73 (19) b
½[400]
B(E2, 3 ~ 3) B(MI, 3 ~ l) B(E2,3 ~ 3 ) B(MI, 3 --* 3) B(E2,3~½) 6(3 ~ ½) 6(3 --, 3) #(3) /~(3)
0.27 e z ' b 2 0.11 Pr~ 0.078 e2-b 2 0.076/a~ 0.27 e2.b 2 +0.14 +0.15 +0.45 /~N +0.94 ~r~
0.250 (36) e 2" b 2 0.078 (10) p2 0.045 ( l l ) e 2 - b 2 0.047 (12) #2N 0.150 (32) e2"b 2 - + 0 . 1 6 (1) +0.149 (11) +0.504 (3) ~N + 1.02 (38) #N
intrinsic matrix elements may be determined. Defining mE2 = (31m(E2)t½) and m~2 = (31m(E2)l-½), the fitted .values are mE2 = +0.20 and rn~2 = +0,50, and the calculated and experimental E2 matrix elements are given in table 6. The agreement of the calculated and measured values is quite good; the only serious disagreement is the relative phase of the 362 keV E2 and M1 matrix elements (that is, the sign of 6), which was also a difficulty in the analogous 19fir transition. The 460 keV level has been assigned as the -32member of the ½1411] band. The transitions to states of the ½[400] band may show effects arising from direct mixing TABLE 6 3[400] 4-*31402] interband transitions ( E 2 ) [e.b) E;. (keV) 41 66 73 178 180 223 362
( M 1 ) [#n)
IlK i --* I l K I
~3t ---,~53 s3 ---,~I ~l ~-~ ~ 1t 33 ~73 ~ ~-~ 31 ~_±a2~~33 ~ _ 1 2 ~~53 ~ I 5--* 3 3
exp
calc
exp
calc
< 1.1 +0.87 (12) +0.663(30) <5.4 +0.562(43) <0.58 _+0.245(16)
-0.66 -0.87 +0.61 -1.04 +0.68 -0.72 +0.36
< 0.12
-0.20
~0.072 (3)
-0.067
-T-0.180(13) <0.11 -T-0.226(15)
-0.177 -0.18 +0.237
H. H. Ghaleb, K. S. Krane / 1931r
33
of the two bands or from mixing of 3[402] with either band. As argued previously 1), the latter effect is of the order of a small mixing coefficient multiplied by an M1 transition amplitude, while the former effect will involve the static M1 amplitudes, which may be much larger. We thus neglect the effects of mixing with the K = 3 band. The direct mixing of the two K = ½ bands will give M1 matrix elements whose spin dependence is identical with that of the direct M1 transitions between the bands; thus the effect of mixing can be handled by a simple renormalization of the intrinsic M1 matrix elements (½lrn(M1)1½') and (½1m(M1)l-½'), where ~lp refers to the ½1411] state. The M1 amplitudes of the 3 transitions (99, 280, and 387 keV) can be fit by varying the two intrinsic M 1 matrix elements. The fitted values for (½1m(M1)1½')= - 0.024 and ~ > = +0.175 are compared with the experimental values in table 7. <½lm(M1)l 1, The intrinsic matrix elements agree very well with those for the corresponding transitions in 191Ir [respectively, -0.018 and +0.166; in ref. ~) the phase of the latter is given incorrectly]. The ½1411] to ½[400] E2 matrix elements can be computed directly from the Nilsson wave functions; the contribution from direct mixing of the bands vanishes if the bands have the same Qo, contributions from mixing with K = 3 are reduced by the small Coriolis mixing amplitude, and vibrational contributions are of second order. The small change in intrinsic deformation between ag~Ir and 1931r causes a negligible change in the E2 matrix elements, and thus we may use the values computed previously for 191jr, shown in table 7. The transitions from the 460 keV level to the 3[402] band (460 and 322 keV) are analyzed using the procedures described in ref. l). The M I amplitudes are calculated directly from the Nilsson wave functions neglecting mixing, and the E2
TABLE 7
Electromagnetic properties of transitions from the ½1411] band (E2) (e" b) Final band
½[400]
~[402]
( M I ) [,uN)
E~, (keV)
387 280 99 484 377 460 322 103 557 418
exp
calc
+0.123(21) +__0.057(151
-0.071 - 0.006 +0.075 -0.059 -0.322 +0.190 -0.014 +0.149 -0.218
+0.322(25) -+0.190(17)
0.076(10)
a) Assuming transition is mostly MI multipolarity.
exp
calc
T0.166 (14) T-0.273 (25) 0.147 (16)") 0.0374(43) 0.037 (5) a) T0.193 (18) +0.219 [18)
+0.170 -0.268 +0.155 +0.182 -0.170 +0.221 -0.271
+0.087 (11 ~) -
-0.247
34
H. H. Ghaleb, K. S. Krane / 1931r
amplitudes are calculated (not fit, because 2 parameters give 2 matrix elements) with the intrinsic matrix elements, (-~[rn(E2)1½')= +0.091 and (3[m(E2)b-½') = - 0 . 1 6 3 , in good agreement with the respective 191Ir values [+0.092 and -0.102, the latter sign being given incorrectly in ref. l)]. The 193Ir level scheme offers an additional test of this model, because the matrix elements of transitions from the 557 keV level should be calculable using the same parameters, assuming the level is the I = ½ state of the ½1411] band. Using the above deduced intrinsic matrix elements, with no additional parameters, the matrix elements given in table 7 are calculated. The calculated transition matrix elements for the 484, 377, 557, and 418 keV transitions are each a factor of 3-4 smaller than the experimental value. (The mixing ratios of the 377 and 557 keV transitions are not known. We assume both to be mostly of M 1 multipolarity ; any E2 admixture will reduce the experimental M 1 moment and increase the difference with the calculated value.) However, the predicted intensity ratios are in good agreement with the observed values. Using the calculated matrix elements, the ratio I(377)/1(484) is expected to be 0.42, in exact agreement with the experimental value of 0.42. The expected ratio I ( 4 1 8 ) / I ( 5 5 7 ) i s 0.038, in good agreement with the observed value of 0.042. A more sophisticated calculation than the previous one has been done by Vieu et a/. 1o) who treat three Nilsson states coupled to a 7-asymmetric rotor. The resulting transition probabilities are compared with experiment in table 8. The agreement between the calculated and experimental values is comparable to the present calculation, but it must be remembered that the agreement obtained in the present work required the ad hoc introduction of intrinsic transition strengths and coupling parameters that are not required by Vieu et al. The M1 strengths are determined directly from the nucleon 9-factors, and the coupling of bands arises in a natural way from the y-deformation. The calculation of Vieu et al. should then be regarded as considerably more microscopic than the present phenomenological one. An alternative approach to understanding the nuclei of this region is the interacting boson-fermion model (IBFM) of Iachello and coworkers 17' is) in which a single odd fermion is coupled to a core of interacting s-and d-bosons. The 0(6) limit of the interacting boson model (IBM) for even-even nuclei has been successful in accounting for levels and transitions in the region of mass 190 [ref. 19)3. In this limit the model approaches that of the 7-unstable rotor. The SU(3) limit of the IBM corresponds to a specific sort of 7-symmetric rotor and thus more closely approximates the rotational structure observed in 150 < A < 190. Considerable success has therefore been achieved in treating even-even nuclei in the A ~ 190 region as transitional between the 0(6) and SU(3) limits 2o). When the odd fermion is introduced into this model, an accidental isomorphism occurs between 0(6) and the SU(4) group that describes the symmetries of a j = ~ fermion. This additional symmetry permits bosons and fermions to be treated in common as part of a dynamical "supersymmetry." The d3/2 proton dominates the low-lying level
TABLE 8 Reduced transition probabilities in 1931r B(E2) (e 2. b 2)
B(M1) (x 10 -3 U~) Initial level
E~, (keY)
calc
calc
(½), (3)2
73 66 139 41 107 180 219 358 182 223 289 362 99 280 322 387 460 97 377 418 484 557 420 559
exp
present
PAR ~)
2.62(24)
2.25
0.75
71.6
49.3 (4) < 3.5 78(10) 8.1 (12) 68(27)
39 10 110 7.8 52
160 44.5 260 21.4 192
38.5 32.3 33.8 0.5 72.6
47(12) < 2
76 5.4
178 23.2
58.4 27.2
8.5 (11) 5.4 (11) c) 18.6 (34) 12.0 (20) 6.9 (12) 9.3 (17) 49(12) 0.69(19)')
9.4 6.0 18.0 18.4 7.2 12.2
0.70(16) 3.8 (10)c), 117(18) 150(26)
16.6 30.5
a) Ref. 16). b) Refs. 18.22). ~) Assumes transition is M1 multipolarity.
14.5
49.2 43.7 39.0 8.39 11.3 1.86 32.4 0.033 2.51 2.94 30.9 566
exp
present
0.220 (20) 0.126 (36) 0.445 (44) < 0.30 0.250 (361 0.079 (12) 0.36+~28 0.235 (25) 0.045 (11) < 0.06 0.150 (32) 0.0100 (13) 0.00") 0.00081(43) 0.0090 [16) 0.0038 (13) 0.026 (4) 0.30 07) 0.00") 0.0029 (7)
0.186 0.126 0.47 0.11 0.27 0.116 0.29 0.20 0.078 0.086 0.27 0.0216 0.0014 9.0x 10 -6 0.0090 0.0013 0.026
0.00 ~)
0.011
IBFM b)
0.0
< 0.0054 < 0.0013
0.0017 0.024
PAR a) 0.150 0.120 0.635 0.149 0.357 0.145 0.298 0.0261 0.276 0.0261 0.0115 0.00086 0.0152 0.0215 0.0255 0.716 0.441 0.0304 0.00584 0.0021 0.00024
IBFM ~) 0.216 0.0256 0.417 0.204 0.181 0.0018 0.158 0.299 0.0001 0.0388 0.258 0.0003
ta
36
H. H. Ghaleb, K. S. Krane / 193~'F
structure of the o d d - A Ir isotopes, which therefore h a v e the p o t e n t i a l for testing the s u p e r s y m m e t r y schemes2J). In the extreme 0 ( 6 ) limit, the a - a n d z-selection rules 18.21) forbid the 180 a n d 362 keV transitions a n d those d e p o p u l a t i n g the 460 a n d 557 keV levels. It is therefore necessary to i n t r o d u c e a s y m m e t r y - b r e a k i n g term, which can be either a sl/2 fermion or a b o s o n SU(3) limit. T h e results of some p r e l i m i n a r y c a l c u l a t i o n s based on the latter 22) are shown in table 8. T h e t r a n s i t i o n s from the higher-lying states are p a r t i c u l a r l y sensitive to the degree of 0 ( 6 ) s y m m e t r y b r e a k i n g ; for example, the 280 keV t r a n s i t i o n violates b o t h the aa n d z-selection rules in the 0 ( 6 ) limit, a n d as a l r e a d y n o t e d the E2 c o m p o n e n t s of this t r a n s i t i o n a n d its 191Ir a n a l o g u e are hindered by 1-2 o r d e r s of m a g n i t u d e relative to o t h e r t r a n s i t i o n s from t h a t same level. The E 2 / M 1 mixing ratios, such as those r e p o r t e d in the present w o r k and in ref. ~), can serve as p a r t i c u l a r l y sensitive tests of the I B F M c o u p l i n g scheme. If such precise a n g u l a r - d i s t r i b u t i o n a n d a n g u l a r - c o r r e l a t i o n m e a s u r e m e n t s can be similarly d o n e across the m e m b e r s of a s u p e r s y m m e t r y multiplet (perhaps involving decays far from the valley of stability), it w o u l d p r o v i d e further direct s u p p o r t for these new c o u p l i n g schemes. M o r e d e t a i l e d c a l c u l a t i o n s of the effects of various s y m m e t r y - b r e a k i n g terms in the I B F M on E2/M1 m i x i n g ratios ( m a g n i t u d e s and phases) in the m a s s - 1 9 0 region will be presented in a f o r t h c o m i n g work.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22)
W. M. Lattimer, K. S. Krane, N. J. Stone and G. Eska, J. of Phys. G7 (1981) 1713 V. Berg, S. G. Malmskog and A. Backlin, Nucl. Phys. A143 (1970) 177 R. H. Price and M. W. Johns, Nucl. Phys. h187 (1972) 641 V. S. Shirley, Nucl. Data Sheets 32 (1981) 593 S. Gustafsson, K. Johansson, E. Karlsson, L.-O. Norlin and R. G. Svensson, Ark. Fys. 34 (1967) 169 R. Avida, J. Burde, A. Muchadzki and Z. Berant, Nucl. Phys. All4 (1968) 365 T. Badica, A. Gelberg, C. Protop and S. Salageanu, Rev. Roum, Phys. 14 (1969) 471 R. B. Begzhanov, O. S. Kobilov, P. S. Radzhapov and K. S. Sabirov, lzv. Akad. Nauk Uzb. SSR (set. fiz.-mat.) 4 (1972) 48 K. S. Krane and W. A. Steyert, Phys. Rev. C7 (1973) 1555 K. S. Krane and R. M. Steffen, Phys. Rev. C2 (1970) 724 K. S. Krane, Nucl. Phys. A349 11980) 68 M. B. Lewis, Nucl. Data Sheets 8 (1972) 389 R. Avida, I. Ben Zvi, P. Gilad, M. B. Goldberg, G. Goldring, K. H. Speidel and A. Sprinzak, Nucl. Phys. A147 (1970) 200 K. S. Krane and W. A. Steyert, Phys. Rev. C9 (1974) 2063 I. Berkes, R. Haroutunian, G. Marest, J. of Phys. G6 (1980) 775 Ch. Vieu, S. E. Larsson, G. Leander, I. Ragnarsson, W. DeWieclawik and J. S. Dionisio, Z. Phys. A290 (1979) 301 F. Iachello and O. Scholten, Phys. Rev. Lett. 43 0979) 679 F. Iachello and S. Kuyucak, Ann. of Phys. 136 (1981) 19; S. Kuyucak, Ph.D. thesis, Yale University (1982), unpublished J. A. Cizewski, R. F. Casten, G. J. Smith, M. R. MacPhail, M. L. Stelts, W. R. Kane, H. G. B6rner and W. F. Davidson, Nucl. Phys. A323 (1979) 349 R. F. Casten and J. A. Cizewski, Nucl. Phys. A309 (1978) 477 J. A. Cizewski, D. G. Burke, E. R. Flynn, R. E. Brown ana J. W. Sunier, Phys. Rev. C27 (1983) 1040 F. Iachello, private communication
A N G U L A R - C O R R E L A T I O N S T U D Y O F T H E L E V E L S C H E M E OF 19air H. H. GHALEB and K. S. KRANE
Department of Physics, Oregon State University, Corvallis, Oregon 97331, USA
Received 2 February 1984 Abstract: The decay of 193Os to 1931r has been studied by 77 angular correlations. Inconsistencies between previous angular correlations, internal conversion coefficients, and nuclear orientation angular distributions have been satisfactorily resolved by the present results. These data are used to derive a set of E2/M1 multipole mixing ratios of the transitions between low-lying states. The resulting electromagnetic transition moments are compared with calculations based on the Nilsson model with Coriolis mixing and on the interacting boson-fermion model. E I
RADIOACTIVITY 193Os [from Os(n,y)]; measured ?y(0). '93Ir deduced 6(E2/M1).
I
1. I n t r o d u c t i o n
The electromagnetic properties of the low-lying states of odd-mass nuclei are calculable from a variety o f models, from extreme single-particle models to those involving the coupling of the single-particle degrees of freedom to multiparticle and collective excitations. In order to judge the success of such calculations, it is necessary to have the most complete set of experimental values of the static and transitional electromagnetic moments. Unfortunately a reasonably complete and precise set of such data (static moments, branching ratios, lifetimes, internal conversion coefficients, E2/M1 multipole mixing ratios) is available for only very few nuclei. In a previous publication 1) concerning the levels of 191Ir, the available spectroscopic data were combined with precise E2/M1 multipole mixing ratios from angulardistribution and angular-correlation experiments, and it was shown how the deduced E2 and M 1 moments could be used to differentiate a m o n g the competing theories. The present work describes a similar analysis of the levels of 193Ir. When this work was begun, the previous data available for 193Ir did not form a mutually consistent set. It was necessary to remeasure several of the 7? angular correlations, the results of which are reported in the present work. In the process of comparing those results with previous nuclear orientation (n.o.) angular distributions, a small but systematic error in the latter was discovered. The n.o. data are reanalyzed, and it is shown that the present angular correlation data and the reanalyzed nuclear orientation data, along with the other previous 20
H. H. Ghaleb, K. S. Krane / 1931r
21
spectroscopic data, give a consistent set of. multipole matrix elements. The remarkable agreement between the corresponding 191Ir and Jgalr multipole moments is discussed, and it is concluded that the model used previously to describe t91Ir serves equally well to describe ~galr.
2. The 19305 decay scheme The radioactive decay of 193Os to '931r was previously studied by Berg et al. 2) and by Price and Johns 3). The decay scheme is shown in fig. 1. The available spectroscopic data have been recently summarized by Shirley 4), and table 1 shows a summary of the electromagnetic properties of some of the low-lying even-parity levels. For most of the transitions listed in table 1, the E2 admixtures are not determined with sufficient precision to permit meaningful comparisons withtheory. In order to improve that situation, several ~;), angular-correlation measurements have been reported 5-a). In many cases these data lead to improved values of the E2/M1 multipole mixing ratios, but there are remaining unresolved discrepancies and inconsistencies in the data. A further improvement in the knowledge of the electromagnetic transition moments resulted from measurement of the 7-ray 31.5 h
,93
'
\
3 / 2 - 3/2 [512]
760SI17 ' ~ I ~ -
0.03
8.6
0.3
8.2
0.5 0.1
8.0 8.8
874
¢~
r4o '
712 ~
~5/23/2
--
e.ON ~ q" iO ,~1"'q" i,";
0.1
I0.0
0.7 2.4
8.3 7.8
8
0.02
7.5 8.7 10.4
0.05
I0.1
2.0 12
8.6 7.9
leo 139 80
19
7.8 7.5
o
0.8
( 3 / 2 +, 5/2 + ) r o e d ed ,~ ~- - ;.N ,~ ~,.~ ~ OJ ~ g~ON
559
I
356 \ 299
. . . . . ]
I~(%}
Io~
ft
3/2 ÷ I/2 [4H]
II IIIII I!111 -
I
l'iiiiii fill illi , ° wo
.
54
3/2"
I
460 362
.
I I I II I I I
• II II
I I!
I I
I
I
.
.
+
E (keV)
m
-
III
/_3/2~-
~-5/2+ •),--,,,'2I12 +
1/2 [400]
I II3,2-3,2t4o2
I'K [ Nnz A] 193. 77Lr116
Fig. 1. Decay scheme of 193Os to 1931r.
22
H. H. Ghaleb, K. S. Krane / xgalr
TABLE 1 Electromagnetic transitions from 1931r levels Level E (keV)
Mean life (ns)
73 139
8.79 (22) 0.1150 (3)
180
0.085 (10)
358
0.029 (4)
362
0.052 (10)
460
0.016 (3)
557
0.049 (11)
559
0.0015 (2)
712
0.022 (20)
E:,
y-intensity
~0 E2
(keV) 73 66 139 41 107 180 219 358 182 289 362 99 280 322 387 460 97 377 418 484 557 420 559 155 252 532 573 712
82.0 ( 1 2 )
27.8(10)
108.0 (5)
9.1 (8)
16.1 (8) 4.6 (5) 0.22 (5) 0.25 (8) 4.9 (5) 3.6 (3) 7.5 (6) 0.42 ~6~ 31.5 116) 32.3 (16) 31.9 (16) 100 (5) 2.5 (2) 1.8 12~ 1.38(14) 4.3 (3) 33 (3) 4.2 (3) 12.3 (12) 0.76(11 ) 5.5 (4) 2.10(15) O.49 (5) O.39 (6)
1.7 (4) 20 (8) 100 15 (13) 100 < 8 < < < 17 4
10 8 10 (7) ~2)
100 < 12 < 4 < 8 < 20 < 24
a n g u l a r d i s t r i b u t i o n s f o l l o w i n g l o w - t e m p e r a t u r e nuclear o r i e n t a t i o n g). T h e analyses o f the a n g u l a r - d i s t r i b u t i o n a n d a n g u l a r - c o r r e l a t i o n d a t a suffer from similar difficulties-there is a lack of a sufficient n u m b e r of transitions of pure m u l t i p o l a r i t y in parallel o r in coincidence with the transitions of m i x e d M1 + E 2 m u l t i p o l a r i t y . F o r example, in the a n g u l a r - d i s t r i b u t i o n analysis, four mixed transitions (280, 322, 387, 460 keV) d e p o p u l a t e the 460 keV level, a n d an a c c u r a t e k n o w l e d g e of the m u l t i p o l e mixing ratio of any one w o u l d p e r m i t analysis of the o t h e r three. T h e 322-139 keV a n g u l a r c o r r e l a t i o n has been previously m e a s u r e d 5-8), and its analysis could in principle yield 6(322), which c o u l d in turn serve for analysis of the other transitions, but the results of the previous a n g u l a r - c o r r e l a t i o n w o r k are not in g o o d m u t u a l a g r e e m e n t ; in fact, the r e m e a s u r e m e n t of this correlation, which is critical for the analysis of the previous a n g u l a r - d i s t r i b u t i o n work, was the p r i m a r y m o t i v a t i o n for the present work. O u r results indicate t h a t the previous results are systematically incorrect, a n d thus
H. H. Ghaleb, K. S. Krane / 1931r
23
many of the decay parameters deduced previously 9) based on this correlation are incorrect. As we show below, the 322-139 keV angular correlation has an unusually large anisotropy, and thus even small admixtures of other correlations are liable to have a substantial effect; previous angular correlation work using NaI detectors may show effects of interfering cascades, while the present work using Ge(Li) detectors is relatively free of such interference.
3. Experimental details 3.1. SAMPLE PREPARATION Radioactive samples of 193Os were prepared by neutron activation of Os metal powder in natural isotopic abundance. Samples in the range of 10-100 mg were irradiated for approximately one hour in a thermal neutron flux of 1013 n/cm2/s, resulting in activities in the range of 100 pCi. The accompanying longerTlived 191Os activity did not interfere with the measurement, since it gives only a single 7-ray of energy 129 keV. Each sample was measured for approximately one half-life, and the present results represent data from more than 50 individual samples. The samples were used in the original chemical form, since the short lifetimes of the levels make it unlikely that extranuclear perturbations can attenuate the correlations. [Even the longest-lived level at 139 keV shows an attenuation of only about 10~o in a magnetized ferromagnetic alloy 5).] Since the present results show a larqer anisotropy for the 322-139 keV correlation than previous work using liquid s'6) or crystalline salt v) environments, the assumption of negligible attenuation of the present results seems justified. 3.2. APPARATUS The angular correlations were measured using a Ge(Li)-Ge(Li) system in two different modes. (A sample 7-ray spectrum is shown in fig. 2.) The first mode was a conventional one in which single channel analyzer (SCA) windows were set on each detector and coincidence counts were accumulated at up to 9 angles between 90 ° and 270 °. Four cascades could be simultaneously measured in this mode lo). In the second mode, a complete coincidence spectrum gated by a SCA window on one detector was routed into one of four quadrants of a multichannel analyzer (MCA) for four different positions of the movable detector. In this latter mode, corrections for effects on the measured correlations from coincident Compton backgrounds could be made directly. As discussed in a previous publication 11), angular correlations can be subject to systematic errors in cases in which an intense cross-over transition competes with the cascade under investigation. In the case of the 193Os decay, the intense 460 keV transition can Compton-scatter from one detector to another, and in the process
24
H. H. Ghaleb, K. S. Krane I
I
139 129 .:. 107 ~.,.
1931r
I
I
180
-. " "
280 r.
+
: ""
182
219
252
~'--"~"~" <"~"/"'~,,.,'-.,~,""k,,,,,___,,'
t-
/
:522
',;'-,,,-",
587
/ :'
362
:":
r.,
"--.-.~....:~..,.:~
:". 4 6 0 ••
418
557
+
g 0
-
420
'
-...,., j...~
.
'. ~,.-.:',.:~
+
(-559
...
":'r':.V.,.~:S=....;:" !-... 5". ;'~* \':.~,'.,..~..':-..,,/~".
6"
" ::/::-';~'~:::<:'/:':'!:'<:'::*'5
L
i
I
200
500
700
800
,
[
i
400 900 Channel
I
500
,
I
,__
600
1000 Number
Fig. 2. 7-spectrum of the 193Os decay.
energies can be deposited that simulate 280-180 keV coincidences. In particular, when the angle between the two detectors is 0 = 90 ° (in which case the Compton scattering angle is about q~ = 135°), the scattered photon has energy E' = 181 keV, while 279 keV is left with the first detector. Lead shields used in the present study block the path of the scattered p h o t o n and eliminate this problem at that particular position. However, when 0 > 120° (4~ > 150°), it is not possible for lead shields to eliminate this effect without also blocking direct radiation from the source, and in fact the present results for the 280-180 keV correlation showed anomalously large coincidence counting rates when 0 --- 120°. (Such counting rates must be spurious, because only a large A44 term in the correlation could give such an increase in the counting rate near 120 °, but an an A44 term is forbidden for the 280-180 keV correlation with its spin-~ intermediate state.) For 135° < 0 < 180°, the scattered photon has energy E' = 164 to 168 keV, and no interference is to be expected when using Ge(Li) detectors, but the poorer energy resolutions of NaI detectors may result in contributions from these Compton coincidences. This effect would tend to increase the counting rates near 180°, contributing a positive anisotropy to the measured correlation. Indeed, the previously reported 7.8) 280180 keV correlations both show a positive anisotropy, while the present results show a negative anisotropy. The positive anisotropy does n o t give a solution for the 280 and 180 keV mixing ratios consistent with the conversion data and with other measured correlations, as discussed in the previous A = 193 compilation 12). The presently reported negative anisotropy, on the other hand, is entirely consistent with previous spectroscopic results.
H. H. Ghaleb, K. S. Krane / tgalr
25
3.3. DATA ANALYSIS The coincidence counting rates~ corrected for background and accidental coincidences, were fit to the usual angular-correlation function W(O) = 1 + Q 2 2 A e 2 P 2 ( c o s O)+Q,,4A,,,,P4(cos 0),
(1)
where Qkk are the geometrical factors that correct for finite detector solid angle and where the angular correlation coefficients Akk are Akk = Bk(y l)UkAk(y2).
(2)
The coefficients Bk(~;1) and Ak(Y2) depend on the y-ray multipole mixing ratios of the transitions under study ; the U k correct for the effects of unobserved radiations intermediate between ?~ and Y2. The dependence of these coefficients on the y-ray mixing ratios is discussed in ref. lo). For comparison with the angular-correlation data, the n.o. angular distributions are written W(O) = 1 + Q2a2P2(cos 0),
(3)
a 2 = B 2 ( T ) U 2 A e ( y ).
(4)
where
The orientation parameter B E ( T ) depends on the orientation of the parent state; U2 and A 2 have the same meaning as in eq. (2).
4. Results
The angular-correlation coefficients measured in the present work are compared with those measured in previous work in table 2. Several differences with previous work are notable: (i) the present 322-139 keV anisotropy is larger than that reported in previous work, as was discussed above in sect. 2; (ii) the present 280180 keV anisotropy has the opposite sign compared with those previously reported, as discussed above in subsect. 3.2. Before attempting to compare the present angular-correlation results with those obtained previously from low-temperature nuclear orientation g), a careful review of the latter was made. This review was in part prompted by the new results presently reported for the 322-139 keV correlation, which invalidated the previous analysis for many of the mixing ratios. In re-examining the data from the previous n.o. experiment, it was discovered that a systematic anisotropy amounting to I-2 ~,,,
H. H. Ghaleb, K. S. Krane / 19Sir
26
TABLE 2 Angular correlations in the decay of 1'~3Os Cascade
A 22
A44
Refl
322 139
0.602(14) 0.555 (5) 0.575(12) 0.338(36) 0.676 (8) 0.113{13) 0.137(15) -0.132 (91 -0.139(12) -0.13 (1) - 0.111 (27) -0.098 (9) -0.090(11) -0.199 (7~ -0.187 (7) - 0.420(24) -0.380(29) -0.112 (9) -0.093(10) -0.221(15) -0.210(18) - 0.362(30) - 0.480(40) - 0.477149) -0.152(23) -0.159(27) + 0.206(35 ) +0.225(41)
- 0.024~ 16) 0.006 (7) 0.045(20) - 0.001 16) -0.005(12) 0.052(41 ) -0.029(18)
s) ") ~) s) PW~t 7) s) PW PW ~') 8) PW PW ~') 8) PW PW 7) 8) PW PW 7) PW PW PW PW PW PW
280-180
280-107
420-139
252-460
252-387
252-322 252-280
-0.017(15t 0.02 (3) 0.024(31 ) -0.028(13) 0.02 (2) -0.013(10~ -0.075(44) -0.067(58) +0.055(14) -0.028(27) - 0.022(58) 0.000(55) +0.008(41) -0.042(47)
a) Present work.
was present in those transitions that were expected to show a vanishing anisotropy (K X-rays, 511 keV annihilation radiation, 193Ir transitions from spin-½ levels). The cause of this small and spurious but systematic effect is not known, but it was present in several transitions in both the low-energy and high-energy portions of the spectrum. (Even a spectral line originating from a test pulser fed into the detector preamp showed the effect.) It was therefore decided to correct the anisotropies of all of the 19Sir transitions by an amount determined from the average measured anisotropy of the 7-rays that were expected to show vanishing anisotropies. This correction factor amounts to + 0 . 0 1 8 _ 0 . 0 0 2 , and the corrected angular distributions are shown in table 3. The consistency between the angular-distribution and angular-correlation data can be examined by comparing cases in which several transitions depopulate the same level. Considering first the 460 keV level, since the A22 from the angular
H. H. Ghaleb, K. S. Krane / 19Slr
27
TABLE 3 Corrected results from angular distribution experiment [results from ref. 9) corrected for spurious systematic anisotropy] ~,-ray
a2
";-ray
a2
107 139 155 180 182 219 235 252 280 289
0.056(10) 0.215 (2) 0.006(20) 0.088 (5) 0.019 (5) -0.033 (3) 0.172 (9) -0.099 (3) - 0 . 0 5 0 (2) -0.119 (4)
299 322 362 377 + 379 387 418+420 441 460 532 557+559
- 0.029 14) 0.058 (2) 0.196 (2) 0.009[ 12) 0.129 (2) -0.077 (3) -0.135 (6) 0.065 (2) -0.333 (8} 0.022 (2)
correlation and the a2 from the angular distribution are both proportional to A2()'), we expect the ratios
A22(252-280) : A2z(252-322) : A2z(252-387) : A22(252-460), az(280):a2(322) : az(387) : a2(460) to be identical. The experimental values are, respectively, -0.93+0.17:0.69__+0.11 : 2.17+0.20:1.00___0.07 from table 2, and - 0.77 + 0.03 : 0.89 + 0.03 : 1.98 _ 0.03 : 1.00 + 0.03 from table 3. The agreement between these two sets of ratios is excellent. For the transitions from the 180 keV level, the ratios A22(280- 107) : A22(280- 180), az(107) • a2(180) can be compared. These give, respectively, 0.74 _ 0.07 • 1.00 __+0.07, 0.64+__0.11:1.00+0.06. Again the ratios are in good agreement; in particular, the sign of the 280-180 keV anisotropy is consistent with the sign of the 280-107 keV anisotropy.
28
H. H. Ghaleb, K. S. Krane / 1931r
In all of the reported angular correlations, both transitions are of mixed multipolarity; thus the correlations cannot be independently analyzed for the multipole mixing ratios of both transitions. It is necessary to begin the analysis with a transition of known multipolarity, for which the 139 keV 7-ray can be chosen since its multipolarity has been precisely determined from L-subshell conversion ratios: 16[ = 0.353+_0.021 from Berg et al.Z); 161 = 0.316+_0.015 from Price and Johns 3). The sign of 6 has been determined to be negative from angulardistribution measurements following nuclear orientation 9) and also following Coulomb excitation 13). We therefore take 6(139) = - 0 . 3 2 9 + 0 . 0 1 2 which corresponds to A2(139 ) = +0.882+0.013, A4(139)= +0.069+0.004. The presently measured 322-139 correlation, together with the above deduced value of 6(139), can then be analyzed to give 6(322) = +0.234+0.010. Following the same procedure as ref. 1), the angular distributions of the transitions depopulating the 460 keV level can be analyzed by comparison with the 322 keV angular distribution, according to the relationship
a2(}')
A2(7)
--
a2(322) A2(322)
(5)
which gives for the mixing ratios 6(280) = -0.049+0.012, 6(387) = - 0.24-+ 0.04, 6(460) = - 0.64 + 0.03. These four deduced mixing ratios are in good agreement with the internal conversion results summarized in table 1. With the above deduced value for 6(280), the 280-180 keV and 280-107 keV correlations can be analyzed, with the results 6(107) = +0.16_+0.01, 6(180) = -0.48__.0.02. The internal conversion results 2, 3) give, respectively, 0.14 + 0.01 and 0.59 + 0.10 for the magnitudes of the mixing ratios and are again in excellent agreement with the angular-correlation results.
H. H. Ghaleb, K. S. Krane / 1931r
29
The four cascades involving the 252 keV radiation can be analyzed using the deduced values of the mixing ratios of the four transitions depopulating the 460 keV level, 252-280:
6(252) = -0.16_+0.08,
252-322:
6(252) =
252-387:
6(252) = -0.12_+0.04,
252-460:
6(252) = -0.08_+0.02,
0.00_+0.04,
which give the average value 6(252) = - 0.079_+ 0.020. This value of 6(252) then permits the n.o. data for the angular distributions of the 155 and 532 keV transitions to be analyzed by comparison with the 252 keV angular distribution, yielding 6(155) = +0.26_+0.03, 6(532)
=
-L'f~AR+O'32 ~
~.-r~--O.l
6.
With this value of 6(532) the expected 532-107 keV correlation is A22 = +0.052, in agreement with the measured values A22 = 0.089_+0.030 [ref.°)], A22 = 0.058_+0.018 [ref. 8)]. The present results for the combined (418+420)-139 keV correlation show a larger anisotropy than the results of previous work. Correcting for the 25~o contribution from the pure-E2 418 keV transition, the resulting 420-139 keV correlation gives 6(420) = + 0.030_+ 0.041. This value of 6(420) can then be used to analyze the n.o. data for 6(559) by comparing the angular distributions of the 420 and 559 keV transitions. The result is 6(559) = +0.007+0.031. Finally, the corrected n.o. angular distributions of the 362 and 182 keV transitions can be analyzed in comparison with the angular distribution of the pure-E2 289 keV transition which also depopulates the 362 keV level. The resulting coefficients are A2(362) = +0.881(31) and A2(182) = +0.085(22) and the
30
H. H. Ghaleb, K. S. Krane / tgalr
corresponding mixing ratios are 6(362) = - 0 . 3 2 8 + 0 . 0 2 8 , 6(182) = +0.149-1-0.011. Based on this analysis, the expected 182-.107 keV angular correlation is A22 = - 0 . 0 1 6 ; t h e measured value 6) is Azz = -0.40(8), which does not agree with the value expected on the basis of the angular-distribution data. The re-evaluation and re-analysis of the n.o. data lead to improved value of the ~gaos orientation parameter and the deorientation coefficients of the //-decays. Again assuming the 142 keV transition to be at most 20~o E2, as in ref. 9), the 219 and 299 keV angular distributions give B 2 = 0 . 4 0 + 0 . 0 5 , including a 10~/o correction for the effects of nonalignment of the local and applied fields ~4). The deduced magnetic m o m e n t is q#[.= 0.78___0.07 PN, in better agreement with the systematics of other 3-[512] states in this region than was the original value of 1.30 + 0.19/~N deduced in ref. 9). The A I = 1 first-forbidden fl-decays (those leading to the 5+ final states at 139, 362, and 559 keV) can be mixtures of j~ = 1 and 2 radiations; the jp = 2 contribution is usually of small intensity and is often neglected ((-approximation). Previously g) we found substantial (50~,) contributions from the ja = 2 terms. With the modified analysis described above, theja = 2 contributions to the three decays are, respectively, (12+ 10)~o, (15__9)~, and (18+8)~,~. These values are more consistent with the expected small contribution ofja = 2 decays~ The fl-decays to the 3+ final states (180,460, and 712 keV) can be mixtures ofja = 0, 1, and 2. The decays to the 180 and 712 keV levels show virtually pure Jt~ = 0 decays (U 2 = 1.1+__0.1 and 0.90+_0.11, respectively), while the decay to 460 keV has U2 = 0.45+__0.05 and thus, neglecting the j~ = 2 contribution, the decay is (31 +6)~,jp = 0 and (69+6)~,,jp = 1.
5. Discussion The multipole mixing ratios deduced in the present work are summarized and compared with the analogous 1911r transitions in table 4. The agreement between the two sets is quite remarkable, in magnitude as well as in phase. [This agreement even extends to the transitions from the (3)3 level in 189ir' ref. 15).] The good agreement suggests that the model used previously ~) to describe the levels of 191Ir may be applicable to 193Ir as well. The previous calculations considered the 191Ir states according to the Nilsson model with Coriolis coupling. The states at 0, 139, and 358 keV can be interpreted as the three lowest members of a rotational band based on the 3+1-402] Nilsson state. If such an interpretation is valid, the electromagnetic properties of those states can be calculated from three intrinsic pa.rameters: OR, gr, and Qo. With gR = Z/A = 0.40, g r - g ~ = -0.52, and
H. H. Ghaleb, K. S. Krane [ 'gait
31
TABLE 4 Comparison of 19~Ir and '93Ir 3,-ray multipole mixing ratios ,9tlr E:, (½), ._. (3), (3), --" (3), (3)2 ~ (½h (3)2 ~ (3), (3)2 --* (3)2 (3)2 ~ (3), (3)3 ~ (3)2 (3)3 --~ (3)2 (3)3 --* (3), (3)3~(½) I (3)3--,-(3) t (3)3 -" (3)~ (3)3 --" (3), (3), __. (½)z (3)4 3 (~)3 (~)4 (3)2 (3),, -" (3),
1931r 6
82 129 97 179 172 351 188 360 409 456 539
0.839(17) -0.403 (4) +0.141 19) -0.75 (3) +0.072 (6) -0.30 (2) +0.10 (3) +0.023 (9) +0.184 (6) -0.32 (4) -0.68 (2)
E~.
6
73 139 107 180 182 362 99 280 322 387 460 420 559 155 252 532 573
-0.558 (5) -0.329(12) +0.16 (1) -0.48 (2) +0.149(11) -0.328(28) -0.049(12) +0.234(10) -0.24 (4) -0.64 (3) +0.030(41) +0.007(31) +0.26 (3) -0.079(20) i.a--n v . 4~ v _+o .°'32 16 +0.03 (2)
Qo = 3.7 b, the calculated properties are compared with the experimental values in table 5. The good agreement suggests that the model may serve as a reasonable basis for a calculation of the properties of the levels. Also shown in table 5 is a similar analysis of the ½+[400] band, consisting of the states at 73, 180 and 362 keV. For these states also the agreement between theory and experiment is good. The transitions connecting the 3+[402] and ½+[400] bands should be related in intensity by ratios of Clebsch-Gordan coefficients, and thus we expect B(M1,362) : B(M1,180) : B(M1, 73) = 0.067:0.40 : 1, whereas the experimental ratios are 0,71(9) :0.68(10) :1. These ratios can be improved if we consider the direct mixing of the two bands resulting from Coriolis coupling. Fitting the experimental M1 matrix elements to two parameters (a single intrinsic M1 transition strength, m~l = (Ktlm(M1)JKi), and the Coriolis mixing parameter a) gives the results shown in table 6 for rnM1 = +0.023, a = - 0 . 0 8 4 ; . the corresponding values for 191Ir were mM~ = +0.020, a = - 0 . 0 6 5 . Using the same techniques for the E2 matrix elements, and keeping the mixing parameter fixed at -0.084, the interband E2
H. H. Ghaleb, K. S. Krane /
32
1931r
TABLE 5
Electromagnetic properties of the 3+[402] and ½+[400] bands of 1931r Band
Property
Theory
Experiment
2'+[402]
B(E2, 2--* 3) B(M 1, 3 ~ 3) B(E2,-~3) B(M 1, ~ --, -~) B(E2, ~ --, 3) 6(~ ~ 3) 6(~ --, 2) /~(3) g(3) Q(3)
0.47 e2-b ~ 0.039/~2 0.29 e 2 . b 2 0.052 #2 0.20 e 2. b z -0.40 -0.43 +0.132/~N +0.67 ~ +0.74 b
0.445 (44) e2.b 2 0.0493 (4)/ar~ +o282e 2 • b 2 0.36_Ct 0.068 [27) g~ 0.237 (26) e 2. b 2 - 0 . 3 2 9 (12) - 1 0 "4 ~"~+°'14~ - 0 . 0 8 / +0.1591 (6) /~N +0.53 (9) /1N +0.73 (19) b
½[400]
B(E2, 3 ~ 3) B(MI, 3 ~ l) B(E2,3 ~ 3 ) B(MI, 3 --* 3) B(E2,3~½) 6(3 ~ ½) 6(3 --, 3) #(3) /~(3)
0.27 e z ' b 2 0.11 Pr~ 0.078 e2-b 2 0.076/a~ 0.27 e2.b 2 +0.14 +0.15 +0.45 /~N +0.94 ~r~
0.250 (36) e 2" b 2 0.078 (10) p2 0.045 ( l l ) e 2 - b 2 0.047 (12) #2N 0.150 (32) e2"b 2 - + 0 . 1 6 (1) +0.149 (11) +0.504 (3) ~N + 1.02 (38) #N
intrinsic matrix elements may be determined. Defining mE2 = (31m(E2)t½) and m~2 = (31m(E2)l-½), the fitted .values are mE2 = +0.20 and rn~2 = +0,50, and the calculated and experimental E2 matrix elements are given in table 6. The agreement of the calculated and measured values is quite good; the only serious disagreement is the relative phase of the 362 keV E2 and M1 matrix elements (that is, the sign of 6), which was also a difficulty in the analogous 19fir transition. The 460 keV level has been assigned as the -32member of the ½1411] band. The transitions to states of the ½[400] band may show effects arising from direct mixing TABLE 6 3[400] 4-*31402] interband transitions ( E 2 ) [e.b) E;. (keV) 41 66 73 178 180 223 362
( M 1 ) [#n)
IlK i --* I l K I
~3t ---,~53 s3 ---,~I ~l ~-~ ~ 1t 33 ~73 ~ ~-~ 31 ~_±a2~~33 ~ _ 1 2 ~~53 ~ I 5--* 3 3
exp
calc
exp
calc
< 1.1 +0.87 (12) +0.663(30) <5.4 +0.562(43) <0.58 _+0.245(16)
-0.66 -0.87 +0.61 -1.04 +0.68 -0.72 +0.36
< 0.12
-0.20
~0.072 (3)
-0.067
-T-0.180(13) <0.11 -T-0.226(15)
-0.177 -0.18 +0.237
H. H. Ghaleb, K. S. Krane / 1931r
33
of the two bands or from mixing of 3[402] with either band. As argued previously 1), the latter effect is of the order of a small mixing coefficient multiplied by an M1 transition amplitude, while the former effect will involve the static M1 amplitudes, which may be much larger. We thus neglect the effects of mixing with the K = 3 band. The direct mixing of the two K = ½ bands will give M1 matrix elements whose spin dependence is identical with that of the direct M1 transitions between the bands; thus the effect of mixing can be handled by a simple renormalization of the intrinsic M1 matrix elements (½lrn(M1)1½') and (½1m(M1)l-½'), where ~lp refers to the ½1411] state. The M1 amplitudes of the 3 transitions (99, 280, and 387 keV) can be fit by varying the two intrinsic M 1 matrix elements. The fitted values for (½1m(M1)1½')= - 0.024 and ~ > = +0.175 are compared with the experimental values in table 7. <½lm(M1)l 1, The intrinsic matrix elements agree very well with those for the corresponding transitions in 191Ir [respectively, -0.018 and +0.166; in ref. ~) the phase of the latter is given incorrectly]. The ½1411] to ½[400] E2 matrix elements can be computed directly from the Nilsson wave functions; the contribution from direct mixing of the bands vanishes if the bands have the same Qo, contributions from mixing with K = 3 are reduced by the small Coriolis mixing amplitude, and vibrational contributions are of second order. The small change in intrinsic deformation between ag~Ir and 1931r causes a negligible change in the E2 matrix elements, and thus we may use the values computed previously for 191jr, shown in table 7. The transitions from the 460 keV level to the 3[402] band (460 and 322 keV) are analyzed using the procedures described in ref. l). The M I amplitudes are calculated directly from the Nilsson wave functions neglecting mixing, and the E2
TABLE 7
Electromagnetic properties of transitions from the ½1411] band (E2) (e" b) Final band
½[400]
~[402]
( M I ) [,uN)
E~, (keV)
387 280 99 484 377 460 322 103 557 418
exp
calc
+0.123(21) +__0.057(151
-0.071 - 0.006 +0.075 -0.059 -0.322 +0.190 -0.014 +0.149 -0.218
+0.322(25) -+0.190(17)
0.076(10)
a) Assuming transition is mostly MI multipolarity.
exp
calc
T0.166 (14) T-0.273 (25) 0.147 (16)") 0.0374(43) 0.037 (5) a) T0.193 (18) +0.219 [18)
+0.170 -0.268 +0.155 +0.182 -0.170 +0.221 -0.271
+0.087 (11 ~) -
-0.247
34
H. H. Ghaleb, K. S. Krane / 1931r
amplitudes are calculated (not fit, because 2 parameters give 2 matrix elements) with the intrinsic matrix elements, (-~[rn(E2)1½')= +0.091 and (3[m(E2)b-½') = - 0 . 1 6 3 , in good agreement with the respective 191Ir values [+0.092 and -0.102, the latter sign being given incorrectly in ref. l)]. The 193Ir level scheme offers an additional test of this model, because the matrix elements of transitions from the 557 keV level should be calculable using the same parameters, assuming the level is the I = ½ state of the ½1411] band. Using the above deduced intrinsic matrix elements, with no additional parameters, the matrix elements given in table 7 are calculated. The calculated transition matrix elements for the 484, 377, 557, and 418 keV transitions are each a factor of 3-4 smaller than the experimental value. (The mixing ratios of the 377 and 557 keV transitions are not known. We assume both to be mostly of M 1 multipolarity ; any E2 admixture will reduce the experimental M 1 moment and increase the difference with the calculated value.) However, the predicted intensity ratios are in good agreement with the observed values. Using the calculated matrix elements, the ratio I(377)/1(484) is expected to be 0.42, in exact agreement with the experimental value of 0.42. The expected ratio I ( 4 1 8 ) / I ( 5 5 7 ) i s 0.038, in good agreement with the observed value of 0.042. A more sophisticated calculation than the previous one has been done by Vieu et a/. 1o) who treat three Nilsson states coupled to a 7-asymmetric rotor. The resulting transition probabilities are compared with experiment in table 8. The agreement between the calculated and experimental values is comparable to the present calculation, but it must be remembered that the agreement obtained in the present work required the ad hoc introduction of intrinsic transition strengths and coupling parameters that are not required by Vieu et al. The M1 strengths are determined directly from the nucleon 9-factors, and the coupling of bands arises in a natural way from the y-deformation. The calculation of Vieu et al. should then be regarded as considerably more microscopic than the present phenomenological one. An alternative approach to understanding the nuclei of this region is the interacting boson-fermion model (IBFM) of Iachello and coworkers 17' is) in which a single odd fermion is coupled to a core of interacting s-and d-bosons. The 0(6) limit of the interacting boson model (IBM) for even-even nuclei has been successful in accounting for levels and transitions in the region of mass 190 [ref. 19)3. In this limit the model approaches that of the 7-unstable rotor. The SU(3) limit of the IBM corresponds to a specific sort of 7-symmetric rotor and thus more closely approximates the rotational structure observed in 150 < A < 190. Considerable success has therefore been achieved in treating even-even nuclei in the A ~ 190 region as transitional between the 0(6) and SU(3) limits 2o). When the odd fermion is introduced into this model, an accidental isomorphism occurs between 0(6) and the SU(4) group that describes the symmetries of a j = ~ fermion. This additional symmetry permits bosons and fermions to be treated in common as part of a dynamical "supersymmetry." The d3/2 proton dominates the low-lying level
TABLE 8 Reduced transition probabilities in 1931r B(E2) (e 2. b 2)
B(M1) (x 10 -3 U~) Initial level
E~, (keY)
calc
calc
(½), (3)2
73 66 139 41 107 180 219 358 182 223 289 362 99 280 322 387 460 97 377 418 484 557 420 559
exp
present
PAR ~)
2.62(24)
2.25
0.75
71.6
49.3 (4) < 3.5 78(10) 8.1 (12) 68(27)
39 10 110 7.8 52
160 44.5 260 21.4 192
38.5 32.3 33.8 0.5 72.6
47(12) < 2
76 5.4
178 23.2
58.4 27.2
8.5 (11) 5.4 (11) c) 18.6 (34) 12.0 (20) 6.9 (12) 9.3 (17) 49(12) 0.69(19)')
9.4 6.0 18.0 18.4 7.2 12.2
0.70(16) 3.8 (10)c), 117(18) 150(26)
16.6 30.5
a) Ref. 16). b) Refs. 18.22). ~) Assumes transition is M1 multipolarity.
14.5
49.2 43.7 39.0 8.39 11.3 1.86 32.4 0.033 2.51 2.94 30.9 566
exp
present
0.220 (20) 0.126 (36) 0.445 (44) < 0.30 0.250 (361 0.079 (12) 0.36+~28 0.235 (25) 0.045 (11) < 0.06 0.150 (32) 0.0100 (13) 0.00") 0.00081(43) 0.0090 [16) 0.0038 (13) 0.026 (4) 0.30 07) 0.00") 0.0029 (7)
0.186 0.126 0.47 0.11 0.27 0.116 0.29 0.20 0.078 0.086 0.27 0.0216 0.0014 9.0x 10 -6 0.0090 0.0013 0.026
0.00 ~)
0.011
IBFM b)
0.0
< 0.0054 < 0.0013
0.0017 0.024
PAR a) 0.150 0.120 0.635 0.149 0.357 0.145 0.298 0.0261 0.276 0.0261 0.0115 0.00086 0.0152 0.0215 0.0255 0.716 0.441 0.0304 0.00584 0.0021 0.00024
IBFM ~) 0.216 0.0256 0.417 0.204 0.181 0.0018 0.158 0.299 0.0001 0.0388 0.258 0.0003
ta
36
H. H. Ghaleb, K. S. Krane / 193~'F
structure of the o d d - A Ir isotopes, which therefore h a v e the p o t e n t i a l for testing the s u p e r s y m m e t r y schemes2J). In the extreme 0 ( 6 ) limit, the a - a n d z-selection rules 18.21) forbid the 180 a n d 362 keV transitions a n d those d e p o p u l a t i n g the 460 a n d 557 keV levels. It is therefore necessary to i n t r o d u c e a s y m m e t r y - b r e a k i n g term, which can be either a sl/2 fermion or a b o s o n SU(3) limit. T h e results of some p r e l i m i n a r y c a l c u l a t i o n s based on the latter 22) are shown in table 8. T h e t r a n s i t i o n s from the higher-lying states are p a r t i c u l a r l y sensitive to the degree of 0 ( 6 ) s y m m e t r y b r e a k i n g ; for example, the 280 keV t r a n s i t i o n violates b o t h the aa n d z-selection rules in the 0 ( 6 ) limit, a n d as a l r e a d y n o t e d the E2 c o m p o n e n t s of this t r a n s i t i o n a n d its 191Ir a n a l o g u e are hindered by 1-2 o r d e r s of m a g n i t u d e relative to o t h e r t r a n s i t i o n s from t h a t same level. The E 2 / M 1 mixing ratios, such as those r e p o r t e d in the present w o r k and in ref. ~), can serve as p a r t i c u l a r l y sensitive tests of the I B F M c o u p l i n g scheme. If such precise a n g u l a r - d i s t r i b u t i o n a n d a n g u l a r - c o r r e l a t i o n m e a s u r e m e n t s can be similarly d o n e across the m e m b e r s of a s u p e r s y m m e t r y multiplet (perhaps involving decays far from the valley of stability), it w o u l d p r o v i d e further direct s u p p o r t for these new c o u p l i n g schemes. M o r e d e t a i l e d c a l c u l a t i o n s of the effects of various s y m m e t r y - b r e a k i n g terms in the I B F M on E2/M1 m i x i n g ratios ( m a g n i t u d e s and phases) in the m a s s - 1 9 0 region will be presented in a f o r t h c o m i n g work.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22)
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