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Rotational bands in the doubly odd 138Pm
NUCLEAR PHYSICS A ELSEVIER
Nuclear Physics A 632 (1998) 307-322
Rotational bands in the doubly odd 138pm U. Datta Pramanik a, Anjali Mukherjee a, A.K. Singh b, S. Chattopadhyay a, G. Gangopadhyay b, A. Goswami a, M. Saha Sarkar a, R.K. Bhowmik c, R.E Singh c, S. Muralithar c, B. Dasmahapatra a, S. Sen a,l, S. B h a t t a c h a r y a a a Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Calcutta - 700 064, India b Department of Physics, University College of Science, Calcutta Universi~, Calcutta - 700 009, hMiu c Nuclear Science Centre, New Delhi - 110 067, India
Received 20 October 1997; accepted 24 December 1997
Abstract The band structures of the doubly- odd 138pro nucleus have been investigated using the ~51n(28Si, 2p3n)~38pm reaction at a beam energy of 145 MeV. The three previously known rotational bands viz., (i) the yrast one based on the ~rhl~/2 ® uh~/2 configuration, (ii) a d l = 2 band with rrhll/2 ® u[400] ½+ configuration at lower frequency but with a change in the neutron configuration to u[660] ½+ at higher frequency, and (iii) one consisting of stretched E2 cascades at lower frequency but of dipole transitions after backbend and with suggested configuration of ~r[413] ~+ ® uhll/2 have been modified and extended to higher spins. Two new bands have been identified. Of these, one consists of only quadrupole transitions, similar to that observed in band (iii), mentioned above, while the other consists of dipole transitions. The observed level properties have been compared to theoretical calculations performed within the Particle Rotor Model (PRM) with axial core and cranked shell model. The experimental branching ratios and B(M1 ) / B ( E 2 ) ratios of the transitions in the yrast band are well reproduced by PRM, assuming an axial prolate core. (~) 1998 Elsevier Science B.V. PACS: 21.10.Re; 23.20.-g; 21.60.Ev; 27.60.+j Keywords: NUCLEAR REACTIONS USln(28Si,2p3n)138pm, E = 145 MeV; measured Ee, I~, y y coin, DCO
ratios. 13Spm deduced levels, 1~', B(MI )/B(E2) ratios.
i Present address: Department of Science and Technology, Govt. of West Bengal, Bikash Bhavan, Bidhan Nagar, Calcutta - 700 091, India. 0375-9474/98/$19.00 (~) 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 7 5 - 9 4 7 4 ( 9 7 ) 0 0 8 16-6
308
U. Datta Pramanik et al./Nuclear Physics A 632 (1998) 307-322
1. Introduction
The study of the deformed odd-odd nuclei provides much useful and interesting information on the interplay between collective rotation and single particle motion of two unpaired non-identical nucleons. In this respect very light rare earth nuclei are of great interest. This set of nuclei can roughly be classified as isotopes of La, Pr, Pm and Eu with neutron numbers ranging from 74 to 78. In these nuclei valence protons and neutrons are expected to be at the same high j-shell viz., hi1~2 orbital, and depending on the configuration of the valence quasiparticles, rich and varied structural properties are expected. However, as is well known, detailed studies in the case of odd-odd nuclei are difficult both experimentally and theoretically due to the complexity of their excitation mechanism. Only very recently experimental investigations, using heavy ion beams and large detector arrays, have been initiated to study the behaviour of such nuclei with large number of valence nucleons, spanning wide range between very low and very high excitation energy and rotational frequency. Within a short span of time various interesting information on the evolution of nuclear shapes, shape coexistence, non-axial deformation, changing role of pairing and coriolis force etc. with rotational frequency, have been obtained. In this paper we report the results of our investigation on the level structure of 138pm carried out using (HI, xpyn) reaction technique. This was done with the following motivations. i) An earlier study [ 1 ] on this isotope (with a four-detector setup) using 116Cd(27A1' 5ny) reaction could establish excited levels upto 3951 keV ( F r = 16 +) based on 7"rhjl/2 ® vh11/2 configuration. Only two other sidebands, one probably based on [413] 35+ ® vhll/2 configuration and the other a AI = 2 band structure having the j+
suggested configuration of 7rh11/2 ® v[400] ~ at low frequency were also populated. It was also observed [ 1 ] that at a frequency of heo ,~ 0.31 MeV the latter band is crossed by a band based on the favoured signature of the 7"rhj1/2 ® ~'i13/2 configuration with an accompanying gain in alignment ,-~6h. However, calculations within the frame work of the cranked shell model, for the nuclei in this region, predict various minima in the potential energy surface, depending on which orbitals are occupied. At higher rotational frequencies, total routhian surface (TRS) calculation predict the existence of highly deformed (/3 ~ 0.3) and triaxial doubly decoupled bands based on the vi13/2 , ~'h9/2, u f7~2 orbitals. Recent experimental studies on the other odd-odd systems in this region and N = 77 isotones in particular [2,3], have confirmed the presence of several such bands. It was, therefore, felt that a more detailed study should be carried out for 138pm with a relatively larger detector array and preferably with a different kind of reaction. ii) All these experimental findings have created an opportunity for testing the predictions of different theoretical models. We have initiated a project to study, in a systematic way, the level properties (energies and transition probabilities) of odd-odd nuclei in this mass region within the framework of a model wherein two quasiparticles (a proton and a neutron) are coupled to an axially symmetric rotor core through coriolis interac-
U. Datta Pramanik et aL/Nuclear Physics A 632 (1998) 307-322
309
tion. Detailed results of such study in the case of positive parity yrast band structure arising from ¢rhlj/2 ® uhll/2 configuration in 128'13°'132'134La [4], 132'134'136'138pr [5] and 136'138pm [6] have been published. In the case of 132'134La [4] (N = 75,77) our calculation favoured an oblate shape and a change in shape was noted as one moved from N = 73 (i.e. 13°La which was predicted to be prolate). For 134'136pr a reasonably good agreement could be obtained by assuming a prolate deformation. The comparison between the experimental and theoretical results for the other N = 75, 77 isotones viz., 136'138pm suggested [6] a prolate shape for the positive parity yrast band in J36pm. However, for 138pm a meaningful comparison could not be carried as it was not possible to estimate the experimental branching ratios and the B(MI)/B(E2) values for most of the states because of the presence of several unresolved doublets in the previous work [ 1]. A more extensive and accurate measurement of the y-ray intensities was felt necessary to arrive at any meaningful conclusion in this regard.
2. Experimental methods and results High spin states of 138pm were populated through l lSIn (28Si, 2p3n) reaction at a beam energy of 145 MeV obtained from 15UD Pelletron Accelerator at Nuclear Science Centre (NSC), New Delhi. The target (,-~800 /zg/cm 2 thick) was prepared by evaporating natural Indium (having 97% llSIn and 3% ll3In) in ~ 1 0 m g / c m 2 gold foil, acting as a backing. The beam energy was fixed through a preliminary study of the excitation function. In this target-projectile combination p4n, p3n and 4n channels were found to be the other dominant ones leading to 138'139Sm and 139Eu respectively. Contributions from 135Nd and 136pm were also observed. The presence of these competing channels introduced complexity in the analysis of the y-ray spectra, owing to the presence of overlapping y-rays. However, the analysis could be carried out satisfactorily with the help of recently published data on these nuclei [7-11']. The y - y coincidence data were collected with a multiple detector array consisting of twelve compton-suppressed HPGe detectors along with fourteen BGO detectors serving as a multiplicity filter to reduce the radioactive background. The detectors were arranged in three groups, each consisting of lour detectors placed at 45 °, 99 ° and 153 ° with respect to the beam direction. The details of the experimental setup and data acquisition system can be found in Ref. [ 12]. A total of 130 million events corresponding to two or higher fold coincidences in HPGe detectors was recorded in List mode. Each coincidence event was qualified with the condition that at least two BGO detectors of the multiplicity filter should fire. The pulse height of each detector was gain matched to 0.5 keV/channel and the y - y coincidence data were sorted out into a 4096 × 4096 total E~-E7 matrix. The energy spectra gated by the y-rays of interest were generated from this matrix. Fig. 1 shows the coincidence spectra with gates on a few y-rays of importance. The multipolarities of the observed yrays were determined through the directional correlation (DCO) ratios. For this purpose a separate 4096 × 4096 matrix was generated with the events recorded at 99 ° along one axis and those recorded at 153 ° along other axis. The DCO ratio was determined as
U. Datta Pramanik et aL/Nuclear Physics A 632 (1998) 307-322
310
Table 1 Energies, intensities, DCO ratios of the y-rays of 138pm populated in the present work Energy a
Intensity
(keV)
DCO
Nature of the
Assignment
ratios
gating transition
1;---*I 7
Band
9 + --* 8 + 8-4--*7 -
1 4
8---*76-458+--,7 6----*614- ~ (13-) (9-) 4 (8-) 14- ~ 13( 1 0 - ) --, ( 9 - ) 1 5 - 4 14(13-) 4 (12-) 7 - ---~ 6 14- ~ 1316- ---* 1513- ~ 11 + 11 + -'~ 10+ 7 - --~ 7 10 + ~ 9 +
4 I 1 2,1 3 4 3 4 3 3 I 2a,2b 3 2,2b I 2,1 1
120.6 132.1 148.4 150.0 173.6 177.4 195.6 227.3 231.1 236.5 241.3
29.1(16) 8.9(5) 4.9(3) 53.5(27) 100 5.8(4) 3.5(3) 21.1(8) 9.5(7) 16.5(6) 10.7(5)
0.83(5) 0.96(15) 0.96(14) 0.91(7) 0.95(7) 0.85(10) 1.52(37) 1.08(13) 0.51(12) 0.86(12) 0.73(11)
D D D D D Q D D D D D
260.8 276 288.0 337 349.5 352.2 356.9 372.5 c 382.6 391.6 392.3 c 396.2 398.8
77.2(26)
0.97(4)
D
1.06(9)
D
0.95(1) 1.10(25) 0.72(5)
D D D
0.60(13)
D
17- ~ 1613 + ----, 12+
3 I
15.1(7) 16.2(8)
0.89(12) 0.49(14)
D D
401.9 409.4 c 410.6 426.2 435.4
23.7(9)
2.05(23)
D
( 1 1 - ) ---* ( 1 0 - ) (12-) 4 (ll-) 1 8 - 4 179-4--,7 -
4 4 3 2
25.4(12) b 6.7(5) 15.0(9)
1.00(11) 0.69(38) 0.40(13)
D D Q
7-459-~87-4614- 4 ( 1 2 - )
! 3 2 3 4
2.5(4) 3.4(3) b
0.55(15)
D
0.32
D
1.57(31) 0.95(33) 0.67(9)
D D D
440.8 c 451.0 452 459.6 465.5 468.2 474.4 477.0 486 494.5 508.8 c 516.8
1.7(3) < 1.0 24.8( 11 ) 3.3(4) 11.9(7) <1.0 3.1(5) 4.2(6) 2.6(3)
15 + 119138II12 + 17 + (19-)
---' 14+ ~ 11 + ~ 9+ 4 12---* 6 ---* 10--~ I1 + ~ 16 + ~ 18-
(20-) ~
(19-)
I 2,1 2,1 3 3,1 3 I I 3 3
U. Datta Pramanik et aL/Nuclear Physics A 632 (1998) 307-322
311
Table 1 - - continued Energy a
Intensity
(keV)
DCO
Nature o f the
ratios
gating transition
518.6 534 544.9 545.6 551.5 ~ 554.6
11.6(8) 2.3(3) 3.9(5) 11.6(8)
1.21(34) 0.89(10)
Q D
1.10(14)
D
576.3 584 596.4 598.5 610.6 618.3 633.6 651.0 684.0
6.6(8) 13.4(10) 12.4(9) 3.4(7) 5.0(6) 4.8(6) 8.6(6) h
1.20(24) 0.93(9) 0.65(7) 1.23(38)
D Q Q D
686.0 c 696 698.4 699.4 706.3 726.6 764.9 782.2 800.8 808.7 c 813.6 825.2 826.7 85O 851.7 861.7 869.1 895 932.6 937.6 938.8 943 c 948 c 954.7 974.5 983.7 995.2 1010.4 1013.0
Assignment
IY---~I ~ t
f
3.5(5)
~1.0 33.4(15) b 12.1(7) 6.5(12) 14.1(11) 2.4(5) <1.0 4.3(6) 9.7(8) 9.2(3) b 3.9(6) 6.7(7) 11.2(10) ~1.0(4) 7.1(5) 6.9(5) 4.5(3) 3.7(5) 7.0(6) 9.1(7) 6.7(8) 2.6(5) 3.3(6) 1.8(6) 2.7(8)
(19 + ) ---, 18 + 13 + ---, 11 + 14 + ~ 13+ ( 1 0 - ) --~ 10 + 19 + --~ 18 + 16+ --~ 15 + 18 + --~ 17 ~11 + - + 1 1 14- ~ 1212- ~ 11(8-) -~89-4--*7 (15 + ) --, 13 +
1.62(13)
D
1.90(18) 2.06(26) 2.75(9)
D D D
2.1(10) 1.3(3) 2.27(30)
D D D
0.97(19) 1.07(10) 1.70(10)
Q D D
1.7(4) 1.80(14) 1.37(40)
D D D
1.07(25) 2.5(12)
D D
1.71(70)
D
14- ~ 12II- --.91 6 - --* 1 4 I1 + ~ 9 + 18 + ~ 16 + 10---+81 4 - ---* 13 + 1 1 - - - - * 10 +
Band 4 I 2b 1 3,1 5 1 I 2b 2a 2a 4,3 3,1 4 2b 3 2 2a I 5, 1 3 3,1 2, I
11(8-) 12 + (17 + ) 1820 + 13 + 21 + 191314 + (7-)
--*9--+7---* 10 ~ ~ (15 + ) ~ 16~ 19 + ----, II ~ ~ 20 + ~ 17~ I1~ 12 + 46-
3 4,1 I 2b 2a 5 I 5 3 2 1 4
(7-) 131215 + (13-) (20-) (12-)
---~ 6 ~ 11~ 10~ 13 + --, I 1 ~ 18--, ( 1 0 - )
4 3 3 I 3 3
U. Datta Pramanik et al./Nuclear Physics A 632 (1998) 307-322
312 Table 1 - - continued Energy a
Intensity
(keV) 1025.9
DCO
Nature of the
ratios
gating transition
2.6(5)
1.92(50)
Assignment
l~l ---+ If~
D
Band
16 + ---* 14 +
1
17 + ---* 15 + 18 + --* 16 +
I I
1072
2 0 - --* 1 8 -
2a
1118
( 1 9 + ) ---* 17 +
I
1063 1070
a The transition energies are accurate to 4-0.1 keV. Energies given as integers are accurate to 4-1 keV. h Total intensity of the doublet. c y-rays, which we strongly feel belong to J38pm but could not be placed in the proposed level scheme (Fig. 1 ).
1200 X3
1000
~
698 keV Gate
r~
800 600 400 200
1600
~
x3
o -
1200 800
~ ~
~
241+383keV Gate
,o
~
400
"
3000 2500 -
2000 1500
-
1000
-
~ -
t-- ,~ e~ea
~,
x3
236+227+396keV Gate
:
_
~
,~
~
,~
~_
~
oo
00-
oo
l 200
400
600 Energy (keV)
800
1000
1200
Fig. 1. Selected y - y coincidence spectra for the three bands of 138pm, obtained by setting gates on the transitions: ( i ) 698 keV for the band 2, 2a and 2b, (ii) 241 + 383 keV for band 3 and (iii) 227 + 236 + 396 keV for band 4. The transitions of interest are labelled by their energies in keV.
R D C O (gq) =
I (3't at 153 ° with ~2 at 99 °) I (3'1 at 99 ° with "Y2 at 153 °) "
The gating transition ~'2 was, as far as possible, the preceding or succeeding the transition of interest. Whenever possible different gating transitions were used and the consistency of the assignments was checked. The multipolarities of a few of the yrays could not be determined conclusively owing to their poor statistics in the DCO
U. Datta Pramanik et al./Nuclear Physics A 632 (1998) 307-322 2b
2
2a
1
313
3
5
4
21 - - V
q-
20
20"
W-Lr. . . . . . ~. . . . . . . .
_1072
IEI*
+
16
+
.
, 6"
/
13 684
14-
.2
15
727
0' I
~k--
J &
16i
'
IJ.- 2--"*~--
~o~3
,2/
02
~177
4eO
~
2
13
e51 K
-
519
9* 7-
/
\
,
12 I
(.-)"F
~
,
T"
(g')
" r t °°
roe ....
6-
~
~g5
I 7-
18
÷ 1~ 782
n--./r.~."
is0 Prn (20")
862
~
e- f
I
,/"
825
- -
|
4[1
Fig. 2. The proposed level scheme o f 13Spm deduced from the present work. The transitions which can only be tentatively placed are indicated by dash lines.
gates, but their presence and intensities in the multiple gates or in the summed gated spectra of the same band indicated that they belong to the relevant bands. The energies, relative intensities and DCO ratios of the y-rays and the assigned spins and parities of the relevant levels of 138pm are given in Table 1. Because of the presence of a few overlapping y-rays arising out of the competing channels, the relative intensities have been determined from the coincidence spectra with gates on uncontaminated y-rays. It should also be noted that in Table 1 we report only one of the obtained DCO ratios for each transition and also specify the type of gating. The level scheme of 138pm has been constructed from the y - y coincidence data, the y-ray intensities and the multipolarities of the y-rays, inferred from the DCO ratio measurements. A total of 76 y-transitions has been placed in the level scheme shown in Fig. 2. Seven distinct band configurations including the positive parity yrast structure have been established. We now briefly discuss each of these bands separately below. Band 1, which is the yrast levels of 13Spm (band 1), is built on the T~/2 = 21 ns state and its spin parity is assumed to be 8 + following the arguments given in the earlier work [1]. The data of the present work allow this yrast band to be extended upto a spin of 19 + and upto an excitation energy of 5455 keV. A characteristic feature of this structure is the stronger population of odd-spin states. The crossover transitions for the favoured signature cascade are, therefore, of higher intensity. Band 2, which is a negative parity band and was also reported by Beausang et al. [ 11. is found to be connected with the yrast band by many transitions. The spin-parity assignments as proposed in the present work differ from that suggested by Beausang et al., as the DCO ratio for the 435 keV y-rays clearly indicates that it is a A I = 1 transition. In the earlier work no angular distribution coefficients were presented for this
314
U. Datta Pramanik et al./Nuclear Physicx A 632 (1998) 307-322
y-ray because of the fact that it was unresolved from the transitions in other nuclei. The present spin-parity assignments are also consistent with nature of the transitions, as suggested by the DCO ratios, for the linking transitions to the yrast band. Above the 11- state at 1863 keV excitation, this band bifurcates into two quite similar band structures (band 2a and 2b). Band 2a, to which a negative parity was assigned by Beausang et al. [1], has not only been confirmed but also has been extended in the present work. However, the presently proposed spin-parities differ from that suggested by the earlier work in view of (i) the different nature of the 435 keV y-rays, observed in the present work as mentioned earlier and (ii) the DCO ratio data strongly indicate that the 611 keV y-ray is of A1 = 1 type transition while in the earlier work it was assumed to be of quadrupole character. The band 2b, to which we have assigned a positive parity, is a newly suggested one, though a preliminary indication of the same could be seen in the earlier work. It should be mentioned that the placements of the 545 keV and the 596 keV y-rays have been altered to satisfy the intensity balance and also by considering the fact that they are of stretched quadrupole and dipole character, respectively. The assignment of spin-parity values for the band 2a and 2b is strongly dependent on the assumption of a MI (AI = 1) and an E1 (AI = 0) nature for the 611 and 596 keV y-rays, respectively. However, as will be presented in the next section, these conjectures and assignments are well supported by the theoretical predictions. Band 3 is another negative parity side band proposed by Beausang et al. [ 1 ], having the suggested configuration of ¢r[413]~5+ ® t.'hll/2. It has been possible to extend this band upto the spin state of I T = 2 0 - having the excitation energy of 5376 keV. Two very weak crossover transitions have been observed in the upper portion of the band and are shown as dashed. In the work of Beasung et al., the spin-parity assignment was on the basis of the systematics and observation of similar bands in the neighbouring doubly odd ~36pm and 134pr nuclei. The character of the 468 and 634 keV interband transitions was assumed by them to be stretched quadrupoles due to the non-availability of angular distribution data. In the present work the DCO ratio measurements confirm this assignment for the 468 keV y-ray but the corresponding quantity for the 634 keV yray cannot be determined convincingly because of weak statistics. This firmly establishes the spin-parity of the low lying portion of this band. The nature of other transitions in this structure viz., the dipole character of the 426 keV and other transitions above the spin of 13- and the quadrupole character of the 765, 813 and 974 keV transitions, are also established through the present DCO measurement. In the work of Beausang et al. [ 1] no connection between these two sequence of stretched E2 transitions was found. However, in the present work we have observed a few weak linking transitions viz., the 465 and 475 keV y-rays, between the two bands. The present work also significantly modifies the scheme proposed by Beausang et al. in the following respect. In their work a very weak 783 keV connecting transition, between the high spin portion of this side band and the yrast band, was very tentatively proposed. In the present work in addition to this, a number of other decay modes from the 14- state of this band are observed, which make the lower portion of the structure quite complicated. Of these, a discussion on the placement of the 554 keV y-ray will be done shortly. With these transitions
U. Datta Pramanik et al./Nuclear Physics A 632 (1998) 307-322
315
it has been possible to establish the connection between in-band dipole transitions to the lower members of the yrast band. These linking transitions were not observed in the earlier work [ 1 ], though definite indication of some relationship between the two configurations (i.e. lower part of the yrast band and the upper part of band 3) was reported. Band 4 is observed for the first time in this nucleus. The upper part of it mainly contains dipole transitions, similar to that in the case of band 3. But unlike the band 3 it is not strongly connected to the positive parity yrast configuration, though definile indications of the 227 and 236 keV y-rays are found in the gated spectra of 173 and 120 keV y-rays and vice versa. However, it has not been possible to identify the linking transitions. It can be noted that this configuration is mainly connected to states having negative parity viz., I ~ = 8 - state of band 3 and I ~ = 7 - level of the ground band through the 618 keV and 825 keV y-rays, respectively. The characters of the 132 and 148 keV transitions are dipole in nature. This is also found to be the case for the 938 and 955 keV transitions, as placed here. They can be either M1 or E1 and in absence of any other supporting evidences, it is difficult to assign any definite spin-parities to the levels of this band. However, a tentative scheme is proposed, mainly based on the observed nature of the above mentioned transitions and the observed linking to the negative parity states. It may be further noted that no spin-parity values could be suggested lbr the upper part of the band. This is because the multipolarities of the y-rays involved (435, 518 and 651 keV), could not be determined because of poor statistics in the related gated spectra. Finally we would like to point out that a cascade of three y-rays (viz., 554.7, 726.7 and 861.7 keV), as noted by the earlier worker [1 ], has also been observed by us. It was further noted [1] that intensities of these y-rays were larger than the intensities of the transitions of the yrast band into which they feed but the linking transitions could not be observed. Because of these, no proper placements of these y-rays could be suggested in the previous work. We, however, differ with these observations to a certain extent and these are as follows. We have noted that the intensity patterns of the y-rays of the yrast band in the gated spectra with gates on the above three yrays, are not quite similar. With the gates on 727 and 862 keV y-rays, the spectra are nearly identical but in the coincidence spectra with 555 keV as gate, there is a sudden increase in the intensities of the y-rays arising from the 10 + state (and below it) of the yrast band. Considering the energy and the intensity balance, a connecting transition of 555 keV between the band 3 and the 10 + state has, therefore, been proposed. This is also in accordance with the coincidence spectra with gates on the dipole transitions in band 3. DCO ratio measurements of these three y-rays suggest that the 555 and 862 keV are of AI = 1 type whereas the 727 keV is of AI = 2 nature. After taking into consideration the other information from different coincidence spectra, we propose a band (5) consisting of 555 and 861 keV y-rays and it is linked to the 16 + state of the yrast structure through the 727 keV transition. In this band we have also tentatively included a 869 keV transition primarily because of the facts that we have observed (i) a 869 keV y-ray in the coincidence spectra with gates on 477 and 869 keV y-rays of
U. Datta Pramanik et al./Nuclear
316
>~->. :- .......
Physics A
632 (1998) 307-322
. , : . = ........
t
1.5 i
1.5
~//~
.....
//
"
~-~
/-
~.
1.0 1.0
)--~
"
// 0.5 0.0
i
'\
/
!i
-0.5
oo
p =o.~ ~t=o \ \ ~
/
- . .
13z=02y= 2(Y'
o, 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
o.o
0.1
0.2
h(~ (MeV)
1.5
~ 1.o= ~ - ~ , ~ > . % . L
"\
-% - .
~
~
0.3 0.4 0.5 11¢00 4 e V )
...... "
1.0 ~
\
0.6
0.7
~.
0.8
/
"~ ~.:~
\ . \3<%"
.o.°!:............................ 0.0
0.1
0.2
0.3 0.4 0.5 li~ (MeV)
0.6
0.7
0.8
0.0
0.1
0.2
0.3
04
0.5
0.6
0.7
0.8
ho~(MeV)
Fig. 3. Quasiparticle routhian diagrams (a) for protons and (b) neutrons. The deformation parameters used in the calculation are indicated in the figures. Parity and signature of the states are as follows: solid: ( + , + 1 / 2 ) ; dotted: ( + , - 1 / 2 ) ; dashed-dotted: ( - , + 1 / 2 ) ; d a s h e d : ( - , - 1 / 2 ) . The relevant lowest neutron orbitals are labelled with the asymptotic Nilsson quantum numbers.
the yrast band, and (ii) the intensity of the 869 keV y-ray in the 555 keV and 727 keV gated spectra is much larger than that expected from the single 869 keV transition in the yrast cascade.
3. Discussion For 138pm the neutron Fermi surface lies in the upper part of the hll/2 shell while for the protons the Fermi surface lies in the lower part of the same shell. Because of this, valence quasineutron drives the nucleus towards 3/ ~ - 6 0 ° and the valence quasiproton tries to induce a prolate shape with 9' ~ 0 ° or slightly negative. The polarising effects of these valence quasiparticles can be well studied in the framework of Cranking Shell Model (CSM). Quite a detailed picture of some of the aspects of different band structures in 138pm, using the same formalism, had been already put forward [ 1]. However, for the sake of completeness and proper understanding, we also present the salient results of our calculation using CSM. We have carried out the calculation with the deformation parameters /32 = 0.2 and /34 = 0.0 (following the systematics in the neighbouring odd-odd nuclei) and for different 9,-deformations. The routhians for proton and neutron are shown in Fig. 3.
U. Datta Pramanik et al./Nuclear Physics A 632 (1998) 307-322
317
14
12
F]
A.
11
10
8
I
6
z
©
x
~
~
4
-3 ! 0.20
i 0.25
0.30
0.35
0.40
0.45
11¢o(MeV)
I
~
0.50
o.ss
2 0.0
i
i
i
E
i
0.1
0.2
0.3
0.4
0.5
0.6
he0 (MeV)
Fig. 4. (a) Experimental routhians and (b) alignments for the observed bands in 138pro.The two signatures of the yrast ~rht 1/2 ® vh II/2 band ( 1) are indicated by the open (favoured) and closed (unfavoured) circles. Similarly the favoured and unfavoured signatures of the ~'14131 5 ® Uhll/2 band (3) are indicated by the closed and open triangles, respectively. The filled square indicates the ~rhlU2 ® ~i13/2 band (2a) while the open square is for the ~rhll/2 ® u[530] ½- band (2b). The experimental routhians and alignments (e' and i) of the bands in 138pm, obtained through the standard procedure prescribed by Bengtsson and Frauendorf [ 13 ], are shown in Figs. 4a and 4b, respectively, where they are plotted as function of rotational frequency hw. In these calculations the value of K ( = 52~. ± ~ , ) was chosen in accordance with Gallagher-Moszkowski rule [ 14]. The angular momentum component of the reference configuration lx.ref is calculated with the following Harris parameters [ 15]: 30 = 12.5h 2 MeV -I and ~j = 16h 4 MeV -3. These set of parameters had been used for 136Nd [ 16], which can be presumed to be the core of 138pm.
3.1. B a n d 1
Band I (yrast) is assumed, following the earlier work [1] and systematics observed in this mass region, to be based on 7rhj j / 2 ® v h l i/2 configuration with band head 1 ~" = 8 ~, arising from the perpendicular coupling between the valence proton and neutron. This yrast cascade is found to possess a relatively larger signature splitting ( ~ 8 5 keV) (compared to that observed in the isotone J36pr [ 3 ] ) which remains constant upto tile highest states which have been established definitely. The corresponding alignment, on the other hand, shows a rather smooth increasing trend from ~ 5 . 7 h to ~ 7 . 0 h upto the rotational frequency of ~0.5 MeV. Energy difference between two signature partners for the proton orbital (7"r[541 ] ~) is much larger than that for the neutron orbital. Keeping in mind the experimentally observed signature splitting, the yrast state can be seen to be based on favoured signature component of the proton state ( a t, = - l ) and separated by the moderate neutron signature splitting. Another positive parity semidecoupled band
318
U. Datta Pramanik et al. /Nuclear Physics A 632 (1998) 307-322 90 0
80 70 50
Z~ 50 40
30 20 10
I 0.25
0.30
1 0.35
I
I
I
0.40
0.45
0.50
0.55
ho~ (MeV) Fig. 5. Dynamical moments of inertia of ~38pm. Symbols have the same meaning as in Fig. 4.
arising from the coupling of the unfavoured signature state of the proton with VhlJ/2 is also expected but at a much higher excitation energy. This has not been observed in the present work. It can be noted that the low frequency breaking of the first pair of h~]/2 particles is blocked. One can, however, try to look for the alignment of the second and third hlz/2 proton and neutron. In the case of the isotone 136pr, it was observed by Petrache et al. [ 3] that the experimentally extracted signature splitting disappeared at high spins for this band and this was interpreted in terms of (h]l/2)2 alignment for the proton. In the present case the experimentally measured signature splitting decreases from Ae' ~ 85 keV at low spins to ~ 5 0 keV in the high spin region, if the states tentatively proposed are considered. The corresponding alignment plot shows an increase in the value to about 9.5h at a frequency ~0.53 MeV. The dynamical moment of inertia plot (Fig. 5) also shows a sudden increase at a rotational frequency of hw ~ 0.5 MeV. In the light of the CSM calculation, the BC and bc crossing frequencies are at 0.52 and 0.55 MeV with a quite large negative y-value ( ~ - 20 °) and the predicted signature splitting is also found to be in agreement with the experimental value. However, as has been pointed out by Petrache et al. [2,3] in their work o n 134'136pr, one has to be careful while assigning a definite y-deformation for the following reasons: (i) a static y-deformation extracted from the TRS calculation, in the case of nuclei with pronounced softness, may involve large uncertainties and (ii) calculation on the transition probabilities within the yrast band, based on two-particle plus triaxial rotor model fails to reproduce the experimental trend while the axial model calculation gives a better agreement. As pointed out in the introduction, we have also carried out a detailed calculation of the energies and transition probabilities of the states in this yrast band [6] within the framework of a Particle Rotor Model (PRM) wherein two quasiparticles (a proton and a neutron) are coupled to axially symmetric rotor core through Coriolis interaction. Further details of the model, the choice of parameters and the calculation can be found in Refs. [4-6]. The theoretical branching ratios and B ( M I ) / B ( E 2 ) values [6] have been compared
U. Datta Pramanik et al./Nuclear Physics A 632 (1998) 307-322
319
Table 2 Calculated and experimental decay modes of the ~'hll/2 ® uh~l/2 yrast band in 138pro Branching ratio
lff
17
Expt. Ia
10+ II~ 12 + 13+ I 14+ f 15+ i 16 ~ f 17 ~ ~
9 ~8+ 10+ 9 +. I 1+ 10+ 12+ 11+ 13+ 12 + 14+ 13+ 15 + 14 + 16 ~15+
60.6 39.4 60.0 40.0
B(MI ) / B ( E 2 ) in /.tn2/ (eb) 2
Theory
Expt.
II b
Ic
II d
llI e
69.0 31.0 61.8 38.2 30.0 70.0 62.0 38.0 43.0 57.0 47.4 52.6
95.4 4.6 65.8 34.2 64.6 35.4 41.1 58.9 55.7 44.3 32.9 67.1 47.5 52.5 29.6 70.4
83.2 16.8 8.1 91.9 44.2 55.8 3.7 96.3 40.0 60.0 1.4 98.6 34.3 65.7 1.0 99.0
91.4 8.6 60.3 39.7 50.5 49.5 39.2 60.8 36.1 63.9 31.5 68.5 23.1 76.9 28.8 71.2
Ia
Theory II b
Ic
II d
I11c
7.8
1.9
4.0
4.4
6.4
5.4
0.4
4.3
3.7
4.0
4.3
2.0
2.4
2.4
3.9
0.2
3.6
5.0
3.7
2.0
1,7
5.7
3.5
0.1
3.4
3.7
3.6
2.1
1.2
3.4
0.4
3.4
a Ref. I I I .
~' Present work. The branching ratios have been calculated from proper gates. c Calculation with prolate deformation ("normar" zt's). d Calculation with prolate deformation (modified An). e Calculation with oblate deformation (modified Ap ). ~ Decay properties of these states can not be calculated from Ref. 111 as the intensities of the transitions involved can not be estimated due to the presence of close lying doublets and contamination lines. g Only the theoretical estimates for the decay from this state is given as the intensities of the y-rays involve cannot be evaluated properly. w i t h t h e p r e s e n t e x p e r i m e n t a l r e s u l t s a n d are g i v e n in T a b l e 2. A s it h a s b e e n p o i n t e d o u t e a r l i e r , t h e r e a r e a f e w y - r a y s in t h e y r a s t b a n d w h i c h h a v e a l s o b e e n p l a c e d e l s e w h e r e in t h e level s c h e m e . T h e r e f o r e , f o r this p a r t o f t h e w o r k , t h e i n t e n s i t i e s o f t h e c o r r e s p o n d i n g y - r a y s o b t a i n e d f r o m t h e p r o p e r g a t e d s p e c t r a , h a v e b e e n u t i l i s e d . It c a n b e s e e n f r o m t h e T a b l e 2 that a g r e e m e n t o b t a i n e d in t h e c a s e o f p r o l a t e d e f o r m a t i o n is quite satisfactory.
3.2. B a n d 2, 2a, 2b B a n d 2 is p o s s i b l y b a s e d o n t h e 7 r h l l / 2 ® t , [ 4 0 0 ]
1+ ~ [ 1 ]. B a n d 2 a ( 2 b ) is a c a s c a d e o f
4 (3) quadrupole transitions and can be the favoured component of a doubly decoupled c o n f i g u r a t i o n . T h e u n f a v o u r e d c o m p o n e n t , in b o t h t h e c a s e s , are p r o b a b l y l y i n g t o o h i g h w i t h r e s p e c t to t h e y r a s t line to a l l o w t h e i r o b s e r v a t i o n . T h i s l a r g e s p l i t t i n g m a y b e i n d i c a t i v e o f t h e f a c t t h a t t h e v a l e n c e p r o t o n a n d n e u t r o n a r e b o t h o c c u p y i n g Iow-.O o r b i t a l s in t h e s e c a s e s . S i m i l a r AI = 2 b a n d h a d b e e n o b s e r v e d in t h e n e i g h b o u r i n g o d d -
320
U. Datta Pramanik et al./Nuclear Physics A 632 (1998) 307-322
odd nuclei and a number of suggestions had been put forward regarding the configuration of these states. In 13°La [ 17] and 136pm [11], for example, this was presumed to be due to the 7rhll/2 ® vii3~2 configuration and associated with high deformation. But in 134pr [2] this was assigned a 7rhll/2 ® v[530] ~1 - structure. In the work of Petrache et al. [3] on 136pr, band based on both the above mentioned configurations were reported. In the present work also it seems that we have been able to observe both these two types of band. Band 2a and 2b also show (Fig. 4b) a gain of aligned angular momentum of Ai ~5.0h and 4.4h respectively, at similar low frequency of h w ~ 0.31 MeV. After this, the experimental alignments remain constant upto the highest observed frequency viz., 0.53h and 0.42h MeV, respectively. As suggested earlier [ 1 ], the negative parity band (2a) is explained by the occupation of vii3~2[660] ~1+ intruder orbital, which comes down very rapidly in energy with increasing rotational frequency. The predicted gain in alignment is Ai ~ 5.8h at the crossing frequency of ha) ~ 0.46 MeV for y = - 5 °. The quasiparticle routhian diagram (Fig. 3; /~2 ---- 0.2 and y ~ - 5 °) also shows that at h w ~ 0.34 MeV (the v[530]½- and v[541]~l - orbitals, of mixed f7/2 and h9/2 parentage, are also introducing from the higher oscillator shell (N = 5). One, therefore, also expects to observe doubly decoupled bands based on these orbitals. The a = +~t neutron signature, corresponding to the v[541 ] ~- orbital is found to be slightly higher in energy than the a = - g 1 of the v[530] ~-. A sequence with odd (even) spins is expected for the v[530]½-(~,[541] l - ) configuration. Based on our spin assignment we propose that the band 2b is the favoured component of the ,'rrhll/2 ® t.'[530]gl configuration. The predicted gain in alignment is Ai = 3.0h at the theoretical crossing frequency. 3.3. B a n d 3
As pointed out earlier in the text this is a negative parity structure which at the low frequency consists of two sequences of stretched E2 transitions, one between the favoured and the other between the unfavoured states. In the present work very weak linking transitions between the two signatures have been observed. At the higher frequency, these two stretched E2 bands merge into a single band having transitions with mixed E2/MI ( z l l = 1) nature. This band shows (Fig. 4b) large alignment (~-,7h) around a rotational frequency of ho9 ~ 0.3 MeV. As suggested by Beausang et al. [ 1 ], this band is probably based on 7rg7/21413]~5 + ®~'hjl/21514] 9 - - configuration. Unlike the yrast band, here the A B crossing is not blocked. In the CSM calculation presented by Beausang et al. [ 1] a rather large negative y-deformation ( - 4 0 °) were suggested for obtaining the experimentally observed A B crossing frequency (~0.37h) and the theoretical value was ~0.42 MeV. In the present calculation we find that without any y-deformation included, the crossing frequency is 0.30 MeV which is in quite good agreement with our experimental results. Furthermore since large negative y-deformation will induce large signature splitting and no such phenomenon has been observed in this band in 138pro,
U. Datta Pramanik et al./Nuclear Physics A 632 (1998) 307-322
321
in either of the experiments, we feel that there is no need to include y-deformation for this band.
3.4. Band 4 It can be based on the 7r[411 ] ~3 + ® uhll/2 configuration, which would generate negative parity states. The ~[411 ] ~3+ , of mixed d5/2 and g7/2 parentage, has a predominant contribution from d5/2 orbital and is quite close to the Fermi level.
3.5. Band 5 It is difficult to suggest any configuration for this structure. One possibility is that this structure is based on a multiparticle configuration involving intruder orbitals from upper shell. The high spin and excitation energy observed will be consistent with this interpretation.
4. Conclusion The high-spin structure of the doubly odd nucleus 138pm has been studied. Several rotational bands have been established in this nucleus and the present result is in agreement, to a quite extent, with the earlier report [ 1] on the three primary bands. However, it has been possible to extend all these three bands upto higher spins and excitation. The AI = 2 band, based on the ~hll/2 ® ~'[400]½ + has been observed to bifurcate into two structures at a frequency hw ~ 0.31 MeV. One of the structures which was reported in the earlier work [ 1 ] and also is observed in the present work, can be explained in terms of the change in neutron configuration to the favoured signature of the ~i13/2. The second one established for the first time in the present experiment, is predicted to arise from a similar change to the 9[530]½- orbital with mixed ]19/2 and f5/2 parentage. A new negative parity band consisting predominantly of transitions with dipole nature has been observed.
Acknowledgements The authors wish to thank Dr. S.K. Dutta, Dr. A.K. Sinha and all the staff members of the Pelletron centre at Nuclear Science Centre, New Delhi for their cooperation during the experiment. A.K. Singh wants to thank U.G.C., New Delhi for financial assistance.
References III C.W. Beausang, P.K. Weng, R. Ma, E.S. Paul, W.F. Piel, Jr., N. Xu and D.B. Fossan, Phys. Rev. C 42 (1990) 541.
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[2] C.M. Petrache, D. Bazzacco, S. Lunardi, C. Rossi Alvarez, G. de Angelis, M. De Poli, D. Bucurescu, C.A. Ur, P.B. Semmes and R. Wyss, Nucl. Phys. A 597 (1996) 106. 131 C.M. Petrache, C.A. Ur, D. Bazzaco, S. Lunardi, C. Rossi Alvarez, M. lonescu-Bujor, A. lordachescu, D. Bucurescu, F. Brandolini, G. de Angelis, G. Maron, D.R. Napoli, P. Pavan, N.H. Medina, R. Venturelli, S. Brant and D. Vretenar, Nucl. Phys. A 603 (1996) 50. 141 U. Datta Pramanik and S. Bhattacharya, Phys. Rev. C 52 (1995) 117. 151 U. Datta Pramanik and S. Bhattacharya, Phys. Rev. C 54 (1996) 1221. 161 U. Datta Pramanik and S. Bhattacharya, Z. Phys. A 356 (1996) 31. 171 E.S. Paul, C.W. Beausang, R.M. Clark, S.A. Forbes, A. Gizon, J. Gizon, K. Hauschild, I.M. Hibbert, P.J. Nolan, D. Santos, A.T. Semple, J. Simpson, R. Wadsworth, L. Walker and J.N. Wilson, J. Phys. G 20 (1994) 1405. I81 C. Rossi Alvarez, D. Vretenar, Zs. Podolyaki, D. Bazzacco, G. Bonsignori, E Bandolini, S. Brant, G. de Angelis, M. De Poli, M. lonescu-Bujor, Y. Li, S. Lunardi, N.H. Medina and C.M. Petrache, Phys. Rev. C 54 (1996) 57. [91 P. Vaska, C.W. Beausang, D.B. Fossan, J.R. Hughes, R. Ma, E.S. Paul, R.J. Poynter, P.H. Regan, R. Wadsworth, S.A. Forbes, S.M. Mullins and P.J. Nolan, Phys. Rev. C 52 (1995) 1270. [ 10] W.E Piel, Jr., C.W. Beausang, D.B. Fossan, L. Hildingsson and E.S. Paul, Phys. Rev. C 35 (1987) 959; E.M. Beck, ES. Stephens, J.C. Bacelar, M.A. Deleplanque, R.M. Diamond, J.E. Draper, C. Duyar and R.J. McDonald, Phys. Rev. Lett. 58 (1987) 2182. 1111 C.W. Beausang, L. Hildingsson, E.S. Paul, W.E Piel, Jr., N. Xu and D.B. Fossan, Phys. Rev. C 36 (1987) 1810. 1121 S.S. Ghugre, S.B. Patel, U. Gupta, R.K. Bhowmik and J.A. Sheikh, Phys. Rev. C 47 (1993) 87. 1131 R. Bengtsson and S. Frauendorf, Nucl. Phys. A 327 (1979) 139. 1141 C.J. Gallagher and S.A. Moszkowski, Phys. Rev. 111 (1958) 1282. 1151 S.M. Harris, Phys. Rev. B 138 (1965) 509. [ 161 E.S. Paul, C.W. Beausang, D.B. Fossan, R. Ma, W.E Piel, Jr., P.K. Weng, and N. Xu, Phys. Rev. C 36 (1987) 153. [ 17] M.J. Godfrey, Y. He, I. Jenkins, A. Kirwan, P.J. Nolan, D.J. Thornely, S.M. Mullins and R. Wadsworth, J. Phys. G 15 (1989) 487.
Nuclear Physics A 632 (1998) 307-322
Rotational bands in the doubly odd 138pm U. Datta Pramanik a, Anjali Mukherjee a, A.K. Singh b, S. Chattopadhyay a, G. Gangopadhyay b, A. Goswami a, M. Saha Sarkar a, R.K. Bhowmik c, R.E Singh c, S. Muralithar c, B. Dasmahapatra a, S. Sen a,l, S. B h a t t a c h a r y a a a Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Calcutta - 700 064, India b Department of Physics, University College of Science, Calcutta Universi~, Calcutta - 700 009, hMiu c Nuclear Science Centre, New Delhi - 110 067, India
Received 20 October 1997; accepted 24 December 1997
Abstract The band structures of the doubly- odd 138pro nucleus have been investigated using the ~51n(28Si, 2p3n)~38pm reaction at a beam energy of 145 MeV. The three previously known rotational bands viz., (i) the yrast one based on the ~rhl~/2 ® uh~/2 configuration, (ii) a d l = 2 band with rrhll/2 ® u[400] ½+ configuration at lower frequency but with a change in the neutron configuration to u[660] ½+ at higher frequency, and (iii) one consisting of stretched E2 cascades at lower frequency but of dipole transitions after backbend and with suggested configuration of ~r[413] ~+ ® uhll/2 have been modified and extended to higher spins. Two new bands have been identified. Of these, one consists of only quadrupole transitions, similar to that observed in band (iii), mentioned above, while the other consists of dipole transitions. The observed level properties have been compared to theoretical calculations performed within the Particle Rotor Model (PRM) with axial core and cranked shell model. The experimental branching ratios and B(M1 ) / B ( E 2 ) ratios of the transitions in the yrast band are well reproduced by PRM, assuming an axial prolate core. (~) 1998 Elsevier Science B.V. PACS: 21.10.Re; 23.20.-g; 21.60.Ev; 27.60.+j Keywords: NUCLEAR REACTIONS USln(28Si,2p3n)138pm, E = 145 MeV; measured Ee, I~, y y coin, DCO
ratios. 13Spm deduced levels, 1~', B(MI )/B(E2) ratios.
i Present address: Department of Science and Technology, Govt. of West Bengal, Bikash Bhavan, Bidhan Nagar, Calcutta - 700 091, India. 0375-9474/98/$19.00 (~) 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 7 5 - 9 4 7 4 ( 9 7 ) 0 0 8 16-6
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U. Datta Pramanik et al./Nuclear Physics A 632 (1998) 307-322
1. Introduction
The study of the deformed odd-odd nuclei provides much useful and interesting information on the interplay between collective rotation and single particle motion of two unpaired non-identical nucleons. In this respect very light rare earth nuclei are of great interest. This set of nuclei can roughly be classified as isotopes of La, Pr, Pm and Eu with neutron numbers ranging from 74 to 78. In these nuclei valence protons and neutrons are expected to be at the same high j-shell viz., hi1~2 orbital, and depending on the configuration of the valence quasiparticles, rich and varied structural properties are expected. However, as is well known, detailed studies in the case of odd-odd nuclei are difficult both experimentally and theoretically due to the complexity of their excitation mechanism. Only very recently experimental investigations, using heavy ion beams and large detector arrays, have been initiated to study the behaviour of such nuclei with large number of valence nucleons, spanning wide range between very low and very high excitation energy and rotational frequency. Within a short span of time various interesting information on the evolution of nuclear shapes, shape coexistence, non-axial deformation, changing role of pairing and coriolis force etc. with rotational frequency, have been obtained. In this paper we report the results of our investigation on the level structure of 138pm carried out using (HI, xpyn) reaction technique. This was done with the following motivations. i) An earlier study [ 1 ] on this isotope (with a four-detector setup) using 116Cd(27A1' 5ny) reaction could establish excited levels upto 3951 keV ( F r = 16 +) based on 7"rhjl/2 ® vh11/2 configuration. Only two other sidebands, one probably based on [413] 35+ ® vhll/2 configuration and the other a AI = 2 band structure having the j+
suggested configuration of 7rh11/2 ® v[400] ~ at low frequency were also populated. It was also observed [ 1 ] that at a frequency of heo ,~ 0.31 MeV the latter band is crossed by a band based on the favoured signature of the 7"rhj1/2 ® ~'i13/2 configuration with an accompanying gain in alignment ,-~6h. However, calculations within the frame work of the cranked shell model, for the nuclei in this region, predict various minima in the potential energy surface, depending on which orbitals are occupied. At higher rotational frequencies, total routhian surface (TRS) calculation predict the existence of highly deformed (/3 ~ 0.3) and triaxial doubly decoupled bands based on the vi13/2 , ~'h9/2, u f7~2 orbitals. Recent experimental studies on the other odd-odd systems in this region and N = 77 isotones in particular [2,3], have confirmed the presence of several such bands. It was, therefore, felt that a more detailed study should be carried out for 138pm with a relatively larger detector array and preferably with a different kind of reaction. ii) All these experimental findings have created an opportunity for testing the predictions of different theoretical models. We have initiated a project to study, in a systematic way, the level properties (energies and transition probabilities) of odd-odd nuclei in this mass region within the framework of a model wherein two quasiparticles (a proton and a neutron) are coupled to an axially symmetric rotor core through coriolis interac-
U. Datta Pramanik et aL/Nuclear Physics A 632 (1998) 307-322
309
tion. Detailed results of such study in the case of positive parity yrast band structure arising from ¢rhlj/2 ® uhll/2 configuration in 128'13°'132'134La [4], 132'134'136'138pr [5] and 136'138pm [6] have been published. In the case of 132'134La [4] (N = 75,77) our calculation favoured an oblate shape and a change in shape was noted as one moved from N = 73 (i.e. 13°La which was predicted to be prolate). For 134'136pr a reasonably good agreement could be obtained by assuming a prolate deformation. The comparison between the experimental and theoretical results for the other N = 75, 77 isotones viz., 136'138pm suggested [6] a prolate shape for the positive parity yrast band in J36pm. However, for 138pm a meaningful comparison could not be carried as it was not possible to estimate the experimental branching ratios and the B(MI)/B(E2) values for most of the states because of the presence of several unresolved doublets in the previous work [ 1]. A more extensive and accurate measurement of the y-ray intensities was felt necessary to arrive at any meaningful conclusion in this regard.
2. Experimental methods and results High spin states of 138pm were populated through l lSIn (28Si, 2p3n) reaction at a beam energy of 145 MeV obtained from 15UD Pelletron Accelerator at Nuclear Science Centre (NSC), New Delhi. The target (,-~800 /zg/cm 2 thick) was prepared by evaporating natural Indium (having 97% llSIn and 3% ll3In) in ~ 1 0 m g / c m 2 gold foil, acting as a backing. The beam energy was fixed through a preliminary study of the excitation function. In this target-projectile combination p4n, p3n and 4n channels were found to be the other dominant ones leading to 138'139Sm and 139Eu respectively. Contributions from 135Nd and 136pm were also observed. The presence of these competing channels introduced complexity in the analysis of the y-ray spectra, owing to the presence of overlapping y-rays. However, the analysis could be carried out satisfactorily with the help of recently published data on these nuclei [7-11']. The y - y coincidence data were collected with a multiple detector array consisting of twelve compton-suppressed HPGe detectors along with fourteen BGO detectors serving as a multiplicity filter to reduce the radioactive background. The detectors were arranged in three groups, each consisting of lour detectors placed at 45 °, 99 ° and 153 ° with respect to the beam direction. The details of the experimental setup and data acquisition system can be found in Ref. [ 12]. A total of 130 million events corresponding to two or higher fold coincidences in HPGe detectors was recorded in List mode. Each coincidence event was qualified with the condition that at least two BGO detectors of the multiplicity filter should fire. The pulse height of each detector was gain matched to 0.5 keV/channel and the y - y coincidence data were sorted out into a 4096 × 4096 total E~-E7 matrix. The energy spectra gated by the y-rays of interest were generated from this matrix. Fig. 1 shows the coincidence spectra with gates on a few y-rays of importance. The multipolarities of the observed yrays were determined through the directional correlation (DCO) ratios. For this purpose a separate 4096 × 4096 matrix was generated with the events recorded at 99 ° along one axis and those recorded at 153 ° along other axis. The DCO ratio was determined as
U. Datta Pramanik et aL/Nuclear Physics A 632 (1998) 307-322
310
Table 1 Energies, intensities, DCO ratios of the y-rays of 138pm populated in the present work Energy a
Intensity
(keV)
DCO
Nature of the
Assignment
ratios
gating transition
1;---*I 7
Band
9 + --* 8 + 8-4--*7 -
1 4
8---*76-458+--,7 6----*614- ~ (13-) (9-) 4 (8-) 14- ~ 13( 1 0 - ) --, ( 9 - ) 1 5 - 4 14(13-) 4 (12-) 7 - ---~ 6 14- ~ 1316- ---* 1513- ~ 11 + 11 + -'~ 10+ 7 - --~ 7 10 + ~ 9 +
4 I 1 2,1 3 4 3 4 3 3 I 2a,2b 3 2,2b I 2,1 1
120.6 132.1 148.4 150.0 173.6 177.4 195.6 227.3 231.1 236.5 241.3
29.1(16) 8.9(5) 4.9(3) 53.5(27) 100 5.8(4) 3.5(3) 21.1(8) 9.5(7) 16.5(6) 10.7(5)
0.83(5) 0.96(15) 0.96(14) 0.91(7) 0.95(7) 0.85(10) 1.52(37) 1.08(13) 0.51(12) 0.86(12) 0.73(11)
D D D D D Q D D D D D
260.8 276 288.0 337 349.5 352.2 356.9 372.5 c 382.6 391.6 392.3 c 396.2 398.8
77.2(26)
0.97(4)
D
1.06(9)
D
0.95(1) 1.10(25) 0.72(5)
D D D
0.60(13)
D
17- ~ 1613 + ----, 12+
3 I
15.1(7) 16.2(8)
0.89(12) 0.49(14)
D D
401.9 409.4 c 410.6 426.2 435.4
23.7(9)
2.05(23)
D
( 1 1 - ) ---* ( 1 0 - ) (12-) 4 (ll-) 1 8 - 4 179-4--,7 -
4 4 3 2
25.4(12) b 6.7(5) 15.0(9)
1.00(11) 0.69(38) 0.40(13)
D D Q
7-459-~87-4614- 4 ( 1 2 - )
! 3 2 3 4
2.5(4) 3.4(3) b
0.55(15)
D
0.32
D
1.57(31) 0.95(33) 0.67(9)
D D D
440.8 c 451.0 452 459.6 465.5 468.2 474.4 477.0 486 494.5 508.8 c 516.8
1.7(3) < 1.0 24.8( 11 ) 3.3(4) 11.9(7) <1.0 3.1(5) 4.2(6) 2.6(3)
15 + 119138II12 + 17 + (19-)
---' 14+ ~ 11 + ~ 9+ 4 12---* 6 ---* 10--~ I1 + ~ 16 + ~ 18-
(20-) ~
(19-)
I 2,1 2,1 3 3,1 3 I I 3 3
U. Datta Pramanik et aL/Nuclear Physics A 632 (1998) 307-322
311
Table 1 - - continued Energy a
Intensity
(keV)
DCO
Nature o f the
ratios
gating transition
518.6 534 544.9 545.6 551.5 ~ 554.6
11.6(8) 2.3(3) 3.9(5) 11.6(8)
1.21(34) 0.89(10)
Q D
1.10(14)
D
576.3 584 596.4 598.5 610.6 618.3 633.6 651.0 684.0
6.6(8) 13.4(10) 12.4(9) 3.4(7) 5.0(6) 4.8(6) 8.6(6) h
1.20(24) 0.93(9) 0.65(7) 1.23(38)
D Q Q D
686.0 c 696 698.4 699.4 706.3 726.6 764.9 782.2 800.8 808.7 c 813.6 825.2 826.7 85O 851.7 861.7 869.1 895 932.6 937.6 938.8 943 c 948 c 954.7 974.5 983.7 995.2 1010.4 1013.0
Assignment
IY---~I ~ t
f
3.5(5)
~1.0 33.4(15) b 12.1(7) 6.5(12) 14.1(11) 2.4(5) <1.0 4.3(6) 9.7(8) 9.2(3) b 3.9(6) 6.7(7) 11.2(10) ~1.0(4) 7.1(5) 6.9(5) 4.5(3) 3.7(5) 7.0(6) 9.1(7) 6.7(8) 2.6(5) 3.3(6) 1.8(6) 2.7(8)
(19 + ) ---, 18 + 13 + ---, 11 + 14 + ~ 13+ ( 1 0 - ) --~ 10 + 19 + --~ 18 + 16+ --~ 15 + 18 + --~ 17 ~11 + - + 1 1 14- ~ 1212- ~ 11(8-) -~89-4--*7 (15 + ) --, 13 +
1.62(13)
D
1.90(18) 2.06(26) 2.75(9)
D D D
2.1(10) 1.3(3) 2.27(30)
D D D
0.97(19) 1.07(10) 1.70(10)
Q D D
1.7(4) 1.80(14) 1.37(40)
D D D
1.07(25) 2.5(12)
D D
1.71(70)
D
14- ~ 12II- --.91 6 - --* 1 4 I1 + ~ 9 + 18 + ~ 16 + 10---+81 4 - ---* 13 + 1 1 - - - - * 10 +
Band 4 I 2b 1 3,1 5 1 I 2b 2a 2a 4,3 3,1 4 2b 3 2 2a I 5, 1 3 3,1 2, I
11(8-) 12 + (17 + ) 1820 + 13 + 21 + 191314 + (7-)
--*9--+7---* 10 ~ ~ (15 + ) ~ 16~ 19 + ----, II ~ ~ 20 + ~ 17~ I1~ 12 + 46-
3 4,1 I 2b 2a 5 I 5 3 2 1 4
(7-) 131215 + (13-) (20-) (12-)
---~ 6 ~ 11~ 10~ 13 + --, I 1 ~ 18--, ( 1 0 - )
4 3 3 I 3 3
U. Datta Pramanik et al./Nuclear Physics A 632 (1998) 307-322
312 Table 1 - - continued Energy a
Intensity
(keV) 1025.9
DCO
Nature of the
ratios
gating transition
2.6(5)
1.92(50)
Assignment
l~l ---+ If~
D
Band
16 + ---* 14 +
1
17 + ---* 15 + 18 + --* 16 +
I I
1072
2 0 - --* 1 8 -
2a
1118
( 1 9 + ) ---* 17 +
I
1063 1070
a The transition energies are accurate to 4-0.1 keV. Energies given as integers are accurate to 4-1 keV. h Total intensity of the doublet. c y-rays, which we strongly feel belong to J38pm but could not be placed in the proposed level scheme (Fig. 1 ).
1200 X3
1000
~
698 keV Gate
r~
800 600 400 200
1600
~
x3
o -
1200 800
~ ~
~
241+383keV Gate
,o
~
400
"
3000 2500 -
2000 1500
-
1000
-
~ -
t-- ,~ e~ea
~,
x3
236+227+396keV Gate
:
_
~
,~
~
,~
~_
~
oo
00-
oo
l 200
400
600 Energy (keV)
800
1000
1200
Fig. 1. Selected y - y coincidence spectra for the three bands of 138pm, obtained by setting gates on the transitions: ( i ) 698 keV for the band 2, 2a and 2b, (ii) 241 + 383 keV for band 3 and (iii) 227 + 236 + 396 keV for band 4. The transitions of interest are labelled by their energies in keV.
R D C O (gq) =
I (3't at 153 ° with ~2 at 99 °) I (3'1 at 99 ° with "Y2 at 153 °) "
The gating transition ~'2 was, as far as possible, the preceding or succeeding the transition of interest. Whenever possible different gating transitions were used and the consistency of the assignments was checked. The multipolarities of a few of the yrays could not be determined conclusively owing to their poor statistics in the DCO
U. Datta Pramanik et al./Nuclear Physics A 632 (1998) 307-322 2b
2
2a
1
313
3
5
4
21 - - V
q-
20
20"
W-Lr. . . . . . ~. . . . . . . .
_1072
IEI*
+
16
+
.
, 6"
/
13 684
14-
.2
15
727
0' I
~k--
J &
16i
'
IJ.- 2--"*~--
~o~3
,2/
02
~177
4eO
~
2
13
e51 K
-
519
9* 7-
/
\
,
12 I
(.-)"F
~
,
T"
(g')
" r t °°
roe ....
6-
~
~g5
I 7-
18
÷ 1~ 782
n--./r.~."
is0 Prn (20")
862
~
e- f
I
,/"
825
- -
|
4[1
Fig. 2. The proposed level scheme o f 13Spm deduced from the present work. The transitions which can only be tentatively placed are indicated by dash lines.
gates, but their presence and intensities in the multiple gates or in the summed gated spectra of the same band indicated that they belong to the relevant bands. The energies, relative intensities and DCO ratios of the y-rays and the assigned spins and parities of the relevant levels of 138pm are given in Table 1. Because of the presence of a few overlapping y-rays arising out of the competing channels, the relative intensities have been determined from the coincidence spectra with gates on uncontaminated y-rays. It should also be noted that in Table 1 we report only one of the obtained DCO ratios for each transition and also specify the type of gating. The level scheme of 138pm has been constructed from the y - y coincidence data, the y-ray intensities and the multipolarities of the y-rays, inferred from the DCO ratio measurements. A total of 76 y-transitions has been placed in the level scheme shown in Fig. 2. Seven distinct band configurations including the positive parity yrast structure have been established. We now briefly discuss each of these bands separately below. Band 1, which is the yrast levels of 13Spm (band 1), is built on the T~/2 = 21 ns state and its spin parity is assumed to be 8 + following the arguments given in the earlier work [1]. The data of the present work allow this yrast band to be extended upto a spin of 19 + and upto an excitation energy of 5455 keV. A characteristic feature of this structure is the stronger population of odd-spin states. The crossover transitions for the favoured signature cascade are, therefore, of higher intensity. Band 2, which is a negative parity band and was also reported by Beausang et al. [ 11. is found to be connected with the yrast band by many transitions. The spin-parity assignments as proposed in the present work differ from that suggested by Beausang et al., as the DCO ratio for the 435 keV y-rays clearly indicates that it is a A I = 1 transition. In the earlier work no angular distribution coefficients were presented for this
314
U. Datta Pramanik et al./Nuclear Physicx A 632 (1998) 307-322
y-ray because of the fact that it was unresolved from the transitions in other nuclei. The present spin-parity assignments are also consistent with nature of the transitions, as suggested by the DCO ratios, for the linking transitions to the yrast band. Above the 11- state at 1863 keV excitation, this band bifurcates into two quite similar band structures (band 2a and 2b). Band 2a, to which a negative parity was assigned by Beausang et al. [1], has not only been confirmed but also has been extended in the present work. However, the presently proposed spin-parities differ from that suggested by the earlier work in view of (i) the different nature of the 435 keV y-rays, observed in the present work as mentioned earlier and (ii) the DCO ratio data strongly indicate that the 611 keV y-ray is of A1 = 1 type transition while in the earlier work it was assumed to be of quadrupole character. The band 2b, to which we have assigned a positive parity, is a newly suggested one, though a preliminary indication of the same could be seen in the earlier work. It should be mentioned that the placements of the 545 keV and the 596 keV y-rays have been altered to satisfy the intensity balance and also by considering the fact that they are of stretched quadrupole and dipole character, respectively. The assignment of spin-parity values for the band 2a and 2b is strongly dependent on the assumption of a MI (AI = 1) and an E1 (AI = 0) nature for the 611 and 596 keV y-rays, respectively. However, as will be presented in the next section, these conjectures and assignments are well supported by the theoretical predictions. Band 3 is another negative parity side band proposed by Beausang et al. [ 1 ], having the suggested configuration of ¢r[413]~5+ ® t.'hll/2. It has been possible to extend this band upto the spin state of I T = 2 0 - having the excitation energy of 5376 keV. Two very weak crossover transitions have been observed in the upper portion of the band and are shown as dashed. In the work of Beasung et al., the spin-parity assignment was on the basis of the systematics and observation of similar bands in the neighbouring doubly odd ~36pm and 134pr nuclei. The character of the 468 and 634 keV interband transitions was assumed by them to be stretched quadrupoles due to the non-availability of angular distribution data. In the present work the DCO ratio measurements confirm this assignment for the 468 keV y-ray but the corresponding quantity for the 634 keV yray cannot be determined convincingly because of weak statistics. This firmly establishes the spin-parity of the low lying portion of this band. The nature of other transitions in this structure viz., the dipole character of the 426 keV and other transitions above the spin of 13- and the quadrupole character of the 765, 813 and 974 keV transitions, are also established through the present DCO measurement. In the work of Beausang et al. [ 1] no connection between these two sequence of stretched E2 transitions was found. However, in the present work we have observed a few weak linking transitions viz., the 465 and 475 keV y-rays, between the two bands. The present work also significantly modifies the scheme proposed by Beausang et al. in the following respect. In their work a very weak 783 keV connecting transition, between the high spin portion of this side band and the yrast band, was very tentatively proposed. In the present work in addition to this, a number of other decay modes from the 14- state of this band are observed, which make the lower portion of the structure quite complicated. Of these, a discussion on the placement of the 554 keV y-ray will be done shortly. With these transitions
U. Datta Pramanik et al./Nuclear Physics A 632 (1998) 307-322
315
it has been possible to establish the connection between in-band dipole transitions to the lower members of the yrast band. These linking transitions were not observed in the earlier work [ 1 ], though definite indication of some relationship between the two configurations (i.e. lower part of the yrast band and the upper part of band 3) was reported. Band 4 is observed for the first time in this nucleus. The upper part of it mainly contains dipole transitions, similar to that in the case of band 3. But unlike the band 3 it is not strongly connected to the positive parity yrast configuration, though definile indications of the 227 and 236 keV y-rays are found in the gated spectra of 173 and 120 keV y-rays and vice versa. However, it has not been possible to identify the linking transitions. It can be noted that this configuration is mainly connected to states having negative parity viz., I ~ = 8 - state of band 3 and I ~ = 7 - level of the ground band through the 618 keV and 825 keV y-rays, respectively. The characters of the 132 and 148 keV transitions are dipole in nature. This is also found to be the case for the 938 and 955 keV transitions, as placed here. They can be either M1 or E1 and in absence of any other supporting evidences, it is difficult to assign any definite spin-parities to the levels of this band. However, a tentative scheme is proposed, mainly based on the observed nature of the above mentioned transitions and the observed linking to the negative parity states. It may be further noted that no spin-parity values could be suggested lbr the upper part of the band. This is because the multipolarities of the y-rays involved (435, 518 and 651 keV), could not be determined because of poor statistics in the related gated spectra. Finally we would like to point out that a cascade of three y-rays (viz., 554.7, 726.7 and 861.7 keV), as noted by the earlier worker [1 ], has also been observed by us. It was further noted [1] that intensities of these y-rays were larger than the intensities of the transitions of the yrast band into which they feed but the linking transitions could not be observed. Because of these, no proper placements of these y-rays could be suggested in the previous work. We, however, differ with these observations to a certain extent and these are as follows. We have noted that the intensity patterns of the y-rays of the yrast band in the gated spectra with gates on the above three yrays, are not quite similar. With the gates on 727 and 862 keV y-rays, the spectra are nearly identical but in the coincidence spectra with 555 keV as gate, there is a sudden increase in the intensities of the y-rays arising from the 10 + state (and below it) of the yrast band. Considering the energy and the intensity balance, a connecting transition of 555 keV between the band 3 and the 10 + state has, therefore, been proposed. This is also in accordance with the coincidence spectra with gates on the dipole transitions in band 3. DCO ratio measurements of these three y-rays suggest that the 555 and 862 keV are of AI = 1 type whereas the 727 keV is of AI = 2 nature. After taking into consideration the other information from different coincidence spectra, we propose a band (5) consisting of 555 and 861 keV y-rays and it is linked to the 16 + state of the yrast structure through the 727 keV transition. In this band we have also tentatively included a 869 keV transition primarily because of the facts that we have observed (i) a 869 keV y-ray in the coincidence spectra with gates on 477 and 869 keV y-rays of
U. Datta Pramanik et al./Nuclear
316
>~->. :- .......
Physics A
632 (1998) 307-322
. , : . = ........
t
1.5 i
1.5
~//~
.....
//
"
~-~
/-
~.
1.0 1.0
)--~
"
// 0.5 0.0
i
'\
/
!i
-0.5
oo
p =o.~ ~t=o \ \ ~
/
- . .
13z=02y= 2(Y'
o, 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
o.o
0.1
0.2
h(~ (MeV)
1.5
~ 1.o= ~ - ~ , ~ > . % . L
"\
-% - .
~
~
0.3 0.4 0.5 11¢00 4 e V )
...... "
1.0 ~
\
0.6
0.7
~.
0.8
/
"~ ~.:~
\ . \3<%"
.o.°!:............................ 0.0
0.1
0.2
0.3 0.4 0.5 li~ (MeV)
0.6
0.7
0.8
0.0
0.1
0.2
0.3
04
0.5
0.6
0.7
0.8
ho~(MeV)
Fig. 3. Quasiparticle routhian diagrams (a) for protons and (b) neutrons. The deformation parameters used in the calculation are indicated in the figures. Parity and signature of the states are as follows: solid: ( + , + 1 / 2 ) ; dotted: ( + , - 1 / 2 ) ; dashed-dotted: ( - , + 1 / 2 ) ; d a s h e d : ( - , - 1 / 2 ) . The relevant lowest neutron orbitals are labelled with the asymptotic Nilsson quantum numbers.
the yrast band, and (ii) the intensity of the 869 keV y-ray in the 555 keV and 727 keV gated spectra is much larger than that expected from the single 869 keV transition in the yrast cascade.
3. Discussion For 138pm the neutron Fermi surface lies in the upper part of the hll/2 shell while for the protons the Fermi surface lies in the lower part of the same shell. Because of this, valence quasineutron drives the nucleus towards 3/ ~ - 6 0 ° and the valence quasiproton tries to induce a prolate shape with 9' ~ 0 ° or slightly negative. The polarising effects of these valence quasiparticles can be well studied in the framework of Cranking Shell Model (CSM). Quite a detailed picture of some of the aspects of different band structures in 138pm, using the same formalism, had been already put forward [ 1]. However, for the sake of completeness and proper understanding, we also present the salient results of our calculation using CSM. We have carried out the calculation with the deformation parameters /32 = 0.2 and /34 = 0.0 (following the systematics in the neighbouring odd-odd nuclei) and for different 9,-deformations. The routhians for proton and neutron are shown in Fig. 3.
U. Datta Pramanik et al./Nuclear Physics A 632 (1998) 307-322
317
14
12
F]
A.
11
10
8
I
6
z
©
x
~
~
4
-3 ! 0.20
i 0.25
0.30
0.35
0.40
0.45
11¢o(MeV)
I
~
0.50
o.ss
2 0.0
i
i
i
E
i
0.1
0.2
0.3
0.4
0.5
0.6
he0 (MeV)
Fig. 4. (a) Experimental routhians and (b) alignments for the observed bands in 138pro.The two signatures of the yrast ~rht 1/2 ® vh II/2 band ( 1) are indicated by the open (favoured) and closed (unfavoured) circles. Similarly the favoured and unfavoured signatures of the ~'14131 5 ® Uhll/2 band (3) are indicated by the closed and open triangles, respectively. The filled square indicates the ~rhlU2 ® ~i13/2 band (2a) while the open square is for the ~rhll/2 ® u[530] ½- band (2b). The experimental routhians and alignments (e' and i) of the bands in 138pm, obtained through the standard procedure prescribed by Bengtsson and Frauendorf [ 13 ], are shown in Figs. 4a and 4b, respectively, where they are plotted as function of rotational frequency hw. In these calculations the value of K ( = 52~. ± ~ , ) was chosen in accordance with Gallagher-Moszkowski rule [ 14]. The angular momentum component of the reference configuration lx.ref is calculated with the following Harris parameters [ 15]: 30 = 12.5h 2 MeV -I and ~j = 16h 4 MeV -3. These set of parameters had been used for 136Nd [ 16], which can be presumed to be the core of 138pm.
3.1. B a n d 1
Band I (yrast) is assumed, following the earlier work [1] and systematics observed in this mass region, to be based on 7rhj j / 2 ® v h l i/2 configuration with band head 1 ~" = 8 ~, arising from the perpendicular coupling between the valence proton and neutron. This yrast cascade is found to possess a relatively larger signature splitting ( ~ 8 5 keV) (compared to that observed in the isotone J36pr [ 3 ] ) which remains constant upto tile highest states which have been established definitely. The corresponding alignment, on the other hand, shows a rather smooth increasing trend from ~ 5 . 7 h to ~ 7 . 0 h upto the rotational frequency of ~0.5 MeV. Energy difference between two signature partners for the proton orbital (7"r[541 ] ~) is much larger than that for the neutron orbital. Keeping in mind the experimentally observed signature splitting, the yrast state can be seen to be based on favoured signature component of the proton state ( a t, = - l ) and separated by the moderate neutron signature splitting. Another positive parity semidecoupled band
318
U. Datta Pramanik et al. /Nuclear Physics A 632 (1998) 307-322 90 0
80 70 50
Z~ 50 40
30 20 10
I 0.25
0.30
1 0.35
I
I
I
0.40
0.45
0.50
0.55
ho~ (MeV) Fig. 5. Dynamical moments of inertia of ~38pm. Symbols have the same meaning as in Fig. 4.
arising from the coupling of the unfavoured signature state of the proton with VhlJ/2 is also expected but at a much higher excitation energy. This has not been observed in the present work. It can be noted that the low frequency breaking of the first pair of h~]/2 particles is blocked. One can, however, try to look for the alignment of the second and third hlz/2 proton and neutron. In the case of the isotone 136pr, it was observed by Petrache et al. [ 3] that the experimentally extracted signature splitting disappeared at high spins for this band and this was interpreted in terms of (h]l/2)2 alignment for the proton. In the present case the experimentally measured signature splitting decreases from Ae' ~ 85 keV at low spins to ~ 5 0 keV in the high spin region, if the states tentatively proposed are considered. The corresponding alignment plot shows an increase in the value to about 9.5h at a frequency ~0.53 MeV. The dynamical moment of inertia plot (Fig. 5) also shows a sudden increase at a rotational frequency of hw ~ 0.5 MeV. In the light of the CSM calculation, the BC and bc crossing frequencies are at 0.52 and 0.55 MeV with a quite large negative y-value ( ~ - 20 °) and the predicted signature splitting is also found to be in agreement with the experimental value. However, as has been pointed out by Petrache et al. [2,3] in their work o n 134'136pr, one has to be careful while assigning a definite y-deformation for the following reasons: (i) a static y-deformation extracted from the TRS calculation, in the case of nuclei with pronounced softness, may involve large uncertainties and (ii) calculation on the transition probabilities within the yrast band, based on two-particle plus triaxial rotor model fails to reproduce the experimental trend while the axial model calculation gives a better agreement. As pointed out in the introduction, we have also carried out a detailed calculation of the energies and transition probabilities of the states in this yrast band [6] within the framework of a Particle Rotor Model (PRM) wherein two quasiparticles (a proton and a neutron) are coupled to axially symmetric rotor core through Coriolis interaction. Further details of the model, the choice of parameters and the calculation can be found in Refs. [4-6]. The theoretical branching ratios and B ( M I ) / B ( E 2 ) values [6] have been compared
U. Datta Pramanik et al./Nuclear Physics A 632 (1998) 307-322
319
Table 2 Calculated and experimental decay modes of the ~'hll/2 ® uh~l/2 yrast band in 138pro Branching ratio
lff
17
Expt. Ia
10+ II~ 12 + 13+ I 14+ f 15+ i 16 ~ f 17 ~ ~
9 ~8+ 10+ 9 +. I 1+ 10+ 12+ 11+ 13+ 12 + 14+ 13+ 15 + 14 + 16 ~15+
60.6 39.4 60.0 40.0
B(MI ) / B ( E 2 ) in /.tn2/ (eb) 2
Theory
Expt.
II b
Ic
II d
llI e
69.0 31.0 61.8 38.2 30.0 70.0 62.0 38.0 43.0 57.0 47.4 52.6
95.4 4.6 65.8 34.2 64.6 35.4 41.1 58.9 55.7 44.3 32.9 67.1 47.5 52.5 29.6 70.4
83.2 16.8 8.1 91.9 44.2 55.8 3.7 96.3 40.0 60.0 1.4 98.6 34.3 65.7 1.0 99.0
91.4 8.6 60.3 39.7 50.5 49.5 39.2 60.8 36.1 63.9 31.5 68.5 23.1 76.9 28.8 71.2
Ia
Theory II b
Ic
II d
I11c
7.8
1.9
4.0
4.4
6.4
5.4
0.4
4.3
3.7
4.0
4.3
2.0
2.4
2.4
3.9
0.2
3.6
5.0
3.7
2.0
1,7
5.7
3.5
0.1
3.4
3.7
3.6
2.1
1.2
3.4
0.4
3.4
a Ref. I I I .
~' Present work. The branching ratios have been calculated from proper gates. c Calculation with prolate deformation ("normar" zt's). d Calculation with prolate deformation (modified An). e Calculation with oblate deformation (modified Ap ). ~ Decay properties of these states can not be calculated from Ref. 111 as the intensities of the transitions involved can not be estimated due to the presence of close lying doublets and contamination lines. g Only the theoretical estimates for the decay from this state is given as the intensities of the y-rays involve cannot be evaluated properly. w i t h t h e p r e s e n t e x p e r i m e n t a l r e s u l t s a n d are g i v e n in T a b l e 2. A s it h a s b e e n p o i n t e d o u t e a r l i e r , t h e r e a r e a f e w y - r a y s in t h e y r a s t b a n d w h i c h h a v e a l s o b e e n p l a c e d e l s e w h e r e in t h e level s c h e m e . T h e r e f o r e , f o r this p a r t o f t h e w o r k , t h e i n t e n s i t i e s o f t h e c o r r e s p o n d i n g y - r a y s o b t a i n e d f r o m t h e p r o p e r g a t e d s p e c t r a , h a v e b e e n u t i l i s e d . It c a n b e s e e n f r o m t h e T a b l e 2 that a g r e e m e n t o b t a i n e d in t h e c a s e o f p r o l a t e d e f o r m a t i o n is quite satisfactory.
3.2. B a n d 2, 2a, 2b B a n d 2 is p o s s i b l y b a s e d o n t h e 7 r h l l / 2 ® t , [ 4 0 0 ]
1+ ~ [ 1 ]. B a n d 2 a ( 2 b ) is a c a s c a d e o f
4 (3) quadrupole transitions and can be the favoured component of a doubly decoupled c o n f i g u r a t i o n . T h e u n f a v o u r e d c o m p o n e n t , in b o t h t h e c a s e s , are p r o b a b l y l y i n g t o o h i g h w i t h r e s p e c t to t h e y r a s t line to a l l o w t h e i r o b s e r v a t i o n . T h i s l a r g e s p l i t t i n g m a y b e i n d i c a t i v e o f t h e f a c t t h a t t h e v a l e n c e p r o t o n a n d n e u t r o n a r e b o t h o c c u p y i n g Iow-.O o r b i t a l s in t h e s e c a s e s . S i m i l a r AI = 2 b a n d h a d b e e n o b s e r v e d in t h e n e i g h b o u r i n g o d d -
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odd nuclei and a number of suggestions had been put forward regarding the configuration of these states. In 13°La [ 17] and 136pm [11], for example, this was presumed to be due to the 7rhll/2 ® vii3~2 configuration and associated with high deformation. But in 134pr [2] this was assigned a 7rhll/2 ® v[530] ~1 - structure. In the work of Petrache et al. [3] on 136pr, band based on both the above mentioned configurations were reported. In the present work also it seems that we have been able to observe both these two types of band. Band 2a and 2b also show (Fig. 4b) a gain of aligned angular momentum of Ai ~5.0h and 4.4h respectively, at similar low frequency of h w ~ 0.31 MeV. After this, the experimental alignments remain constant upto the highest observed frequency viz., 0.53h and 0.42h MeV, respectively. As suggested earlier [ 1 ], the negative parity band (2a) is explained by the occupation of vii3~2[660] ~1+ intruder orbital, which comes down very rapidly in energy with increasing rotational frequency. The predicted gain in alignment is Ai ~ 5.8h at the crossing frequency of ha) ~ 0.46 MeV for y = - 5 °. The quasiparticle routhian diagram (Fig. 3; /~2 ---- 0.2 and y ~ - 5 °) also shows that at h w ~ 0.34 MeV (the v[530]½- and v[541]~l - orbitals, of mixed f7/2 and h9/2 parentage, are also introducing from the higher oscillator shell (N = 5). One, therefore, also expects to observe doubly decoupled bands based on these orbitals. The a = +~t neutron signature, corresponding to the v[541 ] ~- orbital is found to be slightly higher in energy than the a = - g 1 of the v[530] ~-. A sequence with odd (even) spins is expected for the v[530]½-(~,[541] l - ) configuration. Based on our spin assignment we propose that the band 2b is the favoured component of the ,'rrhll/2 ® t.'[530]gl configuration. The predicted gain in alignment is Ai = 3.0h at the theoretical crossing frequency. 3.3. B a n d 3
As pointed out earlier in the text this is a negative parity structure which at the low frequency consists of two sequences of stretched E2 transitions, one between the favoured and the other between the unfavoured states. In the present work very weak linking transitions between the two signatures have been observed. At the higher frequency, these two stretched E2 bands merge into a single band having transitions with mixed E2/MI ( z l l = 1) nature. This band shows (Fig. 4b) large alignment (~-,7h) around a rotational frequency of ho9 ~ 0.3 MeV. As suggested by Beausang et al. [ 1 ], this band is probably based on 7rg7/21413]~5 + ®~'hjl/21514] 9 - - configuration. Unlike the yrast band, here the A B crossing is not blocked. In the CSM calculation presented by Beausang et al. [ 1] a rather large negative y-deformation ( - 4 0 °) were suggested for obtaining the experimentally observed A B crossing frequency (~0.37h) and the theoretical value was ~0.42 MeV. In the present calculation we find that without any y-deformation included, the crossing frequency is 0.30 MeV which is in quite good agreement with our experimental results. Furthermore since large negative y-deformation will induce large signature splitting and no such phenomenon has been observed in this band in 138pro,
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in either of the experiments, we feel that there is no need to include y-deformation for this band.
3.4. Band 4 It can be based on the 7r[411 ] ~3 + ® uhll/2 configuration, which would generate negative parity states. The ~[411 ] ~3+ , of mixed d5/2 and g7/2 parentage, has a predominant contribution from d5/2 orbital and is quite close to the Fermi level.
3.5. Band 5 It is difficult to suggest any configuration for this structure. One possibility is that this structure is based on a multiparticle configuration involving intruder orbitals from upper shell. The high spin and excitation energy observed will be consistent with this interpretation.
4. Conclusion The high-spin structure of the doubly odd nucleus 138pm has been studied. Several rotational bands have been established in this nucleus and the present result is in agreement, to a quite extent, with the earlier report [ 1] on the three primary bands. However, it has been possible to extend all these three bands upto higher spins and excitation. The AI = 2 band, based on the ~hll/2 ® ~'[400]½ + has been observed to bifurcate into two structures at a frequency hw ~ 0.31 MeV. One of the structures which was reported in the earlier work [ 1 ] and also is observed in the present work, can be explained in terms of the change in neutron configuration to the favoured signature of the ~i13/2. The second one established for the first time in the present experiment, is predicted to arise from a similar change to the 9[530]½- orbital with mixed ]19/2 and f5/2 parentage. A new negative parity band consisting predominantly of transitions with dipole nature has been observed.
Acknowledgements The authors wish to thank Dr. S.K. Dutta, Dr. A.K. Sinha and all the staff members of the Pelletron centre at Nuclear Science Centre, New Delhi for their cooperation during the experiment. A.K. Singh wants to thank U.G.C., New Delhi for financial assistance.
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