Signature inversion in semi-decoupled bands: Residual interaction between h9/2 protons and i13/2 neutrons

EISEVIER 7 August 1997 Physics Letters B 406 (1997) 193-199 PHYSICS LETTERS B Signature inversion in semi-decoupled bands: residual interaction between h9,~ protons and i1312 neutrons R.A. Bark a,b, J.M. Espino”, W. Reviol d, PB. Semmes e, H. Carlsson b, I.G. Bearden a, G.B. Hagemann ‘, H.J. Jensen a, I. Ragnarsson f, L.L. Riedinger d, H. Ryde b, P.O. Tj@m g a Niels Bohr- Institute, University of Copenhagen, Tandem Accelerator Laboratory, Roskilde, Denmark b Depurtment of Physics, University of Lund, Sweden ’ Department of Physics, University of Sevilla, E-41 080 Sevilla, Spain d Department of’ Physics and Astronomy, University of Tennessee, Knoxville, TN 37996-1200, USA ’ Plzysics Department, Box 5051, Temnessee Technological University, Cuokville, TN 38505, USA ’ Dept. of MLII~. Physics, Lund Inst. of Techn., RO. Box 118, S-221 00 Lund, Sweden g Department of Physics, Universiry of Oslo, Oslo, Norway Received 8 April 1997 Editor: R.H. Siemssen Abstract Semi-decoupled bands based on the z-1x91~ @ z&lz configuration are observed in 16*Trn ‘@Tm and ‘74Ta. Spins assigned to these bands imply an inversion of the expected signature splitting, which is interpreted’as being the result of a residual proton-neutron interaction. @ 1997 Elsevier Science B.V. The Cranked Shell Model [ 11, has been successful in describing the crossing of the ground-state rotational band in even-even rare-earth nuclei by a band of aligned ir3,12 neutrons. However, in odd-2 nuclei, this crossing is delayed systematically to higher rotational frequencies, (w,) , when the odd proton occupies the rTTh912( l/2- [ 54 I] ) orbi ta1 [ 21. This has lead to speculation that residual proton-neutron (p-n) interactions may play a role [ 31. Of interest therefore, is the interaction between irs/z neutrons and h9/2 protons. This can be studied in odd-odd nuclei, where one well known manifestation of p-n interactions are Gallagher-Moszkowski (GM) splittings [4]. Another observable is the signature splitting [l] Ae, corresponding to the difference in energy e,, -e,, between routhians of states in a rotational band with signature czf and LY,. The energetically favoured and unfavoured branches of a two-quasiparticle rotational band of an odd-odd nucleus are expected to have signatures, af and a;, given by the proton and neutron angular momenta jP and j,: “f = 4 (_1)h-v + (_1)“4/2 [ 1 ; ‘Y, = (crf + l)mod2 (1) In the A = 130 and 150 mass regions however, residual interactions have been invoked to explain the observation of rotational bands with LY, favoured in energy [ 5-71. Here we present data on three nuclei: 162,16‘?m and ‘74Ta. In each of these nuclei, both signatures of the band based on the rhg/2 @J vi1312 configuration, of- 0370-2693/97/$17.00 @ 1997 Elsevier Science B.V. All rights reserved. PII SO370-2693(97)00676-X 194 R.A. Bark et d/Physics Letters L3 406 (1997) 193-199 “j2Tm (partial) Bond 1 Bond 2 Band 3 Band 4 1*+ Fig. 1. Partial level scheme of n,,Tr541lmA,**b421 n,,2+,4,,,e”5,2+l64z1, n7,2-15U,~v3,2-1521, n7,Tbm,%6,2*16421 le2Trn, as deduced in the present work. Bands are labelled both numerically and configurations. ten called semi-decoupled [ 81, are observed, (for the first time in the case of ‘62,‘64Tm). The rhg/2 @ ~i13/2 band has been assigned in many nuclei of the rareearth region, but firm spin assignments have not been reported. The present work implies new spin assignments which invert the expected signature splitting. It is shown that this is consistent with a residual p-n interaction. The nuclei were populated in the reactions 16’Gd( “E5n) 174Ta, rsoNd( 19F,5n) 164Tm and 130Te (37C1,5n) ‘62Tm at 105, 85 and 166 MeV beam energy, respectively. A combination of experiments was performed, employing both thin (- 1 mg/cm2) and backed targets (- 10 mg/cm* Au backings). The NORDBALL [9] array was equipped with either 20 HpGe detectors, or 18 HpGe and 2 LEP detectors, when unbacked or backed targets, respectively, were employed. Typically, IO9 y - y coincidences were obtained in each case. Further experimental details for the 174Ta experiment are given in [lo], and early results for 164Tm are reported in [ 111. according : to assigned Partial level schemes for the three nuclei are shown in Figs. 1 and 2. In Fig. 1, the yrast band, (Band 4)) of 162Tm, assigned previously [ 12-141 to the configuration K” = 6-; ~712~[523] @ v5/2+[ 6421, is shown. Its bandhead is depopulated by a transition of 163 keV, which Drissi et al [ 131 argued feeds a 24.3 s 5+ isomer, known from P-decay [ 151. In this work, the isomer was assigned to the configuration Kr = 5+; 1~7/2- [ 5231 @ v3/2- [ 5211. We have now observed the band based on this isomer, (Band 3), and tied it to Band 4 near spin 17fi, with transitions of 703,726,742 and 725 keV. DC0 ratios for these transitions are consistent with stretched dipole character. Two near degeneracies between levels of Bands 2 and 3 occur near spins 8ti and 18ti. The transitions linking the two bands near these spins indicate mixing and fix the spins and parity of Band 2. Band 2 is in turn linked to Band 1 by a series of transitions with energies of around 400 keV. DC0 ratios obtained for a number of these transitions are consistent with stretched dipole character. R.A. Bark et al./Physics Letters B 406 (19971193-199 195 Band 1 le4Trn (partial) v4To (partial) Band 2 Bond 1 Bond 2 Fig. 2. Partial level schemes of ‘@Trn and ‘74Ta, as deduced in the present work. Bands 1 and 2 have large signature splittings, requiring that both the odd proton and neutron reside in low- R orbitals or orbitals subject to strong Coriolis effects. Ther1/2-[541],gl/2+[411] and v5/2+[642] orbitals are the only orbitals near the fermi surface that satisfy these criteria. As Band 2 must have positive parity, (due to mixing with Band 3), it is assigned to the configuration 7~1/2+ [ 4111 @I v5/2+[ 6421. Band 1 must therefore have the configuration ~1/2- [541] I% v5/2+[ 6421. Note that the favoured signature of Band 2 was assigned by Drissi et al. [ 131 to the ~1/2- [ 5411 @ u5/2+[ 6421 configuration. However, this is inconsistent with the present assignment of parity. With our assignments, the transitions linking Bands 1 and 2 are stretched El transitions, and the two bands resemble the 1/2+[411] and l/2- [541] bands of the odd-proton neighbours, le3Trn [16] and 165Tm [ 171. In these nuclei, the 1/2+[411] and l/2-[541] bands are also linked by stretched El transitions. Enhanced electric dipole transitions between these bands are a general feature in the rare-earth region [ 181. Bands 1 and 2 in 164Tm are extended to both higher and lower spins compared to the earlier work [ 12,131 (cf Fig. 2a). Their structure is analogous to that of Bands 1 and 2 of t6’Tm. They have similar transition energies and relative excitation energies and are also linked to each other by transitions with DC0 ratios consistent with stretched El character. Tentative dipole transitions of 70 and 110 keV connect Band 2 to the l+ ground state. However, these lines are contaminated by lines from Au X-rays and tgF Coulomb excitation, respectively. Likely spins and configurations, based on this evidence, and comparison with t6*Tm, are shown in Fig. 2a. In Fig. 2b, two bands in ‘74Ta, assigned by Hojman et al. [19] to the KT = 4-; rrl/2-[541] @ v7/2+[633] and K” = 8-; ti/2-[514] @ v7/2+[633] configurations, are shown. These bands are extended to higher spins and are now linked to each other by transitions due to mixing from the near degeneracy of levels at spins 12/i and 13/i. With the observation of two new transitions of 69 and 51 keV, Band 1 is extended to lower spins as well. The band is depopulated promptly, ( < 2 ns) , by a 98 keV transition, but the possibility of further levels in the band, 196 R.A. Bark et d/Physics Letters B 406 (1997) 193-199 separated by energies < 40 keV cannot be ruled out. A 92 keV transition had been assigned [ 191 as an out- of-band transition, depopulating Band 2, but due to the observation of a weak and therefore tentative 226 keV transition in Band 2, it is now placed in-band. An estimate of the expected E2/M1 branching ratio from the lostate implies that the intensity of the 226 keV transition should be just on the detection limit of the experiment. Alternatively, if the 298 keV transition were identified with the decay of the lostate, as in the earlier work, its intensity would be a factor of N 3 higher than expected. The identification of the 92 keV y-ray with the 9- --) 8- transition is also supported by the observation of delayed (ri,, = 250ns [ 191) transitions of 98 and 153 keV, depopulating the S- level. These feed bandheads newly assigned [20] to the Kr = 7+; ~9/2-[514] @~5/2-[512] and K”= 7+; Z-7/2+[404] @ v7/2+[633] configurations. The transitions linking Bands 1 and 2 fix their relative spins. With the new bandhead assignment for Band 2, the spins of the levels of both bands are raised by one unit compared to the previous assignment [ 191. For all three nuclei, the new spin assignments are consistent with the addition of aligned angular momenta from the corresponding one-quasiparticle bands in the neighbouring nuclei, and delayed crossings are observed in all configurations proposed to include an iI neutron. However, a consequence of these spin assignments, for all three nuclei, is that the favoured signature of the n-h9p @ vi13p bands has a = 0 over substantial ranges of spin, while CY~ = 1 is expected according to (1). The signature inversion is illustrated in the sensitive energy-staggering plots of Fig. 3. In the two Tm isotopes, the signature splitting eventually reverts to the normal ordering at high spin, while in 174Ta, the disappearance of signature splitting is due partly, if not wholly, to a bandcrossing (BC) in the (Y = 1 branch. Signature inversions at low spin are common features in other bands of odd-odd nuclei. For example, the configuration Z-III i/z @ ui13,2 is inverted at low spins in a chain of Tb, Ho and Tm nuclei. Several effects are often invoked to explain such observations. These include Coriolis effects [ 21,221 for spins I 5 j, + j,, triaxial shapes [23], and p-n interactions [ 5,241. To investigate such possibilities here, we use the particle-rotor model code of Ref. [5]. The model Hamiltonian includes the rotational energy of 5‘ 160 g 120 N =. 80 y 40 y 0 =‘ 2 -40 z -80 5 -120 w -160 5 160 g 120 N 2 80 =‘ 40 E -t 0 7 -40 -_ w -80 B -120 -160 s‘ 160 & 120 !z 80 2 ‘; 40 = I 0 T -40 = B -80 E -120 -160 _ ‘74Ta 0 exp.a=O - I I -_ttt 0 explcz=l +--- lwTrn y=o” 0 l . l . 0 0 -1 0000 0 0 162Tm 4 6 8 10 12 14 16 18 20 22 24 26 1 P) Fig.3.ThestaggeringfunctionE(I)-1/2[E(I-l)+E(Z+l)], which compares the energy of a level E(I) at spin I with energy of levels above and below it in spin, for the rhg/z CG vi1312 bands in the three nuclei compared with the results of the particle-rotor calculations. the core (which can be either axially symmetric or triaxial), the quasiparticle energies of the odd proton and neutron, and a residual p-n interaction. The Hamiltonian is diagonalized within the space of low lying lquasiproton, 1-quasineutron states; all neutron orbitals originating from the iIs/ subshell and the six lowest proton orbitals with main components from the f7/2 and h9/2 subshells were included. The K, p parameters of the Modified Oscillator Potential were taken from ref [ 251, and a common deformation (~2, ~4) = (0.27,O.OO) was used for all three cases. This deformation is a reasonable average of values calculated using the code Ultimate Cranker [ 261; these same cd- R.A. Bark et al./ Physics Letters B 406 (1997) 193-199 197 culations also predict that the triaxiality parameter y be restricted within a range jy[ < 4’. A Coriolis attenuation factor of 0.80 and a VMI [27] description of the rotational cores were used. The VMI parameters were obtained from an average of the values fitted to the ground bands of the neighbouring 2 f 1, N i 1 even-even nuclei. Energy staggerings, calculated without a residual interaction, are summarized in Fig. 3. These calculations show a favoured signature of cr = 1 (odd spins favoured), in accord with the CSM, and in agreement with the data for ‘62.164Tm above a spin of 2OtL. However, the prominent signature inversion, or change in phase of the staggering, observed experimentally below spin -2OtZ for ‘62,16?m and below spin -26fi for 174 Ta, is not present in these calculations. Furthermore, the inversion cannot be obtained by including triaxiality with y between &lo”; sample triaxial calculations are shown for ‘74Ta (where y > 0 is simulated by interchanging the x and y moments of inertia [28] ). These triaxial calculations also show a favoured signature of LY = 1, in disagreement with the data. Since triaxiality and Coriolis effects alone are insufficient to explain the data, we consider a residual p-n interaction of the form v,” = JiP ( > $ 3 8 (q, - r,) (4 + zl,c7p.(T”) (2) This interaction has been employed [5-71 to describe signature splitting effects in the A = 130 and 150 regions, in connection with rlzi 1,~ @ ~htt/:! and rrhli,z @ vits/z bands. Reasonable values for the parameters uc and ut were found to be uo = -7.2 MeV and ut = -0.80 MeV. The spin-spin strength parameter ut has been estimated from a fit to available GM splittings [ 29,301, and a relative strength of the two terms ~0 : ~11 = 9 : 1 is suggested from an analysis of p-n multiplets in spherical odd-odd nuclei [ 31,321. For the bands considered here, which have wavefunctions of about 65% n-hgp @ z@,3p character, uc and ur can also be estimated directly from the splitting of the spherical n-hg/z@ vi13/2 multiplet in 208Bi [ 331, which leads to values about half as large as cited above. The overall strength of VP, was adjusted to give approximately the correct inversion spin for ‘64Tm, while keeping the 9 : 1 ratio of LIO : L~I fixed; the parameters 5‘ 160 g 120 174Ta -N 80 & -120 u -160 2 600 Y r s‘ 400 a, 2 200 =; =‘ 6 0 Lu R -200 5 g -400 I g -600 600 s g 400 N 5 200 2 -200 w g -400 3 _ -600 I I I I , / / , , 4 6 8 10 12 14 16 18 20 22 24 26 1 (fi) Fig. 4. As for Fig. 3 with a residual p-n interaction V,, included in the particle-rotor calculations. (Note the change in scale compared to Fig. 3.) adopted here are ~0 = -4.95 MeV and ur = -0.55 MeV. The effect of including V,, with y = 0” is shown in Fig. 4. Qualitatively the agreement with the data is very good. The inverted staggering pattern is clearly present for all three cases, and the spin at which the inversion occurs increases along the sequence 162,16‘?m, ‘74Ta in both the calculations and the data. The magnitude of the staggering is described fairly well for the Tm isotopes, but is too small for ‘74Ta. The qualitative agreement with the data is not sensitive to small changes in the calculations (moment of inertia, Coriolis attenuation, etc.), but appears for a wide range of reasonable parameter values. 198 RA. Bark et d/Physics Letters B 406. (1997) 193-199 The wave functions of these semi-decoupled states are complicated, and a simple qualitative understanding of how VP, affects the signature splitting is elusive. The energy eigenfunctions are minimum energy solutions of the total Hamiltonian, and thus represent a balance between the core rotational energy < E,,, >, the proton and neutron quasiparticle energies < ,?&, > and < Eqn >, and the p-n interaction < VP, >. The effect of the p-n interaction depends on the particle and hole character of the participating quasiparticles; in a weak coupling basis 1 (j,, j,,)J @ R; I), the average p-n interaction can be related to the spherical multiplet splittings ((j,, j,) JI VP, I(&, j,) J). For the n-h912 @ vi13/2 configuration, the proton-particle neutron-particle matrix elements are all attractive, while the related proton-particle neutron-hole matrix elements are all repulsive [33]. The largest matrix elements occur for the low spin J = 2, 3 states and for the stretched state, J = J,,, = 11. At high spins, in 164Tm, near e.g. I N 24& the situation is relatively transparent. The odd spin states have a larger alignment than the even spin states and therefore the odd-spin states have a dominant J = 11 component. This has nearly equal particle-particle and particlehole amplitudes, while the even spin states have nearly equal J = 11 and J = 10 components, both mainly of particle-particle character. Consequently, the contribution to the total energy due to the p-n interaction, < VP, > is more attractive for even spins than for odd spins. However, the overall staggering is dominated by < E,,, >, which favours the normal staggering (cr = 1 favoured). At lower spins the wavefunctions are more complex, with J = 2, 3 components playing a greater role. Here, the contribution < VP, > is actually at its largest, but it does not oscillate with spin. Instead, the contribution due to < E,,, > is forced to change phase, giving rise to the signature inversion. The present results highlight the importance of considering known residual p-n interactions at medium to high spins. It is hoped that the application of the present residual interaction to h9/2 bands in odd-2 nuclei may also shed light on the origin of delayed crossing frequencies. This work was supported by the Swedish Natural Science Research Council, the Danish Natural Science Foundation, the Nordic Committee for Accelerator Based Research, the NORDBALL collaboration, the Royal Swedish Academy of Sciences (R.A.B.), the Spanish CICYT (project PB95-0533) (J.M.E.) and the US Dept. of Energy under the grant DE-FGOS- 92ER40694 (P.B.S.). 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