The Rotational-Vibrational Interface in gamma-soft 101Ru

PHYSICAL REVIEW C 66, 024302 ~2002! High-j proton and neutron alignments in g-soft 101 Ru A. D. Yamamoto,1,2 P. H. Regan,1,2,* C. W. Beausang,1 F. R. Xu,3 M. A. Caprio,1 R. F. Casten,1 G. Gürdal,1,4 A. A. Hecht,1 C. Hutter,1 R. Krücken,1 S. D. Langdown,1,2 D. Meyer,1 J. J. Ressler,1 and N. V. Zamfir1,5,6 1 Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut 06520-8124 2 Department of Physics, University of Surrey, Guildford, GU2 7XH, United Kingdom 3 Department of Technical Physics, Peking University, Beijing, 100871, China 4 Department of Physics, University of Istanbul, Istanbul, Turkey 5 Clark University, Worcester, Massachusetts 01610 6 National Institute for Physics and Nuclear Engineering, Bucharest-Magurele, Romania ~Received 5 May 2002; published 1 August 2002! The near-yrast structure of the weakly deformed, ‘‘transitional,’’ nucleus 101Ru has been investigated using the fusion-evaporation reaction 96Zr( 9 Be,4n) 101Ru at a beam energy of approximately 44 MeV. The experimental data are compared with theoretical calculations using the cranked Woods-Saxon-Strutinsky method. The yrast positive-parity structures are observed to undergo a backbend, consistent with the crossing of an aligned 1 ( n h 11/2 ) 2 configuration. The h 11/2( @ 550# 2 2 ) intruder band configuration is extended to a tentative spin/parity 47 of ( 2 2 ) and excitation energy of more than 9 MeV. This structure exhibits properties which can be explained by the rotational alignment of a pair of midshell g 9/2 protons, in contrast to the behavior observed in the heavier N557, odd-A isotones where the predicted proton crossing is delayed in favor of neutron alignments. The effect of static g deformation on the theoretically predicted alignment properties is investigated by means of the cranked shell model. The observed band crossings are found to be consistent with a significant triaxial rigidity, persistent into the medium-spin regime. DOI: 10.1103/PhysRevC.66.024302 PACS number~s!: 21.10.Re, 21.60.2n, 23.20.Lv, 27.60.1j I. INTRODUCTION The cranked shell model ~CSM! @1–3# and associated cranked Woods-Saxon-Strutinsky mean-field @4 – 6# methods have been spectacularly successful in interpreting the highspin behavior in a wide range of well-deformed ~b>0.25! nuclei. In particular, the predictions of rotational alignments of high-j orbitals due to the Coriolis interaction in rare-earth nuclei are generally well produced @3#. However, the applicability of the CSM to less deformed regions of the Segré chart remains less certain. Paradoxically, the Coriolis effects which give rise to the rotational alignment phenomena are largest in nuclei with small intrinsic deformations ~i.e., in systems where the energy differences between Nilsson states which differ by DV51 are small! and associated large rotational frequencies @7,8#. The spectra of low-lying yrast states of the ruthenium (Z544) isotopes around A;100 have been described in terms of algebraic models such as the interacting boson approximation ~IBA! @9# as good examples of transitional systems between spherical vibrator and g-soft nuclei @10–18#. However, generally speaking, such descriptions break down in the region of the first band crossing, which in these nuclei has been explained @19,20# in the rotational model as arising from the alignment of a pair of low-V h 11/2 neutrons @20– 22#. ~We note that there have been phenomenological attempts to extend the IBA to the higher-spin regime by coupling it to broken pairs, such as those described in Ref. @23#.! Rotational bands in the N557 isotones between the shell *Corresponding author. Email address: [email protected] 0556-2813/2002/66~2!/024302~13!/$20.00 closures at Z540 ~Zr! and Z550 ~Sn! present particularly good laboratories to probe Coriolis-driven alignment effects in weakly deformed nuclei @20,21,24 –29#. The odd-A N 557 isotones systematically exhibit weakly deformed, decoupled bands associated with the population of the @ 550# 21 2 Nilsson orbital, intruding down from the unique-parity h 11/2 subshell. In the rotational model, the quasiparticle alignment properties in these bands in 103Pd and 105Cd have been shown to have a strong dependence on the quadrupole deformation @24#. Specifically the observation of neutron alignments associated with a ~predominantly! g 7/2 pair is proposed to explain the first band crossing in this structure in 105 Cd. In contrast a more complicated scenario has been proposed in 103Pd, where the alignment has been attributed to the simultaneous alignment of both g 7/2 neutrons and g 9/2 protons @24#. As the number of valence proton holes increases away from the Z550 closed shell, the deformation of the h 11/2 configuration is expected to increase. This is consistent with ~i! the observed proton midshell minimization in the excita105 Cd tion energy of the 112 2 state in the N557 isotones, 48 103 101 ~1163 keV @29#!, 46 Pd ~783 keV @28#!, 44 Ru ~527 keV @27#!, and 99 42Mo ~684 keV @21#!; and ~ii! the minimum value 11 2 2 transition at 101Ru ~431 keV for the energy of the 15 11 → 2 compared to 540 keV, 477 keV, and 482 keV and for 105Cd, 103 Pd, and 99Mo, respectively!. In ruthenium, this increased quadrupole deformation might be expected to combine with the lowering of the proton Fermi surface in the g 9/2 shell compared to the palladium and cadmium isotones to produce differing alignment properties at high spins. The situation is further complicated by calculations which suggest that ruthenium nuclei around N560 are expected to 66 024302-1 ©2002 The American Physical Society PHYSICAL REVIEW C 66, 024302 ~2002! A. D. YAMAMOTO et al. FIG. 1. Decay scheme for 101 Ru deduced from the current work. have considerable g softness @30#. We note that all of the N557 isotones discussed above show systematic behavior associated with weakly coupled harmonic vibrators @8#, with the E( 192 2 → 152 2 )/E( 152 2 → 112 2 ) value for all four nuclei lying close to the g-soft limit of approximately 2.5. Indeed, the even-even 100Ru and 102Ru cores appear to be best described as vibrational nuclei at low spins, as evidenced by the energy ratios for the yrast 4 1 and 2 1 states in these nuclei of '2.3 @20#, and the presence of two-phonon quadrupole vibrational states at approximately 1 MeV @10,11,31,32#. The recent study of the low-lying states of 100Ru by Genilloud et al. @11# identified the signatures of a quasi-g vibrational band, with energy spacings consistent with a g-unstable nucleus @33#. The question of the effect and clear signature of triaxial deformation at high spins remains a major question in nuclear structure physics. Motivated by these aspects, in the current work we have studied the near yrast states of the N557 isotone 101Ru. Decoupled, rotational-like structures built on the intruder h 11/2 orbital ( @ 550# 21 2 Nilsson configuration! are a feature of all the odd-N ruthenium (Z544) isotopes between 97Ru53 and 111Ru67 . The medium- to high-spin states of 97Ru 024302-2 HIGH-j PROTON AND NEUTRON ALIGNMENTS . . . PHYSICAL REVIEW C 66, 024302 ~2002! FIG. 2. Total projection of the unfolded g-g coincidence matrix, highlighting the relative populations of the different reaction products of the 46 MeV 9 Be beam on both the 208Pb target support and the isotopically enriched 96Zr target. and 99Ru are accessible via fusion-evaporation reactions with heavy-ion @34 –36# and alpha-particle induced reactions @37#. By contrast, the isotopes with A>103 are too neutron rich to be populated in this manner using stable beam/target combinations and have thus been studied using fusion fission @38,39# and spontaneous ~source! fission @40– 42#. FIG. 4. Sums of double-gated gamma-triples coincidence spec5 7 11 tra highlighting the ~a! 2 2 band, ~b! the 2 1 band, and ~c! the 2 1 band. Band members are shown in larger font with links to other structures in 101Ru highlighted with the smaller sized labels. The insets correspond to expanded regions of the main figures. A number of the near-yrast states of the b-stable nucleus Ru which were observed in the current work have previously been reported by Kajrys et al. @43# and Klamra et al. @44# using alpha-particle induced reactions. While these two studies identified rotational-like structures based on both positive- and negative-parity states, the light-ion nature of these reactions limited the input angular momentum such that the decay schemes could not be extended through the full alignments. Similarly, data obtained following a massive transfer reaction study using a 7 Li beam to populate 101Ru by Haenni et al. @20# was only able to identify states up to I' 252 \. The current work utilizes the combination of a heavier-ion ( 9 Be) induced reaction, together with a state-ofthe-art g-ray spectrometer array to significantly extend the previously published decay scheme, with both positive- and negative-parity bands observed well past the first bandcrossing region. 101 II. EXPERIMENTAL DETAILS FIG. 3. Summed g-ray coincidence spectra highlighting the ~a! band, ~b! the 25 1 band, and ~c! the 27 1 band. The gating transitions are marked with asterisks. Band members are shown in larger font with links to other structures in 101Ru highlighted with the smaller sized labels. The insets correspond to expanded regions of the main figures. 11 2 2 States in 101Ru were populated using the fusionevaporation reaction 96Zr( 9 Be,4n) 101Ru. The dc beam was provided by the Wright Nuclear Structure Laboratory ~WNSL! tandem accelerator at Yale University and impinged on a target consisting of an isotopically enriched ~;85%! metallic zirconium foil of thickness 670 m g/cm2 mounted on a 5 mg/cm2 lead backing. The target was placed with the lead backing facing the beam thus allowing the residual nuclei of 024302-3 PHYSICAL REVIEW C 66, 024302 ~2002! A. D. YAMAMOTO et al. FIG. 5. ~Left hand side! Sum of the 431 and 664 keV (E2) gates from band 3 from the ~90,160! matrix and ~right hand side! 861 keV gate in band 2. Note the different relative intensities of the projected E2 and dipole ~1430 keV and 307 keV! transitions ~see Table I for specific ratio values!. interest to recoil into vacuum. A lead collimator, with a 2 cm diameter exit hole, was placed approximately 4 cm behind the target position in order to protect the target chamber from unwanted reactions induced by beam particles scattered by the target. The beam nuclei with initial energy of 46 MeV were calculated to lose ;2 MeV in the lead support layer, leading to an ‘‘on-target’’ laboratory energy of approximately 44 MeV. This corresponded to a classical maximum angular momentum transferred to the compound system of ;22\. The reaction g rays were detected using the YRASTBALL array @45#, which in this configuration was comprised of six, four-element clover detectors at 90° to the beam direction, together with five smaller ~25%! coaxial germanium detectors at 126°, three at 160°, and five more at 50°. The acquisition master gate was set such that events where three or more g rays were detected within 200 ns of each other were written to tape for subsequent off-line analysis. Typical ontarget beam currents were between two- and four-particle nanoamps, for the duration of the two day experiment. This resulted in master event (> g 3 ) rates of between 500 and 1000 Hz, leading to a total of 4253106 , unfolded g-g coincidence events for off-line analysis. III. DATA REDUCTION, ANALYSIS, AND RESULTS The 90° clover detectors were operated in a standard ‘‘add-back’’ mode. The germanium detectors were calibrated for both energy and efficiency using a 152Eu source, placed at the target position. In the off-line sort a Doppler correction was applied to the g-ray energies using an average recoil velocity of v /c'0.6%, as measured by comparing the gainmatched spectra for the individual detector rings. The v /c 50 gain matching was checked using ~unshifted! lines from 214 Rn, which was formed via beam reactions on the lead FIG. 6. Extracted DCO ratios for transitions in 101Ru, using stretched E2 gates. The filled data points correspond to the 307 and 1430 keV transitions, which are assigned as DI51, while the empty points correspond to stretched DI52 (E2) decays. target support. The data were sorted into standard g - g coincidence matrices and cubes which were sorted into a RADWARE format and analyzed using the SLICE, GF2, LEVIT8R, and ESCL8R software packages @46#. The relative intensity for the transitions at the bottom of the decay scheme ~i.e., 307, 431, and 545 keV! were taken by comparing their intensities with higher-spin decays ~such as the 664 keV transition! in the efficiency corrected g-g total projection. A. Level scheme for 101 Ru 101 The decay scheme for Ru observed in the current work is given in Fig. 1. Figure 2 shows the total projection of the unfolded g-g coincidence matrix for this experiment, highlighting transition from reactions both on the 96Zr target ( 1002102Ru) and on the 208Pb target support ( 214Rn). Figures 3 and 4 give examples of the gated g-g coincidence and double-gated g-triples spectra which were used to build up the 101Ru decay scheme. B. Spin and parity assignments Where statistics allowed, multipolarities for specific transitions identified in 101Ru could be assigned by using the directional correlation from oriented states ~DCO! method @47# on pairs of coincident g rays. In analogy with the technique described in Ref. @48#, the detectors from the YRASTBALL array at 90° and 160° were sorted into a coincidence matrix with transitions detected at 90° sorted on one axis and those detected at 160° sorted on the other. By placing g-ray energy gates on transitions whose multipolarity had been established in previous works @43,44#, a DCO ratio could be extracted using the prescription 024302-4 R DCO 5 I ~ 160° ! gated at 90° 3«, I ~ 90° ! gated at 160° ~1! HIGH-j PROTON AND NEUTRON ALIGNMENTS . . . PHYSICAL REVIEW C 66, 024302 ~2002! TABLE I. Gamma-ray transitions identified in 101Ru in the current work. The relative g-ray intensities were taken from a twodimensional fit to the g - g coincidence matrix using the program ESCL8R ~Ref. @46#!. The intensities are normalized to 1000 units for the entire 101Ru channel by summing the extracted intensities of the 307, 431, 545, and 720 keV transitions. E g ~keV! I g ~rel. 1000! E i ,E f J ip →J pf 91 71 2 ,2 11 2 7 1 2 ,2 11 1 9 1 2 ,2 71 51 2 ,2 15 1 13 1 2 , 2 23 1 21 1 2 , 2 91 71 2 ,2 15 2 11 2 2 , 2 1 25 1 ( 27 2 ), 2 27 25 ( 2 1 ), 2 1 1 29 1 ( 31 2 ), 2 71 51 2 ,2 23 1 19 1 2 , 2 35 1 33 1 2 , 2 23 1 19 1 2 , 2 25 1 21 1 2 , 2 19 2 15 2 2 , 2 21 1 17 1 2 , 2 11 1 7 1 2 ,2 1 23 1 ( 27 2 ), 2 91 51 2 ,2 27 1 23 1 ( 2 ), 2 29 1 25 1 2 , 2 13 1 9 1 2 ,2 1 23 2 ( 27 2 ), 2 31 1 ( 2 1 , 27 2 ) 23 2 19 2 2 , 2 15 1 11 1 2 , 2 17 1 13 1 2 , 2 175.3~3! 46~2! 720,545 221.0~2! 254~10! 528,307 281.0~5! 16~2! 1002,720 307.4~2! 214~20! 307,0 363.0~5! 10~4! 1864,1501 391.8~5! 16~4! 3444,3053 413.7~4! 26~2! 720,307 431.1~2! 586~22! 960,528 459.4~5! 22~2! 4141,3681 500.6~6! 14~2! 4183,3681 516.4~6! 14~2! 4967,4451 545.1~4! 85~30! 545,0 556.3~5! 12~4! 3444,2887 571.4~4! 5~2! 5956,5375 618.4~4! 38~4! 3444,2825 628.8~3! 80~4! 3681,3053 664.3~2! 542~16! 1624,960 673.4~3! 82~6! 3053,2379 695.0~4! 186~8! 1002,307 697.0~7! 20~2! 4141,3444 720.1~3! 115~7! 720,0 739.2~3! 28~4! 4183,3444 769.7~3! 52~6! 4451,3681 781.0~4! 180~6! 1501,720 815.8~8! 22~4! 3291,2475 826.6~7! 26~4! 4967,4141 851.3~3! 310~10! 2475,1624 861.2~4! 88~6! 1864,1002 878.0~3! 86~8! 2379,1501 E g ~keV! R DCO a 0.50~7! 0.97~14!b 1.07~31!a c 0.93~16! 0.98~14!d 0.88~13!c 0.84~19!c 0.98~18!e 0.83~12!b 0.99~18!c E i ,E f 923.7~5! 30~6! 5375,4451 961.7~4! 42~4! 2825,1864 968.6~8! 10~2! 3443,2474 979.0~8! 14~2! 5946,4967 1003.1~3! 146~6! 3478,2475 1023.7~4! 16~2! 2887,1864 1050.4~5! 16~2! 5233,4183 1094.2~5! 18~2! 6469,5375 J ip →J pf R DCO 33 1 29 1 2 , 2 19 1 15 1 2 , 2 23 1 23 2 2 , 2 1 31 1 ( 35 2 , 2 ) 27 2 31 2 2 , 2 19 1 15 1 2 , 2 31 27 ( 2 1, 2 1) 1 33 1 ( 37 2 , 2 ) 39 1 35 1 (2 ,2 ) 31 2 27 2 2 , 2 1.05~24!c 1130.4~8! 8~2! 7077,5946 1138.2~3! 66~4! 4616,3478 1181.0~1.0! 1206.2~8! 10~2! 14~4! 3656,2475 3681,2474 1209.8~6! 6~2! 7679,6469 1214.7~3! 28~2! 5831,4616 1181.0~1.0! 1206.2~8! 10~2! 14~4! 3656,2475 3681,2474 1209.8~6! 6~2! 7679,6469 1214.7~3! 28~2! 5831,4616 1239.0~1.0! 1241.4~1.0! 14~2! 3~1! 3714,2474 8318,7077 1264.5~5! 8~2! 7096,5831 2 35 2 ( 39 2 , 2 ) 1286.4~1.2! 4~1! 5903,4616 33 31 2 ( 35 2 , 2 ), 2 1323.5~7! 2~1! 9002,7679 1 41 1 ( 45 2 , 2 ) 1337.0~7! 4~2! 8433,7096 2 39 2 ( 43 2 , 2 ) 1393.7~8! 1~0.5! 9826,8433 2 43 2 ( 47 2 , 2 ) 1429.6~6! 22~2! 3053,1624 1613.0~1.5! 10~4! 3237,1624 1786.9~1.5! 4~2! 5265,3478 1896.4~1.5! 2~1! 5375,3478 21 1 19 2 2 , 2 19 23 21 ( 2 , 2 ), 2 2 29 27 2 ( 2 , 2 ), 27 2 27 2 31 29 ( 2 , 2 ), 2 a d b e 861 keV gate. 664 keV gate. c 673 keV gate. I g ~rel. 1000! 25 1 23 2 2 , 2 1 37 1 ( 41 2 , 2 ) 35 2 31 2 2 , 2 25 1 23 2 2 , 2 41 37 ( 2 1, 2 1) 35 2 31 2 2 , 2 0.76~19!b 0.67~19!a 0.94~33!d 0.94~33!d 1 39 1 ( 43 2 , 2 ) 0.38~15!a 431 keV gate. 878 keV gate. where I is the number of counts in a peak and « is an efficiency multiplication factor which corrects the experimental value for the detection efficiencies of both the gate and the projected transition. This factor is «5 « g ~ 160° ! 3« p ~ 90° ! , « g ~ 90° ! 3« p ~ 160° ! ~2! where « g is the detection efficiency of the gate and « p is the detection efficiency of the projected transition. The difference in the projected intensity of stretched quadrupole g rays ~assumed to be of E2 character! and DI 51 transitions, when both are gated by an E2 transition, is illustrated in Figs. 5 and 6. Typical values of the DCO ratio of ;1.0 and ;0.6 were found for stretched quadrupole and pure dipole transitions, respectively, when gated by a stretched E2 transition. Where possible, the spin/parity assignments given in Refs. @43,44# were assumed for the lower-spin members of the current decay scheme. The assignments for higher-spin states were then made on the basis of the measured DCO values by restricting the possible mul- 024302-5 PHYSICAL REVIEW C 66, 024302 ~2002! A. D. YAMAMOTO et al. FIG. 7. Gate on the 482 keV band in 99 42Mo57 . 11 2 15 2 2 → 2 member of the h 11/2 tipolarities to E2 or DI51, E1 or mixed M 1/E2 type decays. The usual assumption that heavy-ion fusionevaporation reactions preferentially populate yrast and nearyrast states has also been applied and thus the spins generally increase with increasing excitation energy. C. Comparison with previous work, including 99 Mo The current data correspond to a significant extension of the previously published work for 101Ru @20, 27, 43, 44#. The positive-parity band, built on the 25 1 ground state ~band 1 in Fig. 1! was reported by Klamra et al. @44# up to a spin of ( 212 1 ). This band is extended fully through the first alignment up to a tentative spin/parity of ( 452 1 ). The ordering of FIG. 8. Comparison of the experimental kinematic moments of inertia and quasiparticle alignments for the structures observed in the current work in 101Ru with ~i! the h 11/2 structures in the N 557 isotones ~lower figures! and ~ii! the yrast bands in 100,102Ru ~upper figures!. FIG. 9. TRS calculations for the lowest-energy positive-parity, positive signature structure in 101Ru. The energy contours are at 200 keV intervals. The deformation parameters for the individual minima are, upper left: \v50.3 MeV, b 2 50.20, b 4 50.02, and g5–19°; upper right: \v50.4 MeV, b 2 50.23, b 4 50.03, and g5117°; lower left: \v50.5 MeV, b 2 50.24, b 4 50.03, and g5118°; lower right: \v50.6 MeV, b 2 50.14, b 4 50.01, and g5113°. the lower-lying band members in the current work differs from that reported by Klamra et al. @44# in that the 673 keV, 172 1 → 132 1 transition reported in Ref. @44# is replaced by one with 878 keV. The revised ordering places the 673 and 628 keV transitions reported by Klamra et al. above the 878 keV transition. ~Note that this change in ordering has significant consequences when extracting the alignment properties of this band, see below.! The identification of the 1430 keV, stretched dipole ( 212 1 → 192 2 ) and 1207 keV, 252 1 → 232 2 transitions which link this positive-parity band with the negative-parity structure provide confirmation of the new ordering. Klamra et al. also observed the band built on the 27 1 state at 307 keV ~band 2 in Fig. 1! up to a tentative spin/parity of ( 232 1 ). In the current work this is extended through the first backbend, up to a tentative spin/parity of ( 432 1 ). The decays between this structure and the negative-parity band are also established via the observation of the weak 1206 keV and 969 keV transitions. The decoupled rotational band built on the 112 2 isomeric bandhead, which was observed by Klamra et al. up to spin 352 2 , is extended to a tentative spin/parity of ( 472 2 ) ~band 3 in Fig. 1!. 024302-6 HIGH-j PROTON AND NEUTRON ALIGNMENTS . . . PHYSICAL REVIEW C 66, 024302 ~2002! FIG. 10. TRS calculations for the lowest-energy positive-parity, negative signature structure in 101Ru. The energy contours are at 200 keV intervals. The deformation parameters for the individual minima are upper left: \v50.3 MeV, b 2 50.20, b 4 50.01, and g5222°; upper right: \v50.4 MeV, b 2 50.24, b 4 50.02, and g5123°; lower left: \v50.5 MeV, b 2 50.23, b 4 50.02, and g5121°; lower right: \v50.6 MeV, b 2 50.15, b 4 50.01, and g5110°. Figure 7 shows a spectrum identifying the band built 99 Mo, on the yrast 112 2 state in the lighter N557 isotone, 42 which was populated in the current work via the a 2n evaporation channel. This band was extended by two transitions ~979 and 1055 keV! from that reported in Ref. @21#. By comparison with the N557 systematics, these transitions are assumed to be of a stretched E2 nature and represent the continuation of the h 11/2 decoupled structure. The 845 keV, 23 2 → 192 2 transition reported in Ref. @21# is confirmed in the 2 current work. FIG. 11. TRS calculations for the lowest-energy negative-parity, negative signature ( n h 11/2 ) structure in 101Ru. The energy contours are at 200 keV intervals. The deformation parameters for the individual minima are upper left: \v50.2 MeV, b 2 50.22, b 4 50.02, and g5119°; upper right: \v50.3 MeV, b 2 50.22, b 4 50.02, and g5117°; lower left: \v50.5 MeV, b 2 50.22, b 4 50.02, and g5114°; lower right: \v50.6 MeV, b 2 50.15, b 4 50.01, and g515°. v5 dE ~ I ! ' E ~ I11 ! 2E ~ I21 ! dI x ~ I ! I x ~ I11 ! 2I x ~ I21 ! ' Eg AS D 3 I1 2 2 2K 2 2 AS D 1 I2 2 . 2 2K 2 ~3! Subsequently, the quasiparticle angular momentum i x was extracted using the Harris parametrization, such that @2# i x ~ v ! 5I x ~ v ! 2I ref~ v ! IV. DISCUSSION AND COMPARISON WITH NÄ57 ISOTONES 5 AI ~ I11 ! 2K 2 2 ~ I (0) 1I (1) v 2 ! v . The rotational-like cascades observed for 101Ru in the current work suggest that these structures might be applicable for analysis in terms of the cranking model. To this end, the rotational frequency for the band members was extracted using the standard, canonical expression for states between spins I11 and I21 @1–3#, ~4! Figure 8 shows the quasiparticle alignments for the bands in 101Ru. Harris parameters of I (0) 57.0\ 2 /MeV and I (1) 515.0\ 4 /MeV3 @24, 39, 49# were used for all the structures in this analysis. We note that a number of differing values for the Harris variable moment of inertia fits have been used to extract alignments in this region ~see, e.g., Refs. 024302-7 PHYSICAL REVIEW C 66, 024302 ~2002! A. D. YAMAMOTO et al. are dependent on the rotational frequency ~v! and deformation. In order to include such dependence in the TRS, we have performed pairing-deformation-frequency selfconsistent TRS calculations, i.e., for any given deformation and frequency, pairings are self-consistently calculated by the HFB-like method @54#. At a given frequency, the deformation of a state is determined by minimizing the calculated TRS. Figures 9, 10, and 11 show the results of the TRS calculations for the lowest-lying positive- and negative-parity structures in 101Ru, corresponding to the structures labeled as bands 1, 2, and 3 in Fig. 1, respectively. Figure 12 shows a comparison between the experimentally extracted total aligned angular momentum, I x , and that extracted from the angular momentum projections in the TRS calculations. A. Positive-parity bands FIG. 12. Comparison of the experimentally extracted total aligned angular momentum (I x ) for the bands in 101Ru with the results of the TRS calculations. The ground state band in 102Ru is also shown for discussion purposes. The open squares correspond to proton contributions, with the smaller filled squares representing the predicted neutron contribution. The line is the total I x value predicted by the TRS calculations and the large black filled diamonds are the values extracted from the experimental data. @20, 21, 38, 50, 51#!. The Harris parameters in the current work were chosen specifically to enable a direct comparison between the decoupled h 11/2 bands across the N557 isotonic chain, and thus those used in Ref. @24# were taken for all nuclei. ~The general effect of this choice of parametrization is an increase in the extracted alignment at higher frequencies compared to the alternative parameters suggested by Haenni et al. @20# and Fotiades et al. @38#.! To enable an unambiguous comparison between isotones, we have also plotted the extracted kinematic moment of inertia, J (1) 5I/ v , which is shown with the alignments in Fig. 8. In order to compare the experimental data with theoretical predictions in the band crossing region, the effect of collective rotation on the microscopic structures in 101Ru was investigated in the framework of the cranked Woods-SaxonStrutinsky model by means of total-routhian-surface ~TRS! calculations @5# in a three-dimensional deformation b 2 , b 4 , g space. Both monopole and quadrupole pairings are included in these calculations. The monopole pairing strength G is determined by the average gap method @52# and the quadrupole strengths are obtained by restoring the Galilean invariance broken by the seniority pairing force @53#. To avoid the spurious phase transition encountered in the BCS approach, we have used an approximate particle-number projection, described by Lipkin-Nogami pairing @54#. Pairing correlations Two main positive-parity sequences ~labeled bands 1 and 2! have been observed in the current work. Band 1 is built on the 25 1 gound state and band 2 on the 27 1 excited state at 307 keV. The moment of inertia and alignment plots for both bands ~Fig. 8! show a clear discontinuity, associated with a backbend at a rotational frequency of \v'0.4 MeV. The extracted quasiparticle alignment was calculated assuming a value of K5 25 for both structures. This assumption was made on the basis that the deformed, 25 1 ground state corresponds to the @ 413# 25 1 Nilsson orbital, which is the only likely candidate for a weakly prolate deformed I p 5 25 1 intrinsic state in this region. Band 2 is assumed to be the signature partner of band 1. The alignment is consistent with the behavior observed in the yrast sequences of the even-even neighboring isotopes, 100,102 Ru @20, 22, 55#, where the first band crossing is associated with the rotational alignment of a pair of h 11/2 neutrons. The extracted increase in quasiparticle alignment through the backbend in bands 1 and 2 of '10\ is also consistent with this picture. We note, however, that the increasing slope of this plot above the backbending region may be indicative of an inappropriate choice of values for the Harris parameters in this spin regime, particularly as significant changes in the core deformation are expected due to band termination effects ~see below!. Figure 12 compares the extracted total aligned angular momenta, (I x ), for these two bands with the predictions of total routhian-surface calculations for the lowest-energy positive-parity structures in 101Ru. The TRS calculations shown in Figs. 9 and 10 highlight the predicted triaxial softness of this configuration, with a wide minimum observed spanning a valley between g'620° and b 2 '0.2. Extracting the predicted aligned angular momentum at the minimum energy value for a given cranking frequency allows a direct comparison between the experimental values and theoretical predictions for the total aligned angular momentum (I x ) to be made. The calculations allow the components of the proton and neutron contributions to the total aligned angular momentum value to be decoupled. They predict that a neutron quasiparticle alignment 024302-8 HIGH-j PROTON AND NEUTRON ALIGNMENTS . . . 103 PHYSICAL REVIEW C 66, 024302 ~2002! FIG. 13. Comparison of the low-lying positive-parity near-yrast states in the even-Z, N557 isotones. The partial decay schemes for Pd and 105Cd are taken from Refs. @25,35,51,55#, respectively. See text for discussion. is responsible for the first band crossing, with the first proton alignment for this configuration not predicted until rotational frequencies of \v50.6 MeV and higher. In general, the agreement between the experimental and theoretical I x values is remarkably good, suggesting that a rotational picture for these nominally ‘‘transitional, g-soft’’ structures may indeed be appropriate. At higher values of rotational frequency ~\v>0.7 MeV, corresponding to aligned spin values of 26\ and above! the TRS calculations predict a significant decrease in the quadrupole deformation for the yrast positive-parity configurations. This is consistent with a reduction in collectivity due to a band-termination effect. Here, as the valence spin is exhausted, in order to generate higher values of angular mo90 Zr50) core must be broken @56#. Such phementum, the ( 40 nomena are well known in this region, with terminating states ~relative to the closed 90Zr core! identified by Timár et al. at spins between 25 and 32 \ in 98,99,100Ru @35#. The N557 isotones 103Pd and 105Cd both have similar 51 ground states to 101Ru. However, in those nuclei the posi2 tive parity structures built on this state differ considerably ~see Fig. 13!. As pointed out by Jerrestam et al. @51# the sequence of stretched E2 transitions built on the yrast 27 1 state in 105Cd resembles the weak coupling of an I p 5 27 1 neutron to the 104Cd core. Such an interpretation implies a @ 420# 21 1 Nilsson configuration ~from a mainly g 7/2 spherical parentage! for the odd particle. Inspection of the Nilsson diagram for this region shows that one would expect this orbital to lie higher in excitation for (N557) isotones with increased deformation, and thus lie higher in excitation for 101 Ru than in 105Cd. The first three yrast states which are linked by stretched E2 transitions in 105Cd from the 25 1 ground state ~i.e., 29 1 , 132 1 , 172 1 ) resemble the structure expected of a spherical 25 1 state coupled to a vibrational structure. Note that in contrast to the 101Ru case, neither positiveparity sequence in 105Cd is observed to undergo a backbend below \v'0.5 MeV. The most up-to-date decay scheme for 103Pd, published in Ref. @25#, shows three distinct low-lying positive-parity structures, one built on the 25 1 ground state, and two built on low-lying 27 1 states. Such a picture is consistent with an increased core deformation compared to 105Cd, which allows rotational structure built on the @ 413# 25 1 state to evolve with increasing spin. The competing levels of the nominally decoupled band arising from the @ 420# 21 1 Nilsson orbital interact at low spins giving rise to a highly mixed structure in this nucleus. The ~weakly! deformed nature of these bands is confirmed by the observed backbending at I p '10\, consisent with the typical (h 11/2 ) 2 neutron crossing in this region. In 101Ru, the apparent observation of only two interacting bands ~1 and 2 in Fig. 1! favors the interpretation that 024302-9 PHYSICAL REVIEW C 66, 024302 ~2002! A. D. YAMAMOTO et al. these are the two signatures of the @ 413# 25 1 configuration. However, an interaction with the ~unobserved! @ 420# 21 1 decoupled band, possibly associated with the 27 1 state at 545 keV, might explain the signature splitting present between bands 1 and 2. Kajrys et al. @43# reported a candidate for the next level built on this proposed decoupled 27 1 bandhead, with a tentative 112 1 state reported at 1322 keV. However, the 1322 keV level was not found in the study of Klamra et al. @44# nor in the current work. This anomaly may be explained by the nonyrast nature of this state in contrast to the typical feeding preferences in fusion-evaporation reactions. 1 B. †550‡ 2 À band Figure 8 compares the experimental quasiparticle alignments and kinematic moments of inertia for the h 11/2 decoupled bands in the N557 isotones, 99Mo @21,57#, 103Pd @24,26,25# and 105Cd @24,51# with that extracted for the analogous structure observed in the current work. In contrast to the Z548 case of 105Cd, the new data for 101Ru shows a distinct up-bend above \ v '0.6 MeV. Although the h 11/2 band in 103Pd also shows an increase in alignment in this region, the increase is not so smooth, and has been described in terms of a possible dual alignment of both g 7/2 neutrons and g 9/2 protons. The lower frequency of the first alignment in the 105Cd case has been discussed in terms of a (g 7/2 ) 2 neutron alignment from blocking arguments and by comparison with the yrast structure in 106Cd @49#. However, as pointed out in Ref. @24#, the theoretically predicted crossing frequencies for these different configurations are highly sensitive to the quadrupole deformation. Figure 14 shows the evolution of the excitation energy of the 112 2 yrast bandheads for the N557, even-Z isotones from Zr (Z540) to Sn (Z550). The minimum value for 101Ru is consistent with it having the largest quadrupole deformation at low excitation energy, as is also apparent from the yrast 2 1 energies @58# in the even-even N556 and N558 isotonic chains. As pointed out in Ref. @24#, for axially symmetric prolate shapes, the CSM predicts the second ~‘‘BC’’! (h 11/2 ) 2 neutron alignment to become favored over both the (g 7/2 ) 2 neutron ~‘‘EF’’! and (g 9/2 ) 2 ~‘‘ab’’! proton crossings as the core deformation increases. However, the alignment pattern observed for the h 11/2 band in 101Ru does not show the signature backbending pattern usually associated with the BC alignment in the heavier Cd @39,59# and Pd @50,60– 64# nuclei at \v;0.5–0.6 MeV. The theoretical quasiparticle routhians for 101Ru shown in Fig. 15 highlight the effect of a substantial positive g deformation on the rotation frequency of the proton and neutron crossings. These calculations predict an alignment associated with (g 9/2 ) 2 protons at a frequency of \v'0.6 MeV for g5120°. This is consistent with the TRS calculations for the lowest negative-parity configuration ~see Figs. 11 and 12!, which predict a sudden increase in aligned angular momentum due to a proton crossing in the vicinity of \v50.55–0.6 MeV. We note, however, that this static picture of deformation is probably not appropriate for these structures. The TRS cal- 2 bandFIG. 14. Comparison of the excitation energies of the 11 2 head in the even-Z, N557 isotones and the excitation energies of the lowest 2 1 states in the neighboring even-even N556 and N 11 15 558 nuclei. The 2 2 → 2 2 transition energies in the decoupled h 11/2 bands for the N557 isotones are also shown. The data for this figure were taken from Refs. @20, 49, 51, 60, 65–70#, respectively. See text for discussion. culations predict that the h 11/2 , b 2 '0.2 collective miminum terminates at \v'0.6 MeV ~see Fig. 11!. The TRS calculations also predict a sudden reduction in quadrupole deformation from b 2 '0.2 to b 2 '0.15 and thus the sharp increase in the predicted proton total aligned angular momentum, I x , should include both the proton (g 9/2 ) 2 alignment and shape effect. From the quasiparticle routhians ~as in Fig. 15!, the (g 9/2 ) 2 proton alignment is predicted to occur around \v 50.6 MeV. V. SUMMARY AND CONCLUSIONS In summary, the high-spin states of the nominally transitional nucleus 101Ru have been investigated. The decay scheme has been extended for both positive- and negativeparity structures well past the first band-crossing region. When parametrized using the Harris formalism, the positiveparity bands show a backbend which can be associated with the rotational alignment of a pair of h 11/2 neutrons. This alignment is blocked in the negative-parity band, which shows an up-bend at higher frequencies. In contrast with the heavier N557 isotones, comparison with cranked WoodsSaxon-Strutinsky calculations suggests that this alignment is due to midshell g 9/2 , rather than g 7/2 neutrons. The calculations also predict a more defined triaxial minimum with in- 024302-10 HIGH-j PROTON AND NEUTRON ALIGNMENTS . . . PHYSICAL REVIEW C 66, 024302 ~2002! FIG. 15. Cranked shell model quasiparticle routhians for ~a! neutrons and ~b! protons in 101Ru with static deformation parameters of b 2 50.21, b 2 50.01, and g50°. ~c! and ~d! are the same as for ~a! and ~b! but with g5120°. This work was supported by EPSRC ~UK! and the U.S. Department of Energy, under Grant Nos. DE-FG02-91ER40609 and DE-FG02-88ER-40417. P.H.R. acknowledges support from Yale University via both the Flint and the Sci- ence Development Funds. A.D.Y. and S.D.L. acknowledge the receipt of EPSRC postgraduate studentships. F.R.X. acknowledges support from the Major State Basic Research Development Program of China ~Grant No. G2000077400! and the Chinese Ministry of Education. We gratefully acknowledge the expertise of the WNSL Accelerator technicians ~J. Ashenfelter, S. Ezeokoli, W. Garnett, and R. McGrath! for the excellent beam quality during the experiment. @1# R. Bengtsson and S. Frauendorf, Nucl. Phys. A327, 139 ~1979!. @2# S. Frauendorf, Phys. 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