Shape Coexistence and Mixing in 152Sm
W. D. Kulp, J. L. Wood, P. E. Garrett, C. Y. Wu, D. Cline, J. M. Allmond, D. Bandyopadhyay, D. Dashdorj, S. N. Choudry, A. B. Hayes, H. Hua, S. R. Lesher, M. Mynk, M. T. McEllistrem, C. J. McKay, J. N. Orce, R. Teng, S. W. Yates
aa r X i v : . [ nu c l - e x ] J un Shape Coexistence and Mixing in Sm W. D. Kulp, J. L. Wood, P. E. Garrett,
2, 3
C. Y. Wu, ∗ D. Cline, J. M. Allmond, D. Bandyopadhyay, † D. Dashdorj, S. N. Choudry, A. B. Hayes, H. Hua, S. R. Lesher, ∗ M. Mynk, M. T. McEllistrem, C. J. McKay, J. N. Orce, R. Teng, and S. W. Yates School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA Department of Physics, University of Guelph, Guelph, Ontario N0B 1S0, Canada TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T 2A3, Canada Nuclear Structure Research Laboratory, Department of Physics,University of Rochester, Rochester, New York, 14627, USA Department of Physics and Astronomy, Universityof Kentucky, Lexington, Kentucky 40506, USA Department of Physics, North Carolina StateUniversity, Raleigh, North Carolina, 27695-8202, USA Department of Chemistry, University of Kentucky, Lexington, Kentucky 40506, USA (Dated: November 19, 2018)
Abstract
Experimental studies of
Sm using multiple-step Coulomb excitation and inelastic neutronscattering provide key data that clarify the low-energy collective structure of this nucleus. No can-didates for two-phonon β -vibrational states are found. Experimental level energies of the ground-state and first excited (0 + state) rotational bands, electric monopole transition rates, reducedquadrupole transition rates, and the isomer shift of the first excited 2 + state are all describedwithin ∼
10% precision using two-band mixing calculations. The basic collective structure of
Smis described using strong mixing of near-degenerate coexisting quasi-rotational bands with differentdeformations. Y + Y − multipole mode) and “beta” vibrations ( Y multipole mode). There is a voluminous literature that discusses one-phonon β -vibrationaland γ -vibrational states in deformed nuclei and the lowest-lying excited K π = 0 + and 2 + states, respectively, are generally identified with these modes. However, vibrations in quan-tum systems should exhibit multi-phonon eigenstates. Evidence for multiple (two) phononexcitations in deformed nuclei is sparse and has been difficult to obtain. The best examplesare limited to evidence for two-phonon γ vibrations, but controversy over this structuralinterpretation exists (see, e.g., [2, 3, 4, 5, 6, 7, 8]). There is no unequivocal evidence fortwo-phonon β vibrations.The nucleus Sm is particularly well-suited as a case study for the existence of multi-phonon β and γ vibrations in a deformed nucleus. It has one of the lowest-energy candidate β vibrations in any deformed nucleus (and a fairly low-energy candidate γ vibration), suchthat 2- and even 3-phonon excitations should be below the pairing gap, if they exist. Indeed,recently it has been suggested [9] that Sm (and its neighboring isotone,
Gd) are thebest candidates for establishing the β -vibrational mode in deformed nuclei. This suggestionis supported by exploration of phase transitions in nuclei which places Sm right at acritical point between spherical and deformed nuclear phases and supports the expectationof multi-phonon vibrational behavior [10].To address the expectation that these simple quantum excitation modes should exist in
Sm, we have carried out a very high statistics study using multiple-step Coulomb excita-tion (multi-Coulex). This study was made using the Gammasphere array [11] of Compton-suppressed Ge detectors in conjunction with the CHICO charged-particle detector array [12].The experiment was conducted using a beam of
Sm ( E = 652 MeV, an energy insufficientto surmount the Coulomb barrier) incident on a thin Pb target (400 µ g/cm , 99.86%enrichment) at the Lawrence Berkeley National Laboratory’s 88-Inch Cyclotron. Signalsfrom two ions detected by CHICO in coincidence with at least one “clean” γ ray signal inGammasphere (i.e., a p-p- γ coincidence) triggered an event. The CHICO array providedkinematic characterization of scattered ions and recoiling target nuclei so that Doppler cor-rections could be applied to the γ rays emitted from the Coulomb-excited beam nuclei. Highangular resolution was provided both by CHICO, which has 1 ◦ angular resolution, and byGammasphere, which was operated with 104 Ge detectors. A total running time of 62 hoursprovided 7 × p-p- γ , 8 × p-p- γ - γ , and 1 × p-p- γ - γ - γ events.The spectroscopic information pertinent to the existence of multi-phonon β -vibrationalstates is presented in Figs. 1 and 2 which show the γ rays in coincidence with the 689-122 keV (2 +2 → +1 → +1 ) cascade and 841 keV (1 − → +1 ) transitions, respectively. Figure1 reveals feeding of the 2 +2
810 keV state (the “2 + β ” state): there are strong γ rays at 213,288, 356, and 414 keV which correspond to the known [13] rotational band built on the 0 +2
685 keV state; there are strong γ rays at 273 and 482 keV which arise from the pairingisomeric band [14] built on the 0 +3 γ ray is a known 13 − (2833) → +1 (2149) transition [13]. At a much higher2 IG. 1: Double-coincidence gate indicating γ rays in coincidence with the 2 +2 (810) → +1 (122) → +1 (0), 122 and 689 keV cascade γ -ray transitions in Sm. Lines indicated by a dot above thetransition are “contaminants” from an overlap with the 13 − (2833) → +1 (2149) 685 - 2 +1 (122) → +1 (0) 122 keV double-coincidence gate.FIG. 2: Coincidence gate on the 1 − (963) → +1 (122) 841 keV γ -ray transition in Sm. Detailsof the transitions are discussed in the text. energy there are two γ rays that correspond to a known transition of 959 keV from a 2 + state at 1769 keV [13] and a 1097 keV transition, which we propose as de-exciting a newstate in Sm at 1907 keV.The 841 gate shown in Fig. 2 exhibits feeding of the 1 −
963 keV state and provides animportant view of 0 + , 1 − , and 2 + states in Sm. The 320 and 329 keV γ rays come fromthe pairing isomeric band (the 320 feeds through the 329 keV transition [14]); the 696 keV γ ray arises from the known [13] 0 + γ ray comes from a new 0 + state at 1755 keV (see discussion later); the 806 keV γ ray de-excites the 2 + γ rays are all known (see below) to feed the 963 keV state and nearly all3re observed in the β decay of Pm ( T / = 4 . J π = 1 + ) which preferentially populatesstates in Sm with J ≤ + states in Sm.However, there is no evident candidate 0 + state corresponding to a two-phonon β -vibration.A two-phonon to one-phonon transition is expected to have significant collective E +2 (810) → +1 (122) 563 keV transition is a collective transitionwith a B ( E
2) of 33 Weisskopf units (W.u.) [13]. If the 0 +2
685 keV state is a one-phononvibrational state, then the transition to this level from a two-phonon state should have a B ( E
2) = 45 W.u. [10]; our further investigation of this issue is described below.To complement the multi-Coulex results, we carried out an ( n, n ′ γ ) study of Sm at theUniversity of Kentucky with monoenergetic neutrons. The data obtained included excitationfunctions ( E n in 0.1 MeV increments from 1.2 to 3.0 MeV), γ -ray angular distributions,Doppler-shifted γ -ray energy profiles, and γ − γ coincidences (details of similar analysesmay be found in [15]). These data provide comprehensive information on low-spin states,including spins, decay branches, and lifetimes to ≥ . + two-phonon β vibration.The previously known [13] excited 0 + states in Sm are at 684.7 (the putative one-phonon β vibration [9]), 1082.9 (a pairing isomer [14]), and 1659.5 keV. We establish a new0 + state at 1755.0 keV and tentatively assign J π = 0 + or 1 − states at 1892.4, 1944.7, 2042.8,2091.2, and 2284.9 keV based upon spectroscopy selection rules (cf. Fig. 2). We focushere on the 1659.5 and 1755.0 keV 0 + states. Excitation function data for these states areshown in Fig. 3. These data can be compared with the plotted curves of theoretical directpopulation of the level as a function of neutron energy and level spin, calculated with theCINDY computer code [16] using input optical model parameters from the RIPL-2 database[17]. The best agreement between plotted data and theoretical curves indicates the 1659.5and 1755.0 keV levels are spin-0 states. From Doppler-shifted energies of decaying γ rays,lifetimes of 177 +65 − and 242 +129 − fs are deduced, respectively, for the 1659.5 and 1755.0 keVstates, and the data are shown in Fig 4. From the decay paths established (from thepresent work and [13]) for these states we deduce B ( E
2; 0 + , → +2 , B ( E
2; 0 + , → +2 , < β vibrations exist in Sm. Thus, it does not seem useful to interpret the0 + β vibration. We discuss the large B ( E
2; 0 +2 → +1 ) below. (Thecollectivity implied by the observation of the 959 and 1097 keV γ rays in Coulomb excitation,cf. Fig. 1, is assigned to a K π = 2 + collective excitation associated with the 0 +2 β -vibrational 0 + state in the energy rangestudied, i.e., up to ∼ + state at 685 keV should notbe interpreted as a β vibration. Rather, we explore a shape coexistence interpretation ofthe ground band and “ β ” band in Sm, and have carried out a simple two-band mixingcalculation. The band energies for the less-deformed structure were taken from [18, 19] theground-state band of
Ce and for the more-deformed structure from
Sm: these are less-deformed and more-deformed nuclei adjacent to the region formed by
Nd,
Sm,
Gd,and
Dy.The key to fixing the relative energies of these two bands lies in the ρ ( E
0) values [20, 21]between them which is a maximum for J ≥
4. If the monopole strength is taken to be given4
IG. 3: Gamma-ray excitation functions and angular distributions for transitions that depopulatethe 0 +4 +5 γ rays following the ( n, n ′ γ ) reaction on Sm.Lifetimes of the 0 +4 +5 by the Eu isotope shift [22] at N = 90, i.e., δ h r i = 0 .
39 fm , then using [21] ρ J ( E · = Z R (cid:2) ∆ h r i (cid:3) · α J β J (1)the two unmixed bands should be degenerate at J ≃
6. This will produce maximal mixing( α = β = 1 /
2) and maximal ρ → ( E
0) = 1 / Z /R [ δ h r i ] = 87 × − . With thisprescription, a mixing strength of V J = 310 keV for all J values reproduces the energiesof the lowest two K = 0 + bands very closely, as shown in Table I. The ρ ( E
0) valuesbetween the bands are given in Table I. The isomer shift between the 0 +1 and 2 +1 states δ − h r i / h R i = 4 . × − (calc.), cf. 5 . × − (expt. [23]). The agreement supportsthis description.The B ( E
2) values between, and within, these bands can be simply described usingGrodzins’ rule [24] relating E (2 +1 ) to B ( E
2; 0 +1 → +1 ) and rotor J-value dependence of5 ABLE I: Comparison of experimental data for the lowest two K = 0 bands in Sm with valuescalculated using a two-band mixing model.
Level energy (keV)Expt. [13] Calc. J π band 1 band 2 band 1 band 20 + +
122 810 140 7974 +
366 1023 393 10236 +
706 1311 730 13508 + × ρ ( E +2 → +1
51 (5) 722 +2 → +1
69 (6) 774 +2 → +1
88 (14) a +2 → +1 +2 → +1 B ( E
2) (W.u.)Transition Expt. [13, 25] Calc.2 +1 → +1
144 (3) 1334 +1 → +1
209 (7) 1976 +1 → +1
245 (9) 2302 +2 → +2
167 (16) 1704 +2 → +2
255 (45) 2330 +2 → +1
33 (4) 312 +2 → +1 .
96 (9) 12 +2 → +1 . +2 → +1
18 (2) 234 +2 → +1 .
75 (13) 14 +2 → +1 . +2 → +1
16 (5) 21 a Calculated using data from [13] and [31]. E B ( E
2) values is closely reproduced. In particular, the excited K = 0 band is correctly de-scribed as more collective [25] than the ground band and B ( E
2; 0 +2 → +1 ) is well reproducedby the mixing, i.e., the significant strength of this transition does not necessitate invoking β -vibrational character.The present results are in disagreement with the concept of a β vibration and with acritical point interpretation of the low-energy collective structure of Sm. (We note thatcertain features of the low-energy collective structure of
Sm were the original motivatingfactor for suggesting critical point behavior in nuclei [26].) However, all of the spectroscopicdata are consistent with coexisting collective structures [27] in
Sm.A possible explanation of the present result is that the shape coexistence is arising fromthe influence of the Z = 64 subshell gap at N = 90, which can give rise to the coexistence ofdifferent proton pair structures, similar to the familiar intruder structures associated withmajor shells [27]. An indication of this effect is implicit in the discussions of Burke [28] andGarrett [9] based on single-proton transfer population of the states in Sm [29]. We notethat in [29] it was found that the ( t, α ) population of the 2 +1 and 2 +2 states in Sm was inthe ratio ∼ Eu target nucleus. This translates into a ratio of β /α = 0 .
707 for the mixingamplitudes of the 2 + states, which can be compared with our band-mixing calculation for6hich β /α = 0 . Z = 64, can be directly investigated through systematicstudies of the N = 90 isotones. There is also a systematic picture [30] of band mixing at N = 60 near Z = 40 which may possess similarities.We wish to thank colleagues at the LBNL 88-Inch Cyclotron and the University of Ken-tucky monoenergetic neutron facility for their assistance in these experiments. This workwas supported in part by DOE grants/contracts DE-FG02-96ER40958 (Ga Tech), DE-AC03-76SF00098 (LBNL), and by NSF awards PHY-0244847 (Rochester) and PHY-0354656 (Ken-tucky). ∗ Present address: Lawrence Livermore National Laboratory, Livermore, California 94551, USA † Present address: TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T 2A3,Canada[1] A. Bohr and B. R. Mottelson,
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