New supersymmetric quartet of nuclei in the A ∼ 190 mass region

RAPID COMMUNICATIONS PHYSICAL REVIEW C 79, 031304(R) (2009) New supersymmetric quartet of nuclei in the A∼190 mass region J. Barea,1,*R. Bijker,2A. Frank,2G. Graw,3R. Hertenberger,3H.-F. Wirth,3,4S. Christen,5J. Jolie,5D. Tonev,5M. Balodis,6 J. B¯ erzin¸ˇ s,6N. Kr¯ amere,6and T. von Egidy4 1Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, P. O. Box 208210, New Haven, Connecticut 06520-8120, USA 2Instituto de Ciencias Nucleares, Universidad Nacional Aut´ onoma de M´ exico, A. P. 70-543, 04510 M´ exico, D. F., M´ exico 3Sektion Physik, Ludwig-Maximilians-Universit¨ at M¨ unchen, D-85748 Garching, Germany 4Physik-Department, Technische Universit¨ at M¨ unchen, D-85748 Garching, Germany 5Institut f¨ ur Kernphysik, Universit¨ at zu K¨ oln, D-50937 K¨ oln, Germany 6Institute of Solid State Physics, University of Latvia, Riga, LV-1063, Latvia (Received 28 November 2008; published 16 March 2009) We present evidence for a new supersymmetric quartet in the A∼190 region of the nuclear mass table. New experimental information on transfer and neutron capture reactions to the odd-odd nucleus 194Ir strongly suggests the existence of a new supersymmetric quartet, consisting of the 192,193Os and 193,194Ir nuclei. We make explicit predictions for the odd-neutron nucleus 193Os and suggest that its spectroscopic properties be measured in dedicated experiments. DOI: 10.1103/PhysRevC.79.031304 PACS number(s): 21.60.−n, 03.65.Fd, 11.30.Pb, 27.80.+w Nuclear supersymmetry is a composite particle phenomenon that should not be confused with fundamental supersymmetry, as used in particle physics and quantum field theory, where it is postulated as a generalization of the Lorentz- Poincar´ e invariance as a fundamental symmetry of nature and predicts the existence of supersymmetric particles, such as the photino and selectron, for which, however, experimental evidence is yet to be found. If experiments about to start at the CERN Large Hadron Collider (LHC) find evidence of supersymmetric particles, the supersymmetry would be badly broken, as their masses must be much higher than those of their normal partners. In contrast to particle physics, nuclear supersymmetry has been subjected to experimental verification. Nuclear supersymmetry was proposed more than 25 years ago [1] in the context of the interacting boson model (IBM) and the interacting boson-fermion model (IBFM), which have proved remarkably successful in providing a unified framework of even-even [2] and odd-even [3] nuclei, respectively. One of its most attractive features is that it gives rise to a simple algebraic description, in which dynamical symmetries and supersymmetries play a central role, both as a way to improve our basic understanding of the importance of (super)symmetry in nuclear dynamics and as a starting point for more precise calculations. Nuclear supersymmetry provides a theoretical framework in which different nuclei are treated as members of the same supermultiplet and whose spectroscopic properties are described by a single Hamiltonian and a single set of transition and transfer operators. Originally, nuclear supersymmetry was formulated as a symmetry among pairs of nuclei consisting of an even-even and an odd-even nucleus [1,4,5]. Subsequently, by including the neutron-proton degree of freedom, it was extended to quartets of nuclei, in which an even-even, an odd-proton, an *Present address: Facultad de F´ ısica, Universidad de Sevilla, Avda. Reina Mercedes s/n, E-4012 Sevilla, Spain. odd-neutron, and an odd-odd nucleus form a supermultiplet [6]. Supersymmetry imposes strong constraints on both the collective (bosonic) and the single-particle (fermionic) degrees of freedom. Nevertheless, various nuclei have been identified as examples. The odd-odd nucleus 196Au, together with the odd-neutron nucleus 195Pt, the odd-proton nucleus 195Au, and the even-even nucleus 194Pt, have been verified experimentally using state-of-the-art techniques [7–9] to closely fulfill the rules that define a supersymmetric quartet [6,10]. The interpretation of these four nuclei as members of a supersymmetric quartet made it possible to predict [6] the properties of 196Au almost 15 years before they were measured experimentally [7,8]. It is the purpose of this paper to present evidence for the presence of a new quartet of supersymmetric nuclei in the mass A∼190 region, consisting of the 192,193Os and 193,194Ir nuclei. The evidence is based both on energies and on transfer strengths. The A∼190 region of the nuclear mass table is a particularly complex one, displaying transitional behavior such as prolate-oblate deformed shapes, γinstability, triaxial deformation, and coexistence of different configurations, which presents a daunting challenge to nuclear structure models. Despite this complexity, the A∼190 mass region has been a rich ore of empirical evidence for the existence of dynamical symmetries and supersymmetries in nuclei both for even-even, odd-proton, odd-neutron, and odd-odd nuclei, as well as for supersymmetric pairs [1,4,5] and quartets of nuclei [6–9,11]. In addition to providing a unified description of collective nuclei, the dynamical (super)symmetries of the IBM and its extensions provide a powerful tool for unraveling and classifying the spectra of complex nuclei by means of a set of closed expressions for energies, electromagnetic transition rates, and spectroscopic factors for one- and two-nucleon transfer reactions, which can be used to analyze, classify, and interpret the experimental data. As an example, we mention the interpretation of the 194,195Pt and 195,196Au nuclei as members of a supersymmetric quartet with U(6/12)ν⊗U(6/4)π 0556-2813/2009/79(3)/031304(5) 031304-1 ©2009 The American Physical Society RAPID COMMUNICATIONS J. BAREA et al. PHYSICAL REVIEW C 79, 031304(R) (2009) supersymmetry [6,7], in which the odd proton is allowed to occupy the 2d3/2orbit of the 50-82 shell, and the odd neutron the 3p1/2,3p3/2,and 2f5/2orbits of the 82-126 shell. This supermultiplet is characterized by Nπ=2 and Nν=5. In this scheme, the excitation spectra of the four nuclei that constitute a quartet are described simultaneously by a single energy formula E=A[N1(N1+5) +N2(N2+3) +N3(N3+1)] +B1(1+4) +2(2+2) +2 3 +Bσ1(σ1+4) +σ2(σ2+2) +σ2 3 +C[τ1(τ1+3) +τ2(τ2+1)] +DL(L+1) +EJ(J+1),(1) using the same values of the coefficients A, B, B,C,D,and Efor all four nuclei. The first three terms in Eq. (1) correspond to vibrational excitations and the final three to rotations. Recently, the structure of the odd-odd nucleus 194Ir was investigated by a series of transfer and neutron capture reactions [12]. The odd-odd nucleus 194Ir differs from 196Au by two protons, the number of neutrons being the same. The latter is crucial, since the dominant interaction between the odd neutron and the core nucleus is of quadrupole type, which arises from a more general interaction in the IBFM for very special values of the occupation probabilities of the 3p1/2,3p3/2,and 2f5/2orbits, i.e., to the location of the Fermi surface for the neutron orbits [13]. This situation is satisfied to a good approximation by the 195Pt and 196Au nuclei, which both have the 117 neutrons. The same is expected to hold for the isotones 193Os and 194Ir. In particular, the new data from the polarized (  d,α) transfer reaction provide crucial new information about and insight into the structure of the spectrum of 194Ir, which has led to significant changes in the assignment of levels from those in previous work [14]. Theoretically, the levels of this nucleus were interpreted successfully in terms of a dynamical symmetry in odd-odd nuclei [12]. The successful description of the odd-odd nucleus 194Ir opens the possibility of identifying a second quartet of nuclei in the A∼190 mass region with U(6/12)ν⊗U(6/4)π supersymmetry. The new quartet consists of the nuclei 192,193Os and 193,194Ir and is characterized by Nπ=3 and Nν=5. The energy spectra of the quartet of nuclei are described simultaneously by the energy formula of Eq. (1) with a single set of parameters. The pair of nuclei 192Os-193Ir has been studied as an example of U(6/4) supersymmetry by Balantekin, Bars, and Iachello [4], who found that the rotational levels in both nuclei can be described to a good approximation by C=40 keV and D+E=10 keV. The JP=0+state at 1206 keV in the even-even nucleus 192Os is interpreted as a vibrational excitation, leading to B+B=−33.5 keV, whereas the JP=3 2+state at 460 keV in the odd-proton nucleus 193Ir has been identified as the bandhead of a vibrational excitation, which gives B=−25.5 keV. More recently, the odd-odd nucleus 194Ir was studied both experimentally and theoretically in Ref. [12]. The rotational levels were described by C=35.1,D =6.3,and E=4.5 keV, in good agreement with the values determined previously for 192Os-193Ir. The available experimental information on 194Ir allowed the determination of two of the three vibrational terms, A+B=35 and B=−33.6keV. Finally, in the absence of detailed experimental information on the odd-neutron nucleus 193Os, this nucleus was not taken into account in the fit. A simultaneous fit to the energy levels in 192Os, 193Ir, and 194Ir with the energy formula of Eq. (1)givesA=41.0,B =−6.0,B=−29.0,C = 38.0,D =6.3,and E=4.5 (all in keV). The main difference with the parametrization of Ref. [14] is due to the new experimental information on the odd-odd nucleus 194Ir, which has led to an interchange in the assignments of the ground band and the first excited bands in 194Ir [12]. The fitted values of B,B,C,and D+Eare essentially the same, since in both studies they are determined from the energy spectra of the pair of nuclei 192Os-193Ir. The difference in the values of Aand D(or E) arises from the fact that in Ref. [14] they were extracted from the (scarce) experimental information on the odd-neutron nucleus 193Os, whereas in the present study we used the new detailed experimental data on the odd-odd nucleus 194Ir to determine their values. In addition, the present parameter set is closer to the parameter values determined for the quartet 194,195Pt-195,196Au [8] than in Ref. [14] (see Table I), indicating systematics in this zone of the nuclear chart. In Figs. 1–4, we compare the experimental and theoretical spectra for the quartet of nuclei 192,193Os-193,194Ir in the U(6/12)ν⊗U(6/4)πsupersymmetry scheme. Given the complex nature of the spectrum of heavy nuclei in the mass A∼190 region, and in particular that of the odd-odd nuclei, the agreement is remarkable. There is an almost one-to-one correlation between the experimental and theoretical level schemes. Whereas the even-even nucleus 192Os, the oddproton nucleus 193Ir, and the odd-odd nucleus 194Ir are wellknown experimentally, the data on the odd-neutron nucleus 193Os are rather scarce. In Fig. 2, we show the predicted spectrum for 193Os as obtained from Eq. (1)usingthe parameter set determined from a fit to the nuclei 192Os and 193,194Ir. The ground state of 193Os has spin and parity JP=3 2−, which implies that the second band with labels [7,1],7,1,0 is the ground state band, rather than [8,0],8,0,0.The assignment of levels in Fig. 2is based in part on preliminary data from the 192Os(  d,p)193Os one-neutron transfer reaction [15], which shows that the j=1 2strength goes to the state at 234 keV, whereas the j=3 2and j=5 2transfers are predominantly to the states at 103 and 73 keV, respectively. The JP=3 2−ground state is populated very weakly, whereas the first excited state at 41 keV is not seen at all in this reaction. Theoretically, these transfer reactions are described by the fermionic generators of the superalgebra which change TABLE I. Values of the parameters in keV. ABB CDERef. Os-Ir 41.0−6.0−29.038.06.34.5Present Os-Ir 63.0−9.3−24.236.1−5.115.9[14] Pt-Au 52.58.7−53.948.88.84.5[8] 031304-2 RAPID COMMUNICATIONS NEW SUPERSYMMETRIC QUARTET OF NUCLEI IN THE ... PHYSICAL REVIEW C 79, 031304(R) (2009) [8,0] 〈8,0〉 〈8,0,0〉 (0,0)0+ (1,0)2+ (2,0)2+ 4+ (3,0) 0+ 3+ 4+ 6+ (4,0) 2+ 4+ [8,0] 〈6,0〉〈6,0,0〉 (0,0)0+ Calculated 0 200 400 600 800 1000 1200 1400 Excitation energy (keV) [8,0]〈8,0〉〈8,0,0〉 (0,0)0+ (1,0)2+ (2,0) 4+ 2+ (3,0) 3+ 4+ 6+ (4,0)4+ [8,0]〈6,0〉 〈6,0,0〉 (0,0)0+ Experimental 0 200 400 600 800 1000 1200 1400 Excitation energy (keV) 192Os FIG. 1. (Color online) Comparison between the theoretical and experimental spectra of the even-even nucleus 192Os. The theoretical spectrum is calculated for the Uν(6/12) ⊗Uπ(6/4) supersymmetry scheme with Eq. (1). The parameter values are given in Table I. a boson into a fermion. In a study of the stripping reaction 194Pt →195Pt, in which the initial and final nuclei have the same number of neutrons as for 192Os →193Os, it was found that the intensities for j=1 2transfers are described by the operator [16] P(1 2)† ν=α1 2 √6˜ sνa† ν, 1 2(1 2)−√2˜ dνa† ν, 3 2(1 2)+√3˜ dνa† ν, 5 2 (1 2). (2) [8,0]〈8,0〉〈8,0,0〉 (0,0)1/2− (1,0)5/2− 3/2− (2,0) 7/2− 5/2− 3/2− [7,1]〈7,1〉 〈7,1,0〉 (1,0)5/2− 3/2− (2,0) 9/2− 7/2− 5/2− 3/2− (3,0) 1/2− (1,1) 7/2− 5/2− 3/2− 1/2− (2,1) 9/2− 7/2− 7/2− 5/2− 5/2− 3/2− 3/2− 1/2− Calculated 0 200 400 600 Excitation energy (keV) [7,1] 〈7,1〉〈7,1,0〉 (1,0)(5/2)− (3/2)− (1,1)3/2− 1/2− 1/2−,3/2− (5/2−) (5/2)− 1/2−,3/2− (5/2− ,7/2−) 1/2−,3/2− (5/2)− Experimental 0 200 400 600 Excitation energy (keV) 193 Os FIG. 2. (Color online) As in Fig. 1, but for the odd-neutron nucleus 193Os. According to the selection rules, only the JP=1 2−state with (τ1,τ 2)=(0,0),L=0 of the symmetric band with [8,0],(8,0,0) are populated. This suggests that we identify the energy level at 234 keV with this state. The one-neutron j=3 2,5 2transfer are described by the operators P(j)† ν=αj √2(˜ sνa† ν,j )(j)−(˜ dνa† ν, 1 2 )(j).(3) This operator can excite the JP=3 2−,5 2−doublets with (τ1,τ 2)=(1,0),L=2 belonging to the bands with [8,0],(8,0,0) and [7,1],(7,1,0) (see Figs. 1and 2). Since ratios of intensities do not depend on the value of the coefficient αjand provide a direct test of the wave functions, we consider the ratio Rfor the excitation of the doublet of the band with [N−1,1],(N−1,1,0) relative to that of the symmetric band [N,0],(N,0,0) [16] R(ee →on) =(N−1)(N+1)(N+4) 2(N+2) ,(4) 031304-3 RAPID COMMUNICATIONS J. BAREA et al. PHYSICAL REVIEW C 79, 031304(R) (2009) 〈15/2,1/2,1/2〉 [7,0]〈7,0〉 (1/2,1/2)3/2+ 3/2,1/2 7/2+ 5/2+ 1/2 + (5/2,1/2) 7/2+ 5/2+ 3/2+ 〈13/2,1/2,−1/2〉 [7,0]〈7,0〉 (1/2,1/2) 3/2+ Calculated 0 200 400 600 800 Excitation energy (keV) 〈15/2,1/2,1/2〉 [7,0]〈7,0〉 (1/2,1/2)3/2+ (3/2,1/2) 7/2+ 5/2+ 1/2+ (5/2,1/2) 5/2+ 3/2+ (7/2)+ 3/2+ (9/2)+ (1/2)+ 5/2+ Experimental 0 200 400 600 800 Excitation energy (keV) 193Ir FIG. 3. (Color online) As in Fig. 1, but for the odd-proton nucleus 193Ir. which gives R=37.8 for the stripping reaction 192Os →193Os (with N=Nπ+Nπ=8), i.e., most of the strength goes to the doublet with [7,1],(7,1,0). For this reason, we assign the states at 103 and 73 keV as the (τ1,τ 2)=(1,0),L=2 doublet of the [7,1],(7,1,0) band. Finally, the ground state and the first excited state of 193Os are assigned as members of a JP=3 2−,1 2−doublet with (τ1,τ 2)=(1,1),L=1ofthe[7,1],(7,1,0) band, since neither of these states can be excited by the transfer operators of Eqs. (2) and (3). 〈15/2,1/2,1/2〉 [7,0]〈7,0〉 (1/2,1/2)2− 1− 3/2,1/2 4− 3− 3− 2− 1− 0− (5/2,1/2) 3− 2− 2− 1− 〈13/2,1/2,1/2〉 (1/2,1/2) 1− 〈13/2,1/2,1/2〉 [6,1]〈6,1〉 (1/2,1/2)2− 1− (3/2,1/2)4− 3− 3− 2− 1− 0− 〈5/2,1/2〉2− 2− 1− 〈13/2,3/2,1/2〉 [6,1]〈6,1〉 (3/2,1/2) 4− 3− 3− 2− 1− 0− (5/2,1/2) 4− 3− 3− 2− 2− 1− (3/2,3/2) 5− 4− 3− 2− 2− 1− (5/2,3/2) 2− 2− 1− 1− 0− 〈11/2,1/2,1/2〉 [6,1]〈6,1〉 (1/2,1/2) 2− 1− Calculated 0 200 400 600 Excitation energy (keV) 〈15/2,1/2,1/2〉 [7,0]〈7,0〉 (1/2,1/2) 2− 1− (3/2,1/2) 4− 3− 3− 2− 1− 0− (5/2,1/2) 2− 2− 〈13/2,1/2,1/2〉 [6,1]〈6,1〉 (1/2,1/2) 2− 1− (3/2,1/2) 4− 3− 2− 1− 0 〈13/2,3/2,1/2〉 [6,1]〈6,1〉 (3/2,1/2) 4− 3− 3− 2− 1− 0− (5/2,1/2) 2− 2− (3/2,3/2) 4− 3− 2− 2− 1− Experimental 0 200 400 600 Excitation energy (keV) 194Ir FIG. 4. (Color online) As in Fig. 1, but for the odd-odd nucleus 194Ir. To establish the assignments of the energy levels of 193Os on a firmer basis and to test the predictions for their doublet structure of either nuclear supersymmetry and/or the particletriaxial rotor model [17], it is of great importance that the nucleus 193Os be studied in more detail experimentally. In conclusion, symmetries and supersymmetries play an important role in analyzing, classifying, interpreting, and understanding the spectra of complex many-body quantum systems. In this manuscript, we presented evidence of the existence of a second quartet of nuclei in the mass A∼190 031304-4 RAPID COMMUNICATIONS NEW SUPERSYMMETRIC QUARTET OF NUCLEI IN THE ... PHYSICAL REVIEW C 79, 031304(R) (2009) region with Uν(6/12) ⊗Uπ(6/4) supersymmetry, consisting of the 192,193Os and 193,194Ir nuclei. An analysis of the energy spectra of the four nuclei that make up the quartet shows that the parameter set obtained in 1981 for the pair 192Os-193Ir [4] is very close to that of 194Ir [12], which indicates that the nuclei 192,193Os and 193,194Ir may be interpreted in terms of a quartet of nuclei with U(6/12)ν⊗U(6/4)πsupersymmetry. The supersymmetry in this new quartet of nuclei is satisfied with an accuracy comparable to, if not better than, that found in the 194,195Pt and 195,196Au nuclei, which was theoretically predicted almost 25 years ago and confirmed in 1999. Nuclear supersymmetry establishes precise links among the spectroscopic properties of different nuclei, a fact that has been used in this Rapid Communication to predict the energy spectrum of the odd-neutron nucleus 193Os from the known properties of the remaining three nuclei that make up the quartet. Similar relations hold for other observables, such as electromagnetic and transfer strengths. 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Frank, and J. Barea, arXiv:0902.4863 (work in progress). 031304-5