application/xmlProton–neutron structure of the N=52 nucleus 92ZrV WernerD BelicP von BrentanoC FransenA GadeH von GarrelJ JolieU KneisslC KohstallA LinnemannA.F LisetskiyN PietrallaH.H PitzM ScheckK.-H SpeidelF StedileS.W Yates92ZrNRF(γ,γ′)Shell modelMixed symmetryIBMA=92Physics Letters B 550 (2002) 140-146. doi:10.1016/S0370-2693(02)02961-1journalPhysics Letters BCopyright © 2002 Elsevier Science B.V. All rights reserved.Elsevier B.V.0370-26935503-419 December 20022002-12-19140-14614014610.1016/S0370-2693(02)02961-1http://dx.doi.org/10.1016/S0370-2693(02)02961-1doi:10.1016/S0370-2693(02)02961-1http://vtw.elsevier.com/data/voc/oa/OpenAccessStatus#Full2014-01-01T00:14:32ZSCOAP3 - Sponsoring Consortium for Open Access Publishing in Particle Physicshttp://vtw.elsevier.com/data/voc/oa/SponsorType#FundingBodyhttp://creativecommons.org/licenses/by/3.0/JournalsS300.2PLB19342S0370-2693(02)02961-110.1016/S0370-2693(02)02961-1Elsevier Science B.V.ExperimentsFig. 1Excitation energies of the lowest states in N=52 isotones. The effect when the p(2p1/2) orbital is filled can clearly be seen in the energy of the 0+2 state. The E2 strengths of the 2+1 and the 2+1,ms states are lowered and enhanced by almost the same factor approaching Z=40, as seen in the middle panel using a logarithmic scale. The lower panel shows the B(M1) strength between the 2+1 and the 2+1,ms states which is lowered towards Z=40, but still large.Fig. 2Comparison of experimental (left) and calculated (right) level energies in 92Zr. Levels that are compared in Table 2 or in the text are connected by dashed lines.Fig. 3Comparison of the low-lying levels of 90Zr, 90Sr and 92Zr. Proton and neutron states of the A=90 nuclei are connected by lines to states in 92Zr with which they can be identified. Known E2 transition strengths to the ground state are given above the corresponding levels.Table 1Amplitudes of the main configurations to the wave functions of the lowest 0+, 2+ and 4+ states. Neglected components contribute each less than 10% to the total wave functions0+10+22+12+24+14+2π(p1/22)0×ν(d5/22)J−0.60−0.61−0.58−0.460.690.29π(g9/22)0×ν(d5/22)J0.58−0.550.580.10−0.63−0.06π(g9/22)J×ν(d5/22)0−−0.26−0.66−0.170.72Table 2Some transitions among positive-parity low-spin states in 92Zr. Shell-model results are compared to data. For some states g-factors are given. Data marked with an asterisk ∗ was measured for the first time in our experiment. The spin assignment was corrected for the level at 3472 keV. For the J=1 states positive parity is assumed for the experimental results and transitions to 2+ states are given under the assumptions of pure M1 and E2 strengths. Some states are labeled by their energies in keV, where experimental uncertanties amount to at most 1 keVJπiJπfB(Πλ)JπiJπfB(Πλ)Exp.SMExp.SM2+10+16.4(6) W.u.6.0 W.u.1(−)33700+10.037(4)∗0+22.9(1) W.u.1.1 W.u.10−3 e2fm2g(2+1)−0.18(1)−0.081+3472∗0+10.094(4) μN2∗0.14 μN22+20+13.7(8) W.u.∗2.7 W.u.2+1(<)8.0(6) W.u.∗1.3 W.u.2+10.46(15) μN2∗0.39 μN2(<)0.089(6) μN2∗0.03 μN20.3(1) W.u.∗0.2 W.u.0+20.08(1) μN2∗0.15 μN2g(2+2)–+0.913638∗0+10.093(4) μN2∗2+32630+11.0(1) W.u.∗0.2 W.u.0+20.08(1) μN2∗2+10.16(2) μN2∗0.20 μN213667∗0+10.0037(6) μN2∗0.004 μN22+35000+10.17(1) W.u.∗0.2 W.u.13697∗0+10.016(2) μN2∗4+12+14.04(12) W.u.4.4 W.u.2+1(<)2.8(5) W.u.∗g(4+1)−0.50(11)−0.32(<)0.036(7) μN2∗4+22+1–3.0 W.u.13915∗0+10.022(3) μN2∗4+1–0.79 μN2–0.1 W.u.Table 3Matrix elements for E2 transitions. The second and third columns give the expectation values of the bare transition quadrupole operator, before taking into account the effective charges, for protons and neutrons, respectively. The last columns give the calculated isoscalar (IS) and isovector (IV) matrix elementsTransition〈(r2Y2)p〉〈(r2Y2)n〉IS (%)IV (%)2+1→0+1−0.8−18.254.445.62+2→0+11.8−1.41.598.5Table 4Orbital and spin contributions to the M1 matrix elements between the calculated 2+2 and 2+7 levels, and the 2+1 as final stateTransition3/4π〈gplLp〉3/4π(〈gpsSp〉+〈gnsSn〉)[μN][μN]2+2→2+1−0.691−0.7092+7→2+1−0.0571.061Proton–neutron structure of the N=52 nucleus 92ZrVWerneravw@ikp.uni-koeln.deDBelicbPvon BrentanoaCFransenacAGadea1Hvon GarrelbJJolieaUKneisslbCKohstallbALinnemannaA.FLisetskiyaNPietrallaaH.HPitzbMScheckbK.-HSpeideldFStedilebS.WYatescaInstitut für Kernphysik, Universität zu Köln, Zülpicher Str. 77, 50937 Köln, GermanybInstitut für Strahlenphysik, Universität Stuttgart, Allmandring 3, 70569 Stuttgart, GermanycDepartments of Chemistry and Physics & Astronomy, University of Kentucky, Lexington, KY 40506-0055, USAdInstitut für Strahlen- und Kernphysik, Universität Bonn, Nußallee 14-16, 53115 Bonn, Germany1Present address: NSCL, Michigan State University, East Lansing, MI 48824, USA.Editor: V. MetagAbstractFollowing the successful identification of mixed-symmetric one- and two-phonon states in the N=52 nuclei 94Mo and 96Ru, we have performed a photon scattering experiment on the N=52 isotone 92Zr. Experimental data and shell model calculations show that both, single particle and collective degrees of freedom are present in the low-lying levels of 92Zr. The second excited quadrupole state shows the signatures of the one-phonon mixed-symmetric 2+ state, while calculations and data indicate an almost pure neutron configuration for the 2+1 state, in contradiction with the F-spin symmetric limit. Furthermore, two strong dipole excitations, which are candidates for the two-phonon quadrupole–octupole coupled E1 excitation and for the mixed-symmetric 1+ two-phonon state, were observed.PACS21.10.Re21.10.Tg21.60.Cs25.20.DcKeywords92ZrNRF(γ,γ′)Shell modelMixed symmetryIBMA=92Recently, the first firm evidence for a comprehensive multi-phonon structure with mixed proton–neutron symmetry was found in the nuclide 94Mo [1–3]. This discovery is significant since it demonstrates the (at least approximate) validity of the F-spin limit of the IBM even in weakly-collective, soft nuclei by the sheer existence of relatively pure mixed-symmetry (MS) states. This information is complementary to the analysis of forbidden M1 transitions or the observation of F-spin multiplets with rather constant energies in deformed nuclei, where the dominating proton–neutron quadrupole–quadrupole interaction ensures anyways an extensive proton–neutron symmetry of low-lying states. However, in weakly-collective nuclei near shell closures other parts of the nuclear Hamiltonian, which much more sensitively depend on the local shell structure, compete with the quadrupole–quadrupole interaction. In the proton–neutron version of the interacting boson model (IBM-2) [4–7], the proton–neutron symmetry of the wave functions is quantified by the bosonic analog of isospin: the F-spin. Wave functions of states with F<Fmax show MS character in that at least one pair of proton and neutron bosons is antisymmetric under the exchange of proton and neutron labels. So far, the breaking of F-spin, important especially for nuclei near closed shells, has not yet been tested experimentally by investigating the properties of MS states. Such breaking of F-spin should appear when the degree of collectivity decreases. Thus, it is important to follow the evolution of collectivity with decreasing number of valence particles. Results from such investigations should also affect the so far investigated N=52 isotones, e.g., the well investigated 94Mo, where certain deviations from a collective picture appear like the small E(4+1)/E(2+1) ratio of 1.8. It has to be clarified how collective and non-collective features interfere in such nuclei with the final aim to eludicate the microscopy underlying the collective excitations. An investigation of MS states of nuclei at sub-shell closures is sensitive to the formation of F-spin symmetry. Our approach will be the investigation of the nucleus 92Zr that can be expected to show single-particle degrees of freedom due to the sub-shell closure at Z=40. We will show that collective MS structures can be identified in this nucleus, together with structures showing considerable F-spin breaking, arising from the Z=38, 40 sub-shell closures. This is important information for the understanding of collectivity in nuclei and the evolution towards the F-spin limit. Our new experimental data on lifetimes in 92Zr is discussed in comparison with shell model calculations.In the F-spin limit, an intuitive picture of the MS states is provided by the Q-phonon scheme [8–10]. In analogy to the isoscalar one-phonon 2+1 state, the lowest MS state is the isovector one-phonon 2+1,ms state with F=Fmax−1. This 2+1,ms state is expected to decay by a weakly collective isovector E2 transition to the ground state and by a strong M1 transition to the 2+1 state. Additional states with F=Fmax−1 are derived by coupling the symmetric and the MS quadrupole phonons, (2+1⊗2+1,ms)(J+), leading to a quintuplet of MS two-phonon states (0+,1+,2+,3+,4+). Such scheme was already suggested for vibrational nuclei in the sixties [11]. The most easily accessible member of this quintuplet is the 1+ms state, which is referred to as the scissors mode [12,13] in well-deformed rotors. While the scissors mode has been well studied in the rare earth region, e.g., in electron-scattering and photon-scattering experiments, there is little data for nuclei near shell closures. Even less data is available for the one-phonon 2+1,ms state. After partial evidence [14] a definite assignment could be made from absolute M1 strengths in a few cases, e.g., in [15–19]. Recently, the discussion of MS states has been strongly stimulated by a series of measurements on the nearly spherical nucleus 94Mo [1–3], where the first firm evidence for such states was found in a photon-scattering experiment. Similar structures have been identified in 96Ru [20,21] and, most recently, in 66Zn [22]. 94Mo and 96Ru are N=52 isotones. Investigations in the shell model for 94Mo [23] showed that collective degrees of freedom compete with non-collective phenomena, e.g., enhanced M1 strength due to spin-flip transitions. Nevertheless, the calculations showed that a considerable amount of the M1 strengths between MS and symmetric states have orbital and thus collective character. This is also supported by a recent, even more realistic, QPM analysis of 94Mo [24], clearly identifying symmetric and MS states.In the A≈90 mass region, we find an interesting situation. These nuclei are near the N=50 neutron shell closure. We find proton sub-shell closures at Z=38 and Z=40. The region is thus ideal for investigating the microscopic origin of collective structures approaching the double shell closures. The nucleus 92Zr with only two neutrons above 90Zr (Z=40, N=50), or two protons and two neutrons above the doubly closed shell nucleus 88Sr (Z=38, N=50), is an ideal testing ground for the evolution of collective structures. Assuming good F-spin, the 2+2 state can be expected to have the simple structure |2+1,ms〉∝|2+π〉−|2+ν〉, compared to the structure |2+1〉∝|2+π〉+|2+ν〉 of the first excited 2+ state. In 92Zr it can be tested whether this simple scheme applies or to what extent F-spin is broken. In addition, the restriction to the small number of valence particles enables us to perform calculations in the shell model, providing information on and an at least qualitative understanding of the delicate interplay between the proton–neutron degrees of freedom.The experiment was performed at the 4.3 MV Dynamitron accelerator of the Stuttgart University. The method of inelastic photon scattering (γ,γ′) was used, where target nuclei are excited by the resonant absorption of real photons. The excited states decay back to the ground state or to lower-lying excited states. This phenomenon is known as nuclear resonance fluorescence (NRF) [25]. The γ radiation from the decay of the excited states is detected in three HPGe detectors (100% efficiency each, relative to a 7.6×7.6 cm2 NaI/Tl detector), which surround the target at angles of 90°, 127° and 150° relative to the beam axis. If ground state transitions from excited states are observed, one can in most cases easily distinguish between dipole or quadrupole excitations. Our target consisted of 1.351 g ZrO2, enriched in 92Zr to 91.4%. For online calibration of the photon flux, 0.761 g of 27Al was added to the target, resulting in a direct measurement of the integrated cross sections Is,0 of excited states in 92Zr. With knowledge of the complete decay behavior of the observed states, ground state decay widths Γ0, lifetimes τ, and absolute transition strengths can be deduced. For more details on the NRF technique and the setup in Stuttgart see [25]. In total we observed the resonance excitation of nine states of 92Zr, three of them having spin and parity Jπ=2+ and the other six spin J=1. The largest part of the observed dipole excitation strength is concentrated in the J=1 states at 3.472 and 3.638 MeV.The lifetime of the 2+2 state in 92Zr was measured here for the first time. From the known small E2/M1 multipole mixing ratio (see [26]) of the dominant M1 2+2→2+1 transition and its measured short lifetime of only 118+33−21 fs, the 2+2 state in 92Zr shows the structure expected for a MS one-phonon quadrupole excitation. The M1 matrix element between both states amounts to |〈2+1||M1||2+2〉|=1.52(26)μN. This is the first time that the 2+2 state of a weakly deformed nucleus is identified as the one-phonon MS state. Combining the data on 96Ru and 94Mo with the new results in 92Zr, one observes a decrease of the energy of the one-phonon 2+1,ms state in the N=52 isotones, as the Z=38 sub-shell closure is approached, as shown in the upper panel of Fig. 1. Additionally, the E2 strengths of the 2+1 and the 2+1,ms states are lowered and enhanced, respectively, by about the same factor as seen in the middle panel of Fig. 1, while the M1 strength of the 2+1,ms state tends to be lowered (bottom panel of Fig. 1). These are the key results of this work which we will discuss in the following.In order to study the structure of the lowest 2+ states microscopically, a shell model calculation was performed for 92Zr. We used the surface delta interaction (SDI) [27] and the code Ritsschil[28], for which a new graphical interface Rits-Tk was developed by H. Klein in Cologne. 88Sr was taken as an inert core, and, as a starting point, the same shell model space and SDI parameters as for 94Mo [23] were used. The energy pattern of 92Zr was predicted well by the shell model, but the M1 excitation strength was overpredicted by at least a factor of three, and the calculated magnetic moment of the 2+1 state had a large positive value, while the experimental value of the g-factor is g(2+1)=−0.18(1) [29]. This negative g-factor hints at a large neutron contribution to the 2+1 state. In order to describe also these data, the parameter for the pn-interaction in the T=0 channel was lowered by almost 50% from the previous value of ApnT=0=0.50 MeV to ApnT=0=0.27 MeV, while the strengths of the pn, nn and pp interactions in the T=1 channel, Aρρ′T=1, were kept. Effective charges were adjusted to reproduce the ground state transition strengths of the 2+1,2 states (ep=2.2 and en=1.0); the bare orbital g-factors were set to gpl=1 and gnl=0 and the free spin g-factors with a quenching factor of 0.7 were used. The new value of ApnT=0 represents a compromise in the description of the 2+2→2+1 M1 transition strength of 0.46(15)μN2 (0.39μN2 in the model) and the g(2+1)-factor of −0.18(1) (−0.08 in the model), the calculated g-factor of the 2+2 state, g(2+2)=+0.9, hints to a substantial proton contribution to this state. A similar problem appears in the magnetic moment of the 2+1 state in 94Mo, where the new experimental value (g(2+1)=0.308(43)) [30] is in favor of a smaller value of ApnT=0, with respect to the earlier calculation [23]. In the present calculation for 92Zr the experimentally known g-factor of the 4+1 state, g(4+1)=−0.50(11) [29] is also reasonably well reproduced by the calculation giving g(4+1)=−0.32. The negative g-factors reflect the shell gap between the 2p1/2 and the 1g9/2 proton orbitals. Thus, 90Zr may, naively, be regarded as a core (see discussion in [29]), but the 2p1/2 orbital is needed for a more accurate description of the structure of the Zr isotopes. In particular, all states of 92Zr were calculated to show a substantial contribution of components with protons occupying the g9/2 orbital. The amplitudes of the main components of the wave functions of some low-lying states of 92Zr are listed in Table 1. The main components of the 0+1,2 states are those with seniority ν=0 and with both neutrons in the d5/2 orbital. The amplitudes of these main components show the similar structure of both 0+1,2 states while the relative signs ensure orthogonality. The conclusion about the almost equal contribution of the π(2p1/2)2 and the π(1g9/2)2 components to the two lowest 0+ states [31] is supported by the observation of almost equally large decay strengths of the two strongest dipole-excited levels to the 0+1 and 0+2 states (see Table 2). The relatively low proton content in the 2+1 state can be explained by the fact that neutrons in the d5/2 orbital may couple to spin J=2, while this is not possible for protons in the p1/2 orbital.Fig. 2 shows a comparison of the calculated and experimental energy patterns of some low-spin states. Besides others, two strongly excited J=1 states have been observed in the experiment. As positive parity is suggested in the Nuclear Data Sheets [26] for the level at 3.472 MeV, this state is compared to the 1+1 state from the shell model calculation in Table 2, which represents the (2+1⊗2+1,ms)1+ms two-phonon state. In this case, the other strongly excited J=1 state at 3.638 MeV should be identified with the expected (2+1⊗3−1)(1−) state and would indicate a large anharmonicity in the quadrupole–octupole coupling. In a harmonic coupling scheme this state would be expected close to the sum-energy E(2+1)+E(3−1)=3.274 MeV of both constituents, where no strong dipole excitation was observed. Nevertheless, positive parity for this state cannot be excluded. For simplicity, all dipole excitations with unknown parities are listed as M1 excitations in Table 2.The experimental and calculated transition strengths of the lowest 2+ states are compared in Table 2 and show good agreement. In order to analyze the isoscalar or isovector character of the lowest 2+ states in 92Zr in the shell model one can examine the extent to which the wave functions are exhausted by components with seniority ν=2 and Jπρ=2+ρ (ρ=p,n), as was done in Ref. [23]. For the 2+1 state we calculate a portion of neutron (ν=2, J=2) configurations of 83%, while the proton configurations of this kind amount to only 9% in squared amplitude. Therefore, the 2+1 state is mainly a neutron excitation, supporting large F-spin breaking. However, the 2+2 state does not have an equally dominant proton character, but the (ν=2, J=2) configurations for protons and neutrons are more similar, namely 59% protons and 26% neutrons. The matrix elements of the bare E2 transition operator without effective charges, 〈(r2Y2)p,n〉, for the transitions 2+1,2→0+1 are shown in Table 3. One finds that the 2+2 state shows isovector character, while neither isoscalar nor isovector character can be assigned to the 2+1 state. The amplitudes of the main components of both 2+ states are given in Table 1.The shell model predicts another 2+ state around 3.5 MeV with a considerable ground state transition strength, which also decays to the 2+1 state by a strong M1 transition. This state may be identified with the 2+ state at 3.263 MeV observed in our experiment. In Table 4 the matrix elements of the orbital part 3/4π〈gplLp+gnlLn〉 (gnl=0) and the spin part 3/4π〈gpsSp+gnsSn〉 of the M1 transition operator are given, where Lρ and Sρ denote the total orbital and spin operators for protons and neutrons, respectively. The structure of the calculated high-lying 2+ state is different from that of the 2+2 state. The M1 transition strength originates to almost 100% from the spin part of the M1 transition operator, while the 2+2→2+1 M1 transition strength decomposes almost equally into orbital and spin parts.In Table 2 the shell model results for the lowest two 4+ states are included. A large M1 strength between the two states is predicted, which hints at an isovector structure for either the 4+1 or the 4+2 state. A similar situation has been observed in 94Mo. Analyzing the (ν=2, J=4) proton and neutron contents of these states in the shell model, we find that 89% of the 4+1 state is exhausted by (ν=2, J=4) neutron configurations and only 4% by (ν=2, J=4) proton configurations, while the 4+2 state contains 11% (ν=2, J=4) neutron configurations but 69% (ν=2, J=4) proton configurations. Again, as shown in Table 1, the main components of the wave functions are those with both neutrons in the d5/2 orbital. Lifetimes of these states and measurements of the multipole mixing ratios of their decays would be very desirable in order to obtain absolute transition strengths.The data and calculations for the low-lying level scheme of 92Zr lead to a very intuitive picture for the proton–neutron structure of the low-lying states, as shown in Fig. 3. In this picture states in 92Zr are regarded as being composed by proton and neutron configurations as found in the even–even neighboring nuclei 90Zr and 90Sr, respectively. The situation that proton and neutron configurations are well separated in energy like in this case leads to severe F-spin breaking as the configurations do not mix strongly. Thus, we get a low-lying neutron 2+1 state and expect a higher-lying proton 2+2 state in 92Zr. But a second higher-lying neutron 2+ configuration from 90Sr mixes with the proton configuration from 90Zr. Thus, the 2+2 state in 92Zr gets contributions from both, valence protons and neutrons. Similar arguments can be given for 4+ states. The low-lying excited 0+2 state is not present in 90Sr due to its two-proton character that is also responsible for its lowering as seen in Fig. 1. The approaching of the excitation strengths of the symmetric and MS 2+ states, and the lowering of the M1 transition strength between them can be explained by the decreasing proton content of the 2+1 state, which was modeled by using a smaller proton–neutron interaction in the calculation. This means that F-spin breaking results from a lowering of the pn interaction, which is known to be mainly due to the quadrupole–quadrupole pn interaction, like Qπ.Qν in the IBM-2. The situation is similar for 94Mo. But, the proton 2+ configuration in 92Mo is much lower than the one in 90Zr and one should take into account an attractive force between neutrons in the d5/2 and protons in the g9/2 orbitals. Thus we can expect better F-spin for states in 94Mo than for 92Zr. This is supported by the data on MS structures in these nuclei.To summarize, based on measurements of absolute B(M1) strengths, the energies of the low-lying levels in 92Zr in comparison to 90Zr and 90Sr, a previous measurement of the g(2+1) factor, and a shell model calculation, we have obtained the following conclusions. (1) The 2+1 state in 92Zr is a rather pure neutron excitation. Thus, it is not an isoscalar excitation and shows that F-spin is severely broken in 92Zr at low energies. (2) The 2+2 state is predominantly an isovector quadrupole excitation. Thus, it can be assigned as the searched for 2+1,ms mixed-symmetry state. (3) There is considerable dipole strength, most concentrated in two dipole excitations, around 3.5 MeV. (4) In accordance with previous authors [31], the 0+1 and 0+2 states are strongly mixed configurations. 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