Evidence for Coexisting Shapes through Lifetime Measurements in Zr98

Abstract

The lifetimes of first excited 2 + , 4 + and 6 + states in 98 Zr were measured with the Recoil-Distance Doppler-Shift method in an experiment performed at GANIL. Excited states in 98 Zr were populated using the fission reaction between a 6.2 MeV/u 238 U beam and a 9 Be target. The γ rays were detected with the EXOGAM array in correlation with the fission fragments identified in mass and atomic number in the VAMOS++ spectrometer. Our result shows very small B(E2; 2 + 1 → 0 + 1 ) value in 98 Zr thereby confirming the very sudden onset of collectivity at N = 60. The experimental results are compared to large-scale Monte Carlo Shell model and beyond mean field calculations. The present results indicate coexistence of two additional deformed shapes in this nucleus along with the spherical ground state.The study of various modes of excitations and the associated evolution of nuclear shapes along spin and isospin axes in atomic nuclei is one of the fundamental quests in nuclear physics. While nuclei with "magic numbers" of protons and/or neutrons have spherical ground states, as one moves away, the polarizing effect of added nucleons leads to deformation. Throughout the nuclear landscape, this onset of deformation is usually a gradual process, however in neutron rich nuclei around mass A ∼ 100 the shape change is rather drastic and abrupt. The ground states of Sr and Zr isotopes with N ranging from the magic number N = 50 up to N < 60 are weakly deformed, however, they undergo a rapid shape transition from nearly spherical to well deformed prolate deformations as N = 60 is approached. The sudden nature of shape transition in Sr and Zr isotopes is evident from the abrupt changes in the two neutron separation energies [1] and mean-square charge radii [2, 3], but also from the excitation energies of 2 + 1 states and B(E2) values [4]. On the other hand, in isotopes with Z ≥ 42 the shape change is rather gradual [1,5] showing also characteristic signatures of triaxiality. This strong dependence of the observed spectroscopic properties, both on the number of protons and neutrons, makes the neutron-rich A ∼ 100 nuclei an excellent mass region for testing various theoretical models.Many experimental and theoretical studies have already been reported on the structure of these nuclei. More specifically for the Zr isotopes, the onset of deformation at N = 60 has been described by a number of theoretical models [6][7][8][9][10][11][12][13][14][15][16][17][18][19], however, none of the models have been able to successfully reproduce the aforementioned rapid change. Very recently, the abrupt shape changes were correctly described by large-scale Monte-Carlo Shell Model (MCSM) calculations [20,21]. In the so-called type-II shell evolution scenario, the (prolate) deformed states in the isotopes with N ≥ 60 are associated with proton excitations to the 0g 9/2 orbital. Driven by the central and tensor components of the effective (proton-neutron) interactions, these excitations result in a lowering and subsequent filling of the neutron 0g ...

Shape transitions between and within Zr isotopes

“…[8,10], as well as the B(E2) value obtained in Ref. [9] of 2.9(6)(2) W.u., having a similar combined uncertainty. Therefore, in the following we will use the average value of the present work and [9] of 2.8(6) W.u.…”

“…[9] of 2.9(6)(2) W.u., having a similar combined uncertainty. Therefore, in the following we will use the average value of the present work and [9] of 2.8(6) W.u. This value is incorporated into the systematics shown in Fig.…”

“…(using the average of this work and Ref. [9]). Hence, the ground state of 98 Zr is the non-collective counterpart of the ground states of the lighter Zr isotopes, and the first excited 0 + 2 state has significant collectivity, with the 2 + 1 state built on it as a collective excitation.…”

“…Another radioactive-beam experiment at GANIL used in-beam U fission reactions to obtain 98 Zr and employed the recoil-distance Doppler-shift (RDDS) technique for a direct lifetime measurement [9]. The resulting lifetime further constrained the B(E2) value of interest to 2.9(6)(2) W.u., where the error bars from the measured lifetime and known branching ratio of the state are given separately.…”

“…to the ground state [7]. For 98 Zr, until recently [8,9] only the rather high excitation energy of the 2 + 1 state of 1223 keV has been known, but it was not clear whether the assumingly coexisting more collective structure already mixes into its wave function. The latter can be determined from the measurement of its B(E2) transition probability to the ground state.…”