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Register a new userAlgebraic benchmark for prolate-oblate coexistence in nuclei
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We present a symmetry-based approach for prolate-oblate and spherical-prolate-oblate shape coexistence, in the framework of the interacting boson model of nuclei. The proposed Hamiltonian conserves the SU(3) and $overline{rm SU(3)}$ symmetry for the prolate and oblate ground bands and the U(5) symmetry for selected spherical states. Analytic expressions for quadrupole moments and $E2$ rates involving these states are derived and isomeric states are identified by means of selection rules.
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The yrast lines in Kr isotopes with $N=42$, 44, and 46 are investigated in a beyond mean field framework with both prolate-oblate coexistence and quasiparticle alignment taken into account. Quasiparticle orbitals with high-$j$ and low-$Omega$ on the oblate side are shown to be responsible for the sharp backbending observed in $^{82}$Kr, by driving the yrast shape from prolate to oblate. This suggests that quasiparticle alignment may not be neglected in the investigation of the shape evolution along the yrast line.
Relativistic mean field theory with the NL3 force is used for producing potential energy surfaces (PES) for series of isotopes suggested as exhibiting critical point symmetries. Relatively flat PES are obtained for nuclei showing the E(5) symmetry, while in nuclei corresponding to the X(5) case, PES with a bump are obtained. The PES corresponding to the Pt chain of isotopes suggest a transition from prolate to oblate shapes at 186-Pt.
We develop a complex scaling method for describing the resonances of deformed nuclei and present a theoretical formalism for the bound and resonant states on the same footing. With $^{31}$Ne as an illustrated example, we have demonstrated the utility and applicability of the extended method and have calculated the energies and widths of low-lying neutron resonances in $^{31}$Ne. The bound and resonant levels in the deformed potential are in full agreement with those from the multichannel scattering approach. The width of the two lowest-lying resonant states shows a novel evolution with deformation and supports an explanation of the deformed halo for $^{31}$Ne.
We consider two competing sets of nuclear magic numbers, namely the harmonic oscillator (HO) set (2, 8, 20, 40, 70, 112, 168, 240,...) and the set corresponding to the proxy-SU(3) scheme, possessing shells 0-2, 2-4, 6-12, 14-26, 28-48, 50-80, 82-124, 126-182, 184-256... The two sets provide 0+ bands with different deformation and band-head energies. We show that for proton (neutron) numbers starting from the regions where the quadrupole-quadrupole interaction, as derived by the HO, becomes weaker than the one obtained in the proxy-SU(3) scheme, to the regions of HO shell closure, the shape coexistence phenomenon may emerge. Our analysis suggests that the possibility for appearance of shape coexistence has to be investigated in the following regions of proton (neutron) numbers: 8, 18-20, 34-40, 60-70, 96-112, 146-168, 210-240,...
The mass region with A~100 and Z~40 is known to experience a sudden onset of deformation. The presence of the subshell closure $Z=40$ makes feasible to create particle-hole excitations at a moderate excitation energy and, therefore, likely intruder states could be present in the low-lying spectrum. In other words, shape coexistence is expected to be a key ingredient to understand this mass region. The aim of this work is to describe excitation energies, transition rates, radii, and two-neutron separation energies for the even-even 94-110Zr nuclei and, moreover, to obtain information about wave functions and deformation. The interacting boson model with configuration mixing will be the framework to study the even-even Zr nuclei, considering only two types of configurations: 0particle-0hole and 2p-2h excitations. On one hand, the parameters appearing in the Hamiltonian and in the E2 transition operator are fixed trough a least-squares fit to the whole available experimental information. On the other hand, once the parameters have been fixed, the calculations allow to obtain a complete set of observables for the whole even-even Zr chain of isotopes. Spectra, transition rates, radii, $rho^2(E0)$, and two-neutron separation energies have been calculated and a good agreement with the experimental information has been obtained. Moreover, a detailed study of the wave function has been conducted and mean-field energy surfaces and deformation have been computed too. The importance of shape coexistence has been shown to correctly describe the A~100 mass area for even-even Zr nuclei. This work confirmed the rather spherical nature of the ground state of 94-98Zr and its deformed nature for 100-110Zr isotopes. The sudden onset of deformation in 100Zr is owing to the rapid lowering of a deformed (intruder) configuration which is high-lying in lighter isotopes.
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