Shape Evolution of C Isotopes in (β, γ) Deformation Plane

Abstract

We study the shape evolution of C isotopes in the full (β, γ) deformation plane using a constrained Skyrme Hartree-Fock + BCS method in coordinate space. It is shown that the deformation of the energy minimum varies markedly in the (β, γ) plane as a function of mass number, which can be viewed as a clear manifestation of the spontaneous symmetry breaking effect in finite many-body systems. We also study the difference in deformations between protons and neutrons in the total (β, γ) plane. It is found that the proton and neutron quadrupole moments are almost the same in light C isotopes, while the neutron quadrupole moment is about 3 times larger than the proton one in C isotopes heavier than 16 C. The isospin symmetry of the mirror nuclei 10 C and 10 Be is also examined in connection with the deformation in the (β, γ) plane.

Quadrupole deformation(β,γ)of lightΛhypernuclei in a constrained relativistic mean field model: Shape evolution and shape polarization effect of theLü1, Zhao2, Zhou3 2011Phys. Rev. C

“…The driving force is so weak that the deformation energy E def is only 0.26 MeV and 0.11 MeV from the PK1 and NLSH parameter sets, respectively. The SHF calculation gives a E def as large as 1 MeV [76,77]. This nucleus is empirically known to be oblate in its ground state from the inelastic scattering experiments [78][79][80], which is in consistent with our result.…”

“…The energy difference between the ground state and the saddle point on the oblate side E po is 0.74 MeV, accounts for more than 1% of the total binding energy. However, this quantity is less than 40 keV in the SHF calculations [57,77], indicating that 10 C is rather γ-soft from the SHF calculations. To examine the parameter dependence of our results, we also performed the RMF calculation using the NLSH parameter set.…”

“…The ground state properties of carbon isotopes have been studied extensively with the axially deformed RMF [73][74][75] and SHF models [76] and the triaxially deformed SHF model [77]. Here we generalize the RMF calculations by considering two additional degrees of freedom: the triaxial degree of freedom for nuclear shape and the hyperon degree of freedom.…”

“…We have performed constrained RMF calculations in the (β, γ) plane for eveneven carbon isotopes from 10 C to the drip line nucleus 22 C as well as for the hyper counterparts. Note that the study of carbon isotopes with triaxially deformed SHF models for normal nuclei [77] and hypernuclei [57] are both available, while that with the RMF model is still absent.…”

“…The isotopic dependence of the deformation with triaxiality has been investigated with the SHF model in Ref. [77], where the PES's of even-even carbon nuclei in the (β, γ) deformation plane are presented and discussed. Next one can find that there are some new features from the RMF calculations.…”