The Effect Of The Softening Of The Symmetry Energy On The Ground-state Properties And Giant Resonance Of Finite Nuclei As Well As Shape Coexistence In Neutron-deficient At Isotopes In Relativistic Mean Field Theory

The effect of the softening of the symmetry energy of nuclear matter on the ground state properties and giant resonance of finite nuclei as well as the shape coexistence in neutron-deficient At isotopes are studied in relativistic mean field theory.The symmetry energy and it's density dependence is important to the study of the nuclei which are farther away fromβstable line and depart from equal numbers of neutrons and protons extremely, as well as astrophysics and so on. Since the density dependence of the symmetry energy is poorly known, even the symmetry energy at saturation density is not well constrained experimentally. In view of this, an additional mixed isoscalar-isovector nonlinear coupling term has been adopted in the model Lagrangian in the framework of relativistic mean field theory, which can soften the symmetry energy without affecting the saturation properties of symmetric nuclear matter as the expectation value of the rho-meson field is identically zero. As a simple prescription, we keep the symmetry energy fixed at an average density of 0.1 fm^-3, which produces a nearly constant proton radius and binding energy for the nucleus ²⁰⁸Pb , both of them are accurately determined experimentally; only the neutron radius, and as a consequence, the neutron skin thickness is modified. The sensitivity of the ground-state properties of neutron-rich Ca isotopes to the density dependence of the symmetry energy is studied. Neutron central density increases with the softening of the symmetry energy, while the proton density essentially remains unchanged; therefore the neutron skin (thickness) S becomes smaller; and the larger the neutron number N, the more prominent the increase of the neutron central density is. This may suggest the larger the neutron number N, the larger the change of the neutron skin S is. In addition, the linear correlation between the neutron skin and the symmetry energy at the saturation density is found. The sensitivity of neutron single particle states in Ca isotopes to the density dependence of the symmetric energy is also investigated. All neutron single orbitals are compressed in each nucleus with the softening of the symmetry energy; therefore, the neutron radius and also the neutron skin decrease. The deeply bound single particle states become deeper, while those loosely bound states become looser. As a result, the binding energy per nucleon remains unchanged.Furthermore, the relativistic mean field model is supplemented with an additional high order nucleon-ω-ρcoupling term again, and the sensitivity of the neutron skin in ²⁰⁸Pb to this additional term is studied. Calculations show that the high order nucleon-ω-ρcorrection can further soften the symmetry energy, and thus can further decrease the neutron radius of ²⁰⁸Pb without affecting other ground-state observables.The effect of the softening of the symmetry energy on the isoscalar giant monopole resonance (ISGMR ) is discussed in the framework of a fully consistent relativistic random phase approximation ( RRPA ), based on the effective Lagrangian with the mixed isoscalar-isovector nonlinear coupling term. The calculated Centroid energies of the ISGMR become larger due to the softening of the symmetry energy. A predicted value of the nuclear matter incompressibility coefficient is given by comparison between experimental and calculated energies of the ISGMR in ²⁰⁸Pb, ¹⁴⁴Sm, ¹¹⁶Sn and ⁹⁰Zr. The Centroid energies of the ISGMR of finite nuclei not only depend on the nuclear matter incompressibility coefficient, but also are related to the symmetry energy. It is found that there is a linear correlation between the Centroid energy of the ISGMR and the symmetry energy at saturation density. The RRPA calculation by using parameter sets NL3 or NLBA with the incompressibility K_nm around 240-270 MeV can reproduce the experimental ISGMR energy with a reasonable symmetry energy, those parameter sets TM1 ( K_nm=281MeV ) and NLC ( K_nm=225MeV ) with too large or too small incompressibility could not.Moreover, correlations between the isovector giant dipole resonance, the Pygmy dipole resonance ( GDR and PDR, respectively) and the symmetry energy, the neutron skin thickness in Ni even-even isotopes are investigated. The Centroid energy of the GDR is related to the variation of the neutron skin obtained by softening the symmetry energy; in contrast, that of the PDR is insensitive to that variation. It is related to the fact that the Pygmy resonance results from the excess neutrons oscillating out of phase with a core composed of equal number of protons and neutrons; and we assume the symmetry energy at the average density fixed, which has little effect on the density distribution of the excess neutrons; therefore, there is little effect on the Pygmy resonance.Finally, the energy surfaces are calculated for neutron-deficient At isotopes from the mass numbers A=190 to 207 with an axially deformed relativistic mean field approach, using a quadratic constraint scheme in a wide range of quadrupole deformations. There are several minima in the energy surface for each nucleus. The shape-coexistence, shape transition and quadrupole deformation are discussed. The shape-coexistence is associated with the occupation of the occupation the proton intruder stateΩ^Ï€= 13/2⁺ in At isotopes.