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Register a new userNuclear incompressibility from spherical and deformed nuclei
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We present an analysis based on the deformed Quasi Particle Random Phase Approximation, on top of a deformed Hartree-Fock-Bogoliubov description of the ground state, aimed at studying the isoscalar monopole and quadrupole response in a deformed nucleus. This analysis is motivated by the need of understanding the coupling between the two modes and how it might affect the extraction of the nuclear incompressibility from the monopole distribution. After discussing this motivation, we present the main ingredients of our theoretical framework, and we show some results obtained with the SLy4 and SkM$^{*}$ interactions for the nucleus ${}^{24}$Mg.
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The incompressibility (compression modulus) $K_{rm 0}$ of infinite symmetric nuclear matter at saturation density has become one of the major constraints on mean-field models of nuclear many-body systems as well as of models of high density matter in astrophysical objects and heavy-ion collisions. We present a comprehensive re-analysis of recent data on GMR energies in even-even $^{rm 112-124}$Sn and $^{rm 106,100-116}$Cd and earlier data on 58 $le$ A $le$ 208 nuclei. The incompressibility of finite nuclei $K_{rm A}$ is expressed as a leptodermous expansion with volume, surface, isospin and Coulomb coefficients $K_{rm vol}$, $K_{rm surf}$, $K_tau$ and $K_{rm coul}$. textit{Assuming} that the volume coefficient $K_{rm vol}$ is identified with $K_{rm 0}$, the $K_{rm coul}$ = -(5.2 $pm$ 0.7) MeV and the contribution from the curvature term K$_{rm curv}$A$^{rm -2/3}$ in the expansion is neglected, compelling evidence is found for $K_{rm 0}$ to be in the range 250 $ < K_{rm 0} < $ 315 MeV, the ratio of the surface and volume coefficients $c = K_{rm surf}/K_{rm vol}$ to be between -2.4 and -1.6 and $K_{rm tau}$ between -840 and -350 MeV. We show that the generally accepted value of $K_{rm 0}$ = (240 $pm$ 20) MeV can be obtained from the fits provided $c sim$ -1, as predicted by the majority of mean-field models. However, the fits are significantly improved if $c$ is allowed to vary, leading to a range of $K_{rm 0}$, extended to higher values. A self-consistent simple (toy) model has been developed, which shows that the density dependence of the surface diffuseness of a vibrating nucleus plays a major role in determination of the ratio K$_{rm surf}/K_{rm vol}$ and yields predictions consistent with our findings.
We developed new parameterizations of local regularized finite-range pseudopotentials up to next-to-next-to-next-to-leading order (N3LO), used as generators of nuclear density functionals. When supplemented with zero-range spin-orbit and density-dependent terms, they provide a correct single-reference description of binding energies and radii of spherical and deformed nuclei. We compared the obtained results to experimental data and discussed benchmarks against the standard well-established Gogny D1S functional.
Within a Bayesian statistical framework using the standard Skyrme-Hartree-Fcok model, the maximum a posteriori (MAP) values and uncertainties of nuclear matter incompressibility and isovector interaction parameters are inferred from the experimental data of giant resonances and neutron-skin thicknesses of typical heavy nuclei. With the uncertainties of the isovector interaction parameters constrained by the data of the isovector giant dipole resonance and the neutron-skin thickness, we have obtained $K_0 = 223_{-8}^{+7}$ MeV at 68% confidence level using the data of the isoscalar giant monopole resonance in $^{208}$Pb measured at the Research Center for Nuclear Physics (RCNP), Japan, and at the Texas A&M University (TAMU), USA. Although the corresponding $^{120}$Sn data gives a MAP value for $K_0$ about 5 MeV smaller than the $^{208}$Pb data, there are significant overlaps in their posterior probability distribution functions.
It is known that nuclear deformation plays an important role in inducing the halo structure in neutron-rich nuclei by mixing several angular momentum components. While previous theoretical studies on this problem in the literature assume axially symmetric deformation, we here consider non-axially symmetric deformations. With triaxial deformation, the $Omega$ quantum number is admixed in a single-particle wave function, where $Omega$ is the projection of the single-particle angular momentum on the symmetric axis, and the halo structure may arise even when it is absent with the axially symmetric deformation. In this way, the area of halo nuclei may be extended when triaxial deformation is considered. We demonstrate this idea using a deformed Woods-Saxon potential for nuclei with neutron number N=13 and 43.
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.
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