Alessandro Pastore

Nuclear energy density optimization: Shell structure

Background: Nuclear density functional theory is the only microscopical theory that can be applied throughout the entire nuclear landscape. Its key ingredient is the energy density functional. Purpose: In this work, we propose a new parametrization unedf2 of the Skyrme energy density functional. Methods: The functional optimization is carried out using the pounders optimization algorithm within the framework of the Skyrme Hartree-Fock-Bogoliubov theory. Compared to the previous parametrization unedf1, restrictions on the tensor term of the energy density have been lifted, yielding a very general form of the energy density functional up to second order in derivatives of the one-body density matrix. In order to impose constraints on all the parameters of the functional, selected data on single-particle splittings in spherical doubly-magic nuclei have been included into the experimental dataset. Results: The agreement with both bulk and spectroscopic nuclear properties achieved by the resulting unedf2 parametrization is comparable with unedf1. While there is a small improvement on single-particle spectra and binding energies of closed shell nuclei, the reproduction of fission barriers and fission isomer excitation energies has degraded. As compared to previous unedf parametrizations, the parameter confidence interval for unedf2 is narrower. In particular, our results overlap well with those obtained in previous systematic studies of the spin-orbit and tensor terms. Conclusions: unedf2 can be viewed as an all-around Skyrme EDF that performs reasonably well for both global nuclear properties and shell structure. However, after adding new data aiming to better constrain the nuclear functional, its quality has improved only marginally. These results suggest that the standard Skyrme energy density has reached its limits, and significant changes to the form of the functional are needed.

Giant monopole resonances and nuclear incompressibilities studied for the zero-range and separable pairing interactions

Background: Following the 2007 precise measurements of monopole strengths in tin isotopes, there has been a continuous theoretical effort to obtain a precise description of the experimental results. Up to now, there is no satisfactory explanation of why the tin nuclei appear to be significantly softer than Pb-208. Purpose: We determine the influence of finite-range and separable pairing interactions on monopole strength functions in semimagic nuclei. Methods: We employ self-consistently the quasiparticle random phase approximation on top of spherical Hartree-Fock-Bogoliubov solutions. We use the Arnoldi method to solve the linear-response problem with pairing. Results: We found that the difference between centroids of giant monopole resonances measured in lead and tin (about 1 MeV) always turns out to be overestimated by about 100%. We also found that the volume incompressibility, obtained by adjusting the liquid-drop expression to microscopic results, is significantly larger than the infinite-matter incompressibility. Conclusions: The zero-range and separable pairing forces cannot induce modifications of monopole strength functions in tin to match experimental data. (Less)

Fitting Skyrme functionals using linear response theory

It has recently been shown that the linear response theory in symmetric nuclear matter can be used as a tool for detecting finite-size instabilities for different Skyrme functionals. In particular, it has been shown that there is a correlation between the density at which instabilities occur in infinite matter and the instabilities in finite nuclei. In this paper, we present a new fitting protocol that uses this correlation to add a new additional constraint in symmetric infinite nuclear matter in order to ensure the stability of finite nuclei against matter fluctuation in all spin and isospin channels. As an application, we give the parameter set for a new Skyrme functional which includes central and spin–orbit parts and which is free from instabilities by construction.

Spurious finite-size instabilities in nuclear energy density functionals

Background: It is known that some well established parametrizations of the nuclear energy density functional (EDF) do not always lead to converged results for nuclei. Earlier studies point towards the existence of a qualitative link between this finding and the appearance of finite-size instabilities of symmetric nuclear matter (SNM) near saturation density when computed within the random phase approximation (RPA). Purpose: We aim to establish a stability criterion based on computationally friendly RPA calculations that can be incorporated into fitting procedures of the coupling constants of the EDF. Therefore, a quantitative and systematic connection between the impossibility to converge self-consistent calculations of nuclei and the occurrence of finite-size instabilities in SNM is investigated for the scalar-isovector (S=0, T=1) instability of the standard Skyrme EDF. Results: Tuning the coupling constant C1ρΔρ of the gradient term that triggers scalar-isovector instabilities of the standard Skyrme EDF, we find that the occurrence of instabilities in finite nuclei depends strongly on the numerical scheme used to solve the self-consistent mean-field equations. Once the critical value of the coupling constant C1ρΔρ is determined in nuclei, one can extract the corresponding lowest density ρcrit at which a pole appears at zero energy in the RPA response function. Conclusions: Instabilities of finite nuclei can be artificially hidden due to the choice of inappropriate numerical schemes or overly restrictive, e.g., spherical, symmetries. Our analysis suggests a twofold stability criterion to avoid scalar-isovector instabilities.

Pairing in exotic neutron-rich nuclei near the drip line and in the crust of neutron stars

Exotic and drip-line nuclei as well as nuclei immersed in a low density gas of neutrons in the outer crust of neutron stars are systematically investigated with respect to their neutron pairing properties. This is done using Skyrme density-functional and different pairing forces such as a density-dependent contact interaction and a separable form of a finite-range Gogny interaction. Hartree-Fock-Bogoliubov and BCS theories are compared. It is found that neutron pairing is reduced towards the drip line while overcast by strong shell effects. Furthermore resonances in the continuum can have an important effect counterbalancing the tendency of reduction and leading to a persistence of pairing at the drip line. It is also shown that in these systems the difference between HFB and BCS approaches can be qualitatively large.

Skyrme effective pseudopotential up to the next-to-next-to-leading order

The explicit form of the next-to-next-to-leading order (N2LO) of the Skyrme effective pseudopotential compatible with all required symmetries and especially with gauge invariance is presented in a Cartesian basis. It is shown in particular that for such a pseudopotential there is no spin–orbit contribution and that the D-wave term suggested in the original Skyrme formulation does not satisfy the invariance properties. The six new N2LO terms contribute to both the equation of state and the Landau parameters. These contributions to symmetric nuclear matter are given explicitly and discussed. Communicated by Jacek Dobaczewski

Fitting N3LO pseudo-potentials through central plus tensor Landau parameters

Landau parameters determined from phenomenological finite-range interactions are used to get an estimation of next-to-next-to-next-to-leading order (N3LO) pseudo-potentials parameters. The parameter sets obtained in this way are shown to lead to consistent results concerning saturation properties. The uniqueness of this procedure is discussed, and an estimate of the error induced by the truncation at N3LO is given.

Linear response of homogeneous nuclear matter with energy density functionals

Abstract Response functions of infinite nuclear matter with arbitrary isospin asymmetry are studied in the framework of the random phase approximation. The residual interaction is derived from a general nuclear Skyrme energy density functional. Besides the usual central, spin–orbit and tensor terms it could also include other components as new density-dependent terms or three-body terms. Algebraic expressions for the response functions are obtained from the Bethe–Salpeter equation for the particle–hole propagator. Applications to symmetric nuclear matter, pure neutron matter and asymmetric nuclear matter are presented and discussed. Spin–isospin strength functions are analyzed for varying conditions of density, momentum transfer, isospin asymmetry, and temperature for some representative Skyrme functionals. Particular attention is paid to the discussion of instabilities, either real or unphysical, which could manifest in finite nuclei.

Collective vibrational states within the fast iterative quasiparticle random-phase approximation method

An iterative method we previously proposed to compute nuclear strength functions [1] is developed to allow it to accurately calculate properties of individual nuclear states. The approach is based on the quasi-particle-random-phase approximation (QRPA) and uses an iterative non-hermitian Arnoldi diagonalization method where the QRPA matrix does not have to be explicitly calculated and stored. The method gives substantial advantages over conventional QRPA calculations with regards to the computational cost. The method is used to calculate excitation energies and decay rates of the lowest lying 2 and 3− states in Pb, Sn, Ni and Ca isotopes using three different Skyrme interactions and a separable gaussian pairing force.

Tools for incorporating a D-wave contribution in Skyrme energy density functionals

The possibility of adding a D-wave term to the standard Skyrme effective interaction has been widely considered in the past. Such a term has been shown to appear in the next-to-next-to-leading order of the Skyrme pseudo-potential. The aim of the present article is to provide the necessary tools to incorporate this term in a fitting procedure: first, a mean-field equation written in spherical symmetry in order to describe spherical nuclei and second, the response function to detect unphysical instabilities. With these tools it will be possible to build a new fitting procedure to determine the coupling constants of the new functional.