Influence of Effective Tensor Forces on the Fission Barriers of Nuclei in the Uranium Region

The influence of effective tensor forces on the fission barriers of nuclei in the uranium region has been studied. A modified Fayans energy density functional (EDF) FaNDF⁰-a, which differs from the initial energy density functional FaNDF⁰ in the inclusion of strong effective tensor interaction, has been proposed. For the ²³⁶U and ²³⁸U isotopes, this results in a significant, about 1 MeV, reduction of the first barrier, approaching the values to the known experimental values. However, a noticeable, about the same order of magnitude, difference from these experimental values remains. Possible reasons for this remaining difference are discussed.     

Interaction of the single-particle and collective degrees of freedom in non-magic nuclei: The role of phonon tadpole terms

A method of consistent treatment of phonon contributions to the self-energy and gap terms in non-magic nuclei is developed in so-called g ² approximation, where g is the creation amplitude of a low-lying phonon. The method simultaneously takes into account both usual non-local and local phonon tadpole terms. Relations that allow the tadpoles to be calculated without introduction of new parameters are derived. As an application of the method, the effect of the phonon tadpoles on the single-particle strength distribution, single-particle energies and gap values is considered. Hypothesis of the surface nature of pairing correlations is discussed in the light of the tadpole effect.     

A realistic model of superfluidity in the neutron star inner crust

A semi-microscopic self-consistent quantum approach developed recently to describe the inner-crust structure of neutron stars within the Wigner-Seitz (WS) method with the explicit inclusion of neutron and proton pairing correlations is further developed. In this approach, the generalized energy functional is used which contains the anomalous term describing the pairing. It is constructed by matching the realistic phenomenological functional by Fayans et al. for describing the nuclear-type cluster in the center of the WS cell with the one calculated microscopically for neutron matter. Previously, the anomalous part of the latter was calculated within the BCS approximation. In this work corrections to the BCS theory which are known from the many-body theory of pairing in neutron matter are included into the energy functional in an approximate way. These modifications have a sizable influence on the equilibrium configuration of the inner crust, i.e. on the proton charge Z and the radius R _c of the WS cell. The effects are quite significant in the region where the neutron pairing gap is larger.     

Kinematically correct optical potentials

The Watson multiple scattering formalism for the optical potential describing elastic nucleon-nucleus scattering is developed while paying careful attention to the kinematics. No approximations are made in handling the recoil of the target nucleus so that internal and external energies can be uniquely separated. The resultant formalism allows a careful examination of the impulse, form-factor, and closure approximations without the confusion of the admixture of recoil energies; it also allows an explicit display of the nuclear correlations due to target recoil. With the many necessary (but incompletely understood) approximations explicity displayed, it appears that their confluence makes it unlikely that meaningful information about dynamical correlations in light nuclei can be obtained from elastic double-scattering experiments.     

Approximation of the microscopic effective pairing interaction by the off-shell T matrix for free nucleon-nucleon scattering

The effective pairing interaction in the ¹ S ₀ channel as calculated microscopically within the Brueckner method for a planar slab of nuclear matter by using the separable version of the Paris nucleon-nucleon potential is investigated. The effective interaction is determined for the model space including all negative-energy single-particle states. An analysis is performed for two values of the chemical potential, μ=?8 and ?4 MeV. It is shown that, to a high precision, the effective interaction can be approximated by the off-shell T matrix for free nucleon-nucleon interaction, the T matrix in question being taken at a negative value of the total energy of two nucleons E=2μ.     

Dependence of nuclear Z factor on the chemical potential

A simple microscopic formula is derived for the renormalization factor Z of Green’s function on the basis of the self-consistency relation of many-body theory and the Brueckner method. This formula involves the derivative of the Brueckner G matrix with respect to energy. Based on the analysis of the properties of the G matrix for a slab of nuclear matter, the G matrix is approximately replaced by the off-mass-shell T matrix taken for free NN scattering at a negative energy E equal to the doubled chemical potential μ of the nucleus under consideration. The Z factor thus calculated depends strongly on μ and decreases with |μ|. This effect is important for analyzing the properties of atomic nuclei near the drip line, where μ is zero.     

Role of the surface in nuclear pairing

Recent results obtained by solving the ab initio equation for the pairing gap in a slab of nuclear matter are reviewed. They conclusively prove a surface nature of nucleon pairing in nuclei. First, the effective pairing interaction in the vicinity of the slab surface makes a dominant contribution to the gap. Second, there is a sizable surface enhancement of the pairing gap Δ(X) itself. Finally, an analysis of spatial correlation features of the anomalous density matrix shows that the local correlation length at the slab surface is very small, about 1.5 fm, but, in the interior of the slab, it is rather large, about the slab thickness. These results are in qualitative agreement with those obtained recently by Pillet and his coauthors for spherical nuclei by using the phenomenological Gogny force. An increase in the concentration of Cooper pairs at the surface of nuclei was yet another result of their study, and our present analysis confirms this indirectly.