On the anomalous <Emphasis Type="Italic">A</Emphasis> dependence of the charge radii of heavy calcium isotopes

The charge radii of calcium isotopes are calculated within the self-consistent theory of finite Fermi systems based on the Fayans energy density functional. The fluctuating contribution of low-energy vibrations, i.e., phonons is taken into account approximately. As a result, an anomalous increase in the charge radii of neutron- rich calcium isotopes observed in a recent experiment has been reproduced.     

Inelastic Neutrino Scattering on Hot Nuclei of Supernova Matter within the Theory of Finite Fermi Systems

The Nozières–Pines method for describing neutron scattering on a heated Fermi liquid (liquid ³He) is used to calculate cross sections for inelastic neutrino scattering on the isotope ⁵⁴Fe, which is an element that plays a key role in the cooling of supernovae. The calculation in question is performed on the basis of the the theory of finite Fermi systems with the aid of the DF3-a Fayans energy density functional.     

Chemical-potential dependence of the pairing gap in a nuclear-matter slab

The equation for the pairing gap Δ in a slab of nuclear matter governed by the Paris nucleon-nucleon potential is solved for various values of the chemical potential μ in the range from −8 MeV, which corresponds to stable nuclei, to −0.1 MeV, which corresponds to nuclei in the vicinity of the nucleon drip line. The slab is placed in a one-dimensional Woods-Saxon potential whose parameters are set to values typical of nuclei. Two models are considered. In the first, the potential-well depth is fixed at U ₀ = −50 MeV, the density within the slab growing as |μ| is reduced. In the second model, the density is fixed at the center of the slab, |U ₀| decreasing as |μ| is reduced. The behavior of the gap Δ as a function of μ is model-dependent. In the first model, Δ decreases with decreasing |μ|, while, in the second, it increases. At the same time, the effect of the surface enhancement of Δ becomes more pronounced with decreasing |μ| in both models. Original Russian Text ? S.S. Pankratov, E.E. Saperstein, M.V. Zverev, 2006, published in Yadernaya Fizika, 2006, Vol. 69, No. 12, pp. 2052–2063.     

Effect of superfluidity on the structure of the inner crust of neutron stars

A self-consistent, completely quantum calculation of the structure of the inner crust of neutron stars is carried out in the Wigner-Seitz approximation with a realistic phenomenological nuclear energy functional, where pair correlations of neutrons and protons are included in the explicit form. It has been shown that the superfluidity of neutrons and protons affects the structure of the ground state of the crust.     

Phonon–particle coupling effects in odd–even double mass differences of semi-magic nuclei

A method is developed to consider the particle–phonon coupling (PC) effects in the calculation of the odd–even double mass differences (DMD) in semi-magic nuclei starting from the free NN potential. The PC correction δΣ^PC to the mass operator Σ is found in g _L ²-approximation, g _L being the vertex of creating the L-phonon. The tadpole term of the operator δΣ^PC is taken into account. The method is based on a direct, without any use of the perturbation theory, solution of the Dyson equation with the mass operator Σ(ε) = Σ₀ + δΣ^PC(ε) for finding the single-particle energies and Z-factors. In its turn, they are used as an input for finding different PC corrections to the DMD values. Results for a chain of even semi-magic nuclei ^200?206Pb show that the inclusion of the PC corrections makes agreement with the experimental data significantly better.     

Local-potential approximation for the Brueckner G matrix and problem of optimally choosing model subspace

The validity of the local-potential approximation, which was proposed previously for the singlet-pairing problem in semi-infinite nuclear matter, is investigated in the Bethe-Goldstone equation for the Brueckner G matrix. For this purpose, use is made of the method developed earlier for solving this equation for a planar slab of nuclear matter in the case of a separable form of NN interaction. The ¹ S ₀ singlet and the ³ S ₁+³ D ₁ triplet channel are considered. The complete two-particle Hilbert space is split into a model and the complementary subspace that are separated by an energy E ₀. The two-particle propagator is calculated precisely in the first subspace, and the local-potential approximation is used in the second subspace. With an eye to subsequently employing the G matrix to calculate the Landau-Migdal amplitude, the total two-particle energy is fixed at E=2μ, where μ is the chemical potential of the system under consideration. Specific numerical calculations are performed at μ=?8 MeV. The applicability of the local-potential approximation is investigated versus the cutoff energy E ₀. It is shown that, in either channel being considered, the accuracy of the local-potential approximation is rather high for E ₀≥10 MeV.     

Finite Fermi systems theory and self-consistency relations

The self-consistent theory of the finite Fermi systems is outlined. This approach is based on the same Fermi liquid theory principles as the familiar theory for finite Fermi systems (FFS) by Migdal. We show that the basic Fermi system properties can be evaluated in terms of the quasiparticle Lagrangian L_q which incorporates the energy dependency effects. This Lagrangian is defined so that the corresponding Lagrange equations should coincide with the FFS theory equations of motion of the quasiparticles. The quasiparticle energy E_q defined in the terms of t he quasiparticle Lagrangian L_q according to the usual canonical rules is shown to be equal to the binding energy E_o of the system. For a given Lagrangian L_q the particle densities in nuclei, the nuclear single-particle spectra, the low-lying collective states (LCS) properties, and the amplitude of the interquasiparticle interaction are also evaluated. The suggested approach is compared with the Hartree-Fock theory with effective forces.     

Magnetic moments of spherical nuclei: Status of the problem and unsolved issues

Dipole magnetic moments of more than 100 odd spherical nuclei are calculated within the theory of finite Fermi systems. For the effective interaction of nucleons within the theory of finite Fermi systems, use is made of a version that takes into account nuclear-medium-modified amplitudes for the exchange of one pion and one rho meson. A new tensor local charge ζ _t is incorporated in the theory of finite Fermi systems in addition to the known orbital (ζ _l ) and spin (ζ _s ) local charges. Good agreement with experimental data, at a level of 0.1 to 0.2μ _N , is obtained for the overwhelming majority of the nuclei considered here. Several cases of a significant discrepancy with experimental data, at a level of 0.3 to 0.5μ _N , are revealed. Possibilities for removing these discrepancies are discussed. A detailed comparison with known results obtained within the multiparticle shell model is performed for 2p-to 1f-shell nuclei. Cases where the standard theory of finite Fermi systems must be extended by taking into account multiparticle configurations are found. Magnetic moments are analyzed for a number of long isotopic chains. Several new experimental values of magnetic moments for copper isotopes far from the beta-stability valleys are known. For the example of the copper-isotope chain, it is shown how the emergence of a deformation in the ground state of a nucleus can be revealed on the basis of a systematic analysis of magnetic moments.     

Self-consistent calculations of alpha-decay energies

On the basis of the self-consistent theory of finite Fermi systems, the energies of alphadecay chains were calculated for several new superheavy nuclei discovered recently in experiments of the Dubna-Livermore Collaboration headed by Yu.Ts. Oganessian. The approach in question is implemented on the basis of the generalized method of the density functional proposed by Fayans and his coauthors. The version used here relies on the functional DF3-a proposed recently for describing a wide array of nuclear data, including data on superheavy nuclei. A detailed comparison of the results obtained on this basis with the predictions of different approaches, including the self-consistent Skyrme-Hartree-Fock method, the micro-macro method in the version developed by Sobiczewski and his coauthors, and the phenomenological method of Liran and his coauthors, is performed. The resulting alpha-decay energies are used to calculate respective lifetimes with the aid of the phenomenological Parkhomenko-Sobiczewski formula.