Self-consistent theory of finite Fermi systems and Skyrme–Hartree–Fock method

Recent results obtained on the basis of the self-consistent theory of finite Fermi systems by employing the energy density functional proposed by Fayans and his coauthors are surveyed. These results are compared with the predictions of Skyrme–Hartree–Fock theory involving several popular versions of the Skyrme energy density functional. Spherical nuclei are predominantly considered. The charge radii of even and odd nuclei and features of low-lying 2⁺ excitations in semimagic nuclei are discussed briefly. The single-particle energies ofmagic nuclei are examined inmore detail with allowance for corrections to mean-field theory that are induced by particle coupling to low-lying collective surface excitations (phonons). The importance of taking into account, in this problem, nonpole (tadpole) diagrams, which are usually disregarded, is emphasized. The spectroscopic factors of magic and semimagic nuclei are also considered. In this problem, only the surface term stemming from the energy dependence induced in the mass operator by the exchange of surface phonons is usually taken into account. The volume contribution associated with the energy dependence initially present in the mass operator within the self-consistent theory of finite Fermi systems because of the exchange of high-lying particle–hole excitations is also included in the spectroscopic factor. The results of the first studies that employed the Fayans energy density functional for deformed nuclei are also presented.

     

Self-consistent theory of finite Fermi systems and radii of nuclei

Present-day self-consistent approaches in nuclear theory were analyzed from the point of view of describing distributions of nuclear densities. The generalized method of the energy density functional due to Fayans and his coauthors (this is the most successful version of the self-consistent theory of finite Fermi systems) was the first among the approaches under comparison. The second was the most successful version of the Skyrme-Hartree-Fock method with the HFB-17 functional due to Goriely and his coauthors. Charge radii of spherical nuclei were analyzed in detail. Several isotopic chains of deformed nuclei were also considered. Charge-density distributions ρ _ch(r) were calculated for several spherical nuclei. They were compared with model-independent data extracted from an analysis of elastic electron scattering on nuclei.     

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.     

Disturbance of the shell structure of neutron-rich nuclei in the oxygen-magnesium region

The effects related to nuclear deformation and their influence on the shell structure and nuclear properties have been investigated. Calculations were performed within the self-consistent theory of finite Fermi systems. The possibility of existence of strongly deformed nuclei at the neutron drip line and behind it, such as ²⁸O, ³⁹Na, and ^41–43Na, is discussed.     

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.     

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.     

Photonuclear data and modern physics of giant resonances

The results of the development (“renaissance”) of giant-resonance physics are briefly discussed from the point of view of their application to creating a photonuclear database. It is indicated that part of the recommendations from corresponding libraries of data are not at the level of the present-day status of giant-resonance physics. A Lorentzian parametrization of the most reliable experimental data on isovector M1 resonances is constructed for seven spherical nuclei, and it is shown that the widths of M1 resonances are severalfold, sometimes an order of magnitude, smaller than the value of Γ₀ = 4 MeV, which was recommended for all nuclei. The need for microscopically taking into account configurations more complex than those that are included within the standard random-phase approximation or within the quasiparticle random-phase approximation is emphasized. To be more precise, it is necessary to take into account coupling to phonons, since this changes the temperature dependence of the resonance width in relation to that which was used earlier and since, without this, one cannot explain the properties of pygmy dipole resonances in the region of the nucleon binding energy. Our calculations of the average energies of the pygmy dipole resonances in the Ca and Sn isotopes within the microscopic extended theory of finite Fermi systems reveal that the inclusion of coupling to phonons reduces these energies considerably toward the improvement of agreement with experimental data. The idea of creating a library of photonuclear data for unstable nuclei, including fission fragments, on the basis of the extended theory of finite Fermi systems is discussed in connection with the fact that information necessary for fitting the parameters of phenomenological theories is absent or insufficient for such nuclei.     

Energy dependence of effective nucleon-nucleon interaction and position of the nucleon drip line

A semimicroscopic version of the self-consistent theory of finite Fermi systems is proposed. In this approach, the standard theory of finite Fermi systems is supplemented with relations that involve the external values of the invariant components of the Landau-Migdal amplitude and which follow from microscopic theory. The Landau-Migdal amplitude at the nuclear surface is expressed in terms of the off-shell T matrix for free nucleon-nucleon scattering at the energy E equal to the doubled chemical potential of the nucleus being considered. The strong energy dependence of the free T matrix at low E changes the properties of nuclei in the vicinity of the nucleon drip line. It is shown that, upon taking into account the energy dependence of the effective interaction, the neutron drip line is shifted considerably toward greater neutron-excess values. This effect is illustrated by considering the example of the tin-isotope chain.     

Impact of the phonon coupling on the radiative neutron capture

Inclusion of the coupling of quasiparticle degrees of freedom with phonon degrees is a natural extention of the standard QRPA approach. The paper presents the quantitative impact of this phonon coupling on the dipole strength and radiative neutron capture for the stable ¹²⁴Sn and very exotic ¹⁵⁰Sn isotopes, as an illustration, using the self-consistent version of the Extended Theory of Finite Fermi Systems. It was found that the phonon contribution to the pygmy-dipole resonance and radiative neutron capture cross section is increased with the (N − Z) difference growth. The results show that the self-consistent nuclear structure calculations are important for unstable nuclei, where phenomenological approaches do not work.     

Quadrupole moments of spherical semi-magic nuclei within the self-consistent Theory of Finite Fermi Systems

The quadrupole moments of odd neighbors of semi-magic lead and tin isotopes and N = 50 , N = 82 isotones are calculated within the self-consistent Theory of Finite Fermi Systems based on the Energy Density Functional by Fayans et al. Two sets of published functionals are used to estimate systematic errors of the present self-consistent approach. They differ by the spin-orbit and effective tensor force parameters. The functional DF3-a leads to quadrupole moments in reasonable agreement with the experimental ones for most, but not all, nuclei considered.     

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.     

Some problems in the generalized theory of finite Fermi systems

A realistic version of the generalization of the theory of finite Fermi systems to the case where some complex configurations involving phonons are explicitly taken into account is proposed. Secular equations describing the fragmentation of simple states in odd and even-even nuclei over complex configurations that belong to, respectively, the quasiparticle ? phonon + quasiparticle ? phonon ? phonon and the two quasiparticles ? phonon type and which are presently of greatest interest are derived on the basis of general relations for nuclei that involve pairing (nonmagic nuclei). These equations take into account effects associated with ground-state correlations due to complex configurations and with the additional quasiparticle-phonon mechanism of Cooper pairing in nuclei. The effects in question were disregarded previously, but they are of interest since they can be observed in present-day experiments.     

Thomas-Fermi theory for atomic nuclei revisited

The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme interactions and from relativistic mean field theory. VWK consists of the Thomas-Fermi part plus a pure, perturbative ?² correction. In external potentials, VWK passes through the average of the quantal values of the accumulated level density and total energy as a function of the Fermi energy. However, there is a problem of overbinding when the energy per particle is displayed as a function of the particle number. The situation is analyzed comparing spherical and deformed harmonic oscillator potentials. In the self-consistent case, we show for Skyrme forces that VWK binding energies are very close to those obtained from extended Thomas-Fermi functionals of ?⁴ order, pointing to the rapid convergence of the VWK theory. This satisfying result, however, does not cure the overbinding problem, i.e., the semiclassical energies show more binding than they should. This feature is more pronounced in the case of Skyrme forces than with the relativistic mean field approach. However, even in the latter case the shell correction energy for e.g., ²⁰⁸Pb turns out to be only ∼−6 MeV what is about a factor two or three off the generally accepted value. As an ad hoc remedy, increasing the kinetic energy by 2.5%, leads to shell correction energies well acceptable throughout the periodic table. The general importance of the present studies for other finite Fermi systems, self-bound or in external potentials, is pointed out.     

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.     

Remnant Fermi surface in a pseudogap regime of the two-dimensional Hubbard model at finite temperature

A precursor effect on the Fermi surface in the two-dimensional Hubbard model at finite temperatures near the antiferromagnetic instability is studied using three different itinerant approaches: the second order perturbation theory, the paramagnon theory (PT), and the two-particle self-consistent (TPSC) approach. In general, at finite temperature, the Fermi surface of the interacting electron systems is not sharply defined due to the broadening effects of the self-energy. In order to take account of those effects we consider the single-particle spectral function A(, 0) at the Fermi level, to describe the counterpart of the Fermi surface at T = 0. We find that the Fermi surface is destroyed close to the pseudogap regime due to the spin-fluctuation effects in both PT and TPSC approaches. Moreover, the top of the effective valence band is located around = (π/2,π/2) in agreement with earlier investigations on the single-hole motion in the antiferromagnetic background. A crossover behavior from the Fermi-liquid regime to the pseudogap regime is observed in the electron concentration dependence of the spectral function and the self-energy. Received 8 September 2000 and Received in final form 20 December 2000     

Der Einflu\ einer Spin-Spinwechselwirkung auf das magnetische Moment schwerer Atomkerne

The corrections to the magnetic moments of heavy nuclei on account of a spindependent two-body-interaction of the form (σ ₁ σ ₂)V(r ₁–r ₂) are determined in the Fermi model calculating the second order contribution for the selfenergy part. It is shown using conservation laws that this contribution is connected to the local Vertex T ^ω [σ] of Migdal's theory of finite Fermi systems.