The Energy Density Functional (EDF) theory is extremely successful within the effective force approach, noticeably the Skyrme or Gogny forces, in reproducing the nuclear binding energies and other nuclear properties along the whole mass table. The EDF is in this case represented formally as the Hartree-Fock (HF) mean field of an effective force, and the associated single particle states can be considered the eigenstates of the corresponding effective mean field. In general, the phenomenological single particle spectrum is not accurately reproduced. To overcome this difficulty one can improve the functional in order to incorporate in the mean field additional correlations in an effective way. In an alternative viable scheme one can introduce explicitly many-body correlations which affect the single particle motion at both dynamic and static levels. In particular, the particle-vibration coupling scheme modifies the positions of the individual single particle energies. In this case one also introduce the fragmentation of the single particle states, a feature that cannot be described at the mean field level. At the same time the so-introduced correlations modify the static single particle potential, and the single particle states that diagonalize the corresponding density matrix are not the orbitals of a mean field with occupation numbers 1 (occupied orbitals) and 0 (unoccupied orbitals) anymore. In this paper we show that both static and dynamic effects on the single particle motion can be introduced within a previously developed scheme, based on the conserving approximations, and that the static part can be identified with the so-called tadpole term introduced by Khodel in the self-consistent theory of finite Fermi systems. The treatment remains at the formal level, but we hope that several aspects of the particle-vibration coupling scheme will be clarified.

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.

A method to evaluate the particle-phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei, based on the direct solution of the Dyson equation with PC corrected mass operator, is presented. It is used for finding the odd-even mass difference between even Pb and Sn isotopes and their odd-proton neighbors. The Fayans energy density functional (EDF) DF3-a is used which gives rather highly accurate predictions for these mass differences already at the mean-field level. In the case of the lead chain, account for the PC corrections induced by the low-laying phonons $2^+_1$ and $3^-_1$ makes agreement of the theory with the experimental data significantly better. For the tin chain, the situation is not so definite. In this case, the PC corrections make agreement better in the case of the addition mode but they spoil the agreement for the removal mode. We discuss the reason of such a discrepancy.

Recent results of the description of quadrupole moments of odd semi-magic nuclei are briefly reviewed. They are based on the self-consistent theory of finite Fermi systems with account for the phonon-particle coupling (PC) effects. The self-consistent model for describing the PC effects was developed previously for magnetic moments. Account for the non-pole diagrams is an important ingredient of this model. In addition to previously reported results for the odd In and Sb isotopes, which are the proton-odd neighbors of even tin nuclei, we present new results for odd Bi isotopes, the odd neighbors of even lead isotopes. In general, account for the PC corrections makes the agreement with the experimental data significantly better.

self-consistent approach to anharmonic effects based on the quantum many-body theory is for the first time used to calculate the quadrupole moments of the lowest 3 – states in Sn and Pb isotopes, including the 100 Sn, 132 Sn, and 208 Pb doubly magic ones. The consistency between the mean nuclear field and the effective interaction is maintained using the energy-density-functional method with known parameters of the Fayans functional. Thereby, the quadrupole moments of the lowest 3 – states of isotopes with nucleon pairing are reliably predicted, and the existing data for the 208 Pb isotope are reproduced. It has been shown that the new three-quasiparticle correlations are responsible for slightly more than half of the observed effect and the remaining part is due to the quadrupole polarizability of the nucleus.

Transition probabilities between low-lying one-phonon states of magic nuclei are for the first time computed self-consistently within an approach to anharmonic effects based on the quantum theory of many-body systems. In the adopted approach, three-quasiparticle correlations in the ground state are taken into account, and the nuclear mean field is interrelated with the effective nucleon–nucleon interaction. These quantities are derived using the energy density functional method with known parameters of the Fayans functional. The E 1 and E 2 transitions in the 132 Sn and 208 Pb nuclei are considered as an example, and a reasonably good agreement with the data on these nuclei is reached. Three-quasiparticle correlations in the ground state are shown to make a significant contribution to the probabilities of the discussed transitions.

Fission barriers in nuclei belonging to the uranium region and their other characteristics are calculated on the basis of the FaNDF 0 energy density functional. In particular, the neutron-separation energies S n and S 2n , the proton-separation energies S p , and the beta-transition energies Q β are calculated for uranium, neptunium, and plutonium isotopes. In addition, the deformation energies and parameters of these nuclei are presented along with their radii. A comparison with the predictions of the Skyrme–Hartree–Fock method implemented with several versions of the Skyrme energy density functionals is performed. The role of the octupole deformation β 3 is studied for the 238 U nucleus. It is shown that this deformation does not have any significant effect on the first-barrier height B (1) f or ground-state properties. At the same time, the second-barrier height B(2) f decreases by a factor of about two upon taking into account β 3 . A phase transition at A ~ 260 is found for the three isotopic chains being considered: this point is a bifurcation point at which B (1) f (A) forks into two curves. Of these, the curve B (2) f (A) splits from it, prolonging the former curve for B (1) f (A) almost continuously, whereas the curve for B (1) f (A) itself goes down sharply.

Recent results of the study of the particle-phonon coupling (PC) effects in odd magic and semi-magic nuclei within the self-consistent theory of finite Fermi systems are reviewed. In addition to the usual pole diagrams, the non-pole ones are considered. Their contributions are often of a crucial importance. PC corrections to the single-particle energies for $^{40}$Ca and $^{208}$Pb are presented. The quadrupole moments of odd In and Sb isotopes, the odd-proton neighbors of even Sn isotopes, are presented also with accounting for the PC corrections. At last, recently announced problem of extremely high values charge radii of heavy Ca isotopes is solved in terms of a consistent consideration of the PC effects. In all the cases, rather good description of the data is obtained.

The Nozières–Pines method for describing neutron scattering on a heated Fermi liquid (liquid 3 He) is used to calculate cross sections for inelastic neutrino scattering on the isotope 54 Fe, 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.

Laser resonant photoionization spectroscopy was used to study the hyperfine structure of the optical \(3d^{8}4s^{2} {}^{3}F_{4}\rightarrow 3d^{8}4s4p {}^{3}G^{\rm o}_{3}\) and \(3d^{9}4s {}^{3}D_{3}\rightarrow 3d^{8}4s4p {}^{3}G^{\rm o}_{3}\) transitions of 63Ni and 61Ni isotopes. Experimental spectra allowed us to derive hyperfine interaction constants and determine the magnetic dipole moment of the nuclear ground state of 63Ni for the first time: \(\mu=+0.496(5)\mu_{\rm N}\). The value obtained agrees well with the prediction of the self-consistent theory of finite Fermi systems.

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 δΣPC to the mass operator Σ is found in gL2-approximation, gL being the vertex of creating the L-phonon. The tadpole term of the operator δΣPC 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 + δΣPC(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.

. Alpha-decay energies for several chains of superheavy nuclei are calculated within the self-consistent mean-field approach by using the Fayans functional FaNDF 0 . They are compared to the experimental data and predictions of two Skyrme functionals, SLy4 and SkM * , and of the macro-micro method as well. The corresponding lifetimes are calculated with the use of the semi-phenomenological formulas by Parkhomenko and Sobiczewski and by Royer and Zhang.

A method is presented to evaluate the particle–phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei. In such nuclei, always there is a collective low-lying 2 + phonon, and a strong mixture of single-particle and particle–phonon states often occurs. As in magic nuclei the so-called g L 2 approximation, where g L is the vertex of the L -phonon creation, can be used for finding the PC correction δΣ PC (ε) to the initial mass operator Σ 0 . In addition to the usual pole diagram, the phonon “tadpole” diagram is also taken into account. In semi-magic nuclei, the perturbation theory in δΣ PC (ε) with respect to Σ 0 is often invalid for finding the PC-corrected single-particle energies. Instead, the Dyson equation with the mass operator Σ(ε) = Σ 0 + δΣ PC (ε) is solved directly, without any use of the perturbation theory. Results for a chain of semi-magic Pb isotopes are presented.

The deformation properties of a long lead isotopic chain up to the neutron drip line are analyzed on the basis of the energy density functional (EDF) in the FaNDF0 Fayans form. The question of whether the ground state of neutron-deficient lead isotopes can have a stable deformation is studied in detail. The prediction of this deformation is contained in the results obtained on the basis of the HFB-17 and HFB-27 Skyrme EDF versions and reported on Internet. The present analysis reveals that this is at odds with experimental data on charge radii and magnetic moments of odd lead isotopes. The Fayans EDF version predicts a spherical ground state for all light lead isotopes, but some of them (for example, 180Pb and 184Pb) prove to be very soft—that is, close to the point of a phase transition to a deformed state. Also, the results obtained in our present study are compared with the predictions of some other Skyrme EDF versions, including SKM*, SLy4, SLy6, and UNE1. By and large, their predictions are closer to the results arising upon the application of the Fayans functional. For example, the SLy4 functional predicts, in just the same way as the FaNDF0 functional, a spherical shape for all nuclei of this region. The remaining three Skyrme EDF versions lead to a deformation of some light lead isotopes, but their number is substantially smaller than that in the case of the HFB-17 and HFB-27 functionals. Moreover, the respective deformation energy is substantially lower, which gives grounds to hope for the restoration of a spherical shape upon going beyond the mean-field approximation, which we use here. Also, the deformation properties of neutron-rich lead isotopes are studied up to the neutron drip line. Here, the results obtained with the FaNDF0 functional are compared with the predictions of the HFB-17, HFB-27, SKM*, and SLy4 Skyrme EDF versions. All of the EDF versions considered here predict the existence of a region where neutron-rich lead isotopes undergo deformations, but the size of this region is substantially different for the different functionals being considered. Once again, it is maximal for the HFB-17 and HFB-27 functionals, is substantially narrower for the FaNDF0 functional, and is still narrower for the SKM* and SLy4 functionals. The two-neutron drip line proved to be A drip 2n = 266 for all of the EDF versions considered here, with the exception of SKM*, for which it is shifted to A drip 2n (SKM*) = 272.

Recent results of the Fayans energy density functional (EDF) for spherical nuclei are reviewed. A comparison is made with predictions of several Skyrme EDFs. The charge radii and characteristics of the first 2+ excitations in semi-magic nuclei are briefly discussed. The single-particle spectra of doubly magic nuclei are considered in more detail. The phonon-particle coupling effects are analyzed including the tadpole term.

The self-consistent model, developed previously to describe phonon coupling (PC) effects in magnetic moments of odd magic and semi-magic nuclei, is extended to quadrupole moments. It is based on the theory of finite Fermi systems with the use of the perturbation theory in $g_L^2$, where $g_L$ is the vertex creating the $L$-phonon. Accounting for the phonon tadpole diagrams is an important ingredient of this model. The calculation scheme is based on the Fayans energy density functional DF3-a and does not contain any adjusted parameters. The odd In and Sb isotopes are considered, which are the proton-odd neighbors of even tin nuclei. The $2^+_1$ phonon is taken into account which quadrupole moment is one ingredient of the calculation scheme. The corresponding values were found by us previously. Two main PC corrections, due to the phonon $Z$-factor and due to the phonon-induced interaction, have opposite signs and cancel strongly each other, leaving room for other `small' corrections, so that the resulting PC correction is much lower than the absolute values of each of two main ones. However, it remains noticeable, making the overall agreement with the data significantly better.

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.

The density profiles of spherical nuclei are calculated with two methods based on the energy density functional approach. Isotopic trends are discussed in nuclear surface diffuseness. The simple parametrizations of the dependencies of nuclear diffuseness and radius on neutron number are suggested. The nucleus-nucleus potentials are calculated with the nucleon densities obtained and are compared with those resulting from the phenomenological treatment. The height of the Coulomb barrier is suggested to be used in the fit of the density-dependent nucleon-nucleon interaction.

A self-consistent model is developed within the theory of finite Fermi systems to describe phonon coupling (PC) effects in moments of odd magic and semimagic nuclei. The model is based on the perturbation theory in g L, where gL is the vertex of creating the L-phonon. The phonon tadpole diagrams are taken into account in an approximate way, which turns out to be exact for the spurious 1 phonon. The calculation scheme is based on the Fayans energy density functional DF3-a and does not contain any adjusted parameters. The odd In and Sb are considered, which are the proton-odd neighbors of even tin nuclei. The 2+1 phonon is taken into account which is the most collective among the low-laying surface states. Its quadrupole moment is one of ingredients of the calculation scheme, with the corresponding values being found by us previously. The value of total PC correction to quadrupole moments turned out to be moderate due to strong cancelation of two main terms, due to the phonon Z-factor and due to the phonon-induced interaction. However, as a rule, the resulting PC correction is noticeable, making the overall agreement with the data significantly better. Self-consistent account for phonon induced corrections to quadrupole moments of odd semi-magic nuclei2

Fayans energy density functional (EDF) FaNDF^0 has been applied to the nuclei around uranium region. Ground state characteristics of the Th, U and Pu isotopic chains, up to the two-neutron drip line, are found and compared with predictions from several Skyrme EDFs. The two-neutron drip line is found for FaNDF^0, SLy4 and SkM^* EDFs for a set of elements with even proton number, from Pb up to Fm.