A self-consistent method for studying second-order anharmonic effects on the basis of many-body quantum field theory is applied for the first time in calculating probabilities for E 1 transitions between the ground state and the [3_1^-× 2_1^+]_1^- two-phonon state in the semimagic tin isotopes ^104-124 Sn. The approach used involves taking into account (i) self-consistency of the nuclear mean field and effective interaction on the basis of the energy density functional method with the parameters of the Fayans functional DF3-a, which were earlier found to provide good results; (ii) ground-state three-quasiparticle correlations; and (iii) nuclear-polarizablility effects. Good agreement with available experimental data, including those for ^112 Sn, is obtained. Values of B ( E 1) are predicted for ^104-110,114 Sn even–even nuclei. It is shown that dynamical ground-state three-quasiparticle correlations make a substantial contribution to the reduced probabilities for the E 1 transitions in question, so that their inclusion is necessary for explaining experimental data.

A self-consistent method for studying second-order anharmonic effects on the basis of many-body quantum field theory is applied for the first time in calculating probabilities for E1 transitions between the ground state and the [3(1)(-)x2(1)(+)]1- two-phonon state in the semimagic tin isotopes Sn104-124. The approach used involves taking into account (i) self-consistency of the nuclear mean field and effective interaction on the basis of the energy density functional method with the parameters of the Fayans functional DF3-a, which were earlier found to provide good results; (ii) ground-state three-quasiparticle correlations; and (iii) nuclear-polarizablility effects. Good agreement with available experimental data, including those for Sn-112, is obtained. Values of B(E1) are predicted for Sn-104-110,Sn-114 even-even nuclei. It is shown that dynamical ground-state three-quasiparticle correlations make a substantial contribution to the reduced probabilities for the E1 transitions in question, so that their inclusion is necessary for explaining experimental data.

The strength distributions of charge exchange spin-dipole excitations are calculated in the continuum quasiparticle random-phase approximation based on the Fayans density functional with modified isovector part. An impact of the isovector parameter h(2)(-) of the DF3-f functional on the strength functions of charge-exchange spin-dipole excitations (0(-),1(-),2(-))are studied for Pb-208, Sn-132 and Zr-90. The sum rules are calculated using both ground state radii and direct integration of the total SD strength distributions. A comparison with the experimental SD sum rule in 90Zr gives one a possibility to check previously estimated h(2)(- )values which described well the recent combined estimate for Delta R(np )in (208)Pband corresponding equation of state parameters-symmetry energy J(0 )= J((rho 0))and a slope parameter L-0 = L(rho(0)).

The strength distributions of charge exchange spin-dipole excitations are calculated in the continuum quasiparticle random-phase approximation based on the Fayans density functional with modified isovector part. An impact of the isovector parameter h_2^- of the DF3-f functional on the strength functions of charge-exchange spin-dipole excitations ( 0^- , 1^- , 2^- ) are studied for ^208 Pb, ^132 Sn and ^90 Zr. The sum rules are calculated using both ground state radii and direct integration of the total SD strength distributions. A comparison with the experimental SD sum rule in ^90 Zr gives one a possibility to check previously estimated h_2^- values which described well the recent combined estimate for Δ R_np in ^208 Pb and corresponding equation of state parameters – symmetry energy J_0=J(ρ_0) and a slope parameter L_0=L(ρ_0) .

A self-consistent method for studying second-order anharmonic effects in the framework of quantum many-body theory is used for the first time to calculate the probabilities of 𝐸1-transitions between the main and two-phonon [3−1 × 2+1 ]1−-state in semi-magical isotopes 104−124Sn. The approach used contains accounting for: 1) self-consistency between the nuclear mean field and effective interaction, based on the use of the energy density functional method with proven parameters of the DF3-a Fayans functional, 2) three-quasiparticle ground state correlations and 3) the effects of nuclear polarizability. Good agreement was obtained with the available experiments, including 112Sn. The values of 𝐵(𝐸1) are predicted for even-even nuclei 104−110,114Sn. It is shown that the new, i.e. dynamic three-quasiparticle ground state correlations make a very significant contribution to the reduced probabilities of such 𝐸1-transitions and their consideration is necessary to explain the experiment.

Charge radii of Tl, Pb and Bi isotopic chains and magnetic moments of the 1/2^+ Tl ^g ground state and 11/2^- Tl ^m isomeric state in thallium isotopic chain are calculated simultaneously within the self-consistent Theory of Finite Fermi Systems (TFFS) based on the Energy Density Functional DF3-a by Fayans et al. The calculated ground-state charge radii R_ch of Tl, Pb and Bi isotopic chains reveal distinctive kink at the N=126 shell closure which has a similar magnitude, as in the neighboring mercury, lead and bismuth isotopic chains. The experimental kink indicator ξ in Tl isotopes is well described by the present calculation. Taking into account the meson exchange in the external field operator and in the effective spin dependent NN -interaction, as well as the regular effects of np-nh configurations and non-regular phonon-coupling (PC) corrections enables an improved description of the ground state magnetic moments in the long isotopic chain of thallium isotopes. The calculated 1/2^+ Tl ^g ground state magnetic moments agree fairly well with the isotopic trend reproducing the ‘‘asymmetric’’ jump at N=126 revealed by the recent ISOLDE (CERN) experiments. For N=82-126 , a ‘‘parabolic’’ N -dependence of the 11/2^- Tl ^m isomeric state magnetic moments is shown and experimental data for ^207 Tl ^m is described without phonon-coupling corrections.

A variational analysis of the Fayans energy-density functional is performed with allowance for the earlier unused isovector parameters h_2^- in the volume part of the functional. The quality of the previous fit to nuclear densities, masses of nuclei, single-particle levels, and charge radii remains unchanged under the additional condition of description of the giant-dipole-resonance energy in the ^208 Pb nucleus. The effect of variations in the isovector parameter h_2^- on the equations of state for infinite symmetric nuclear matter and pure neutron matter is determined. The density dependence of the symmetry energy S(ρ) and of its derivative L(ρ) is studied. For the parameter h_2^- , a range is established that is consistent with the estimated values of the symmetry energy J=S(ρ_0) and its derivative L_0=L(ρ_0) at the equilibrium density ρ_0 , which are parameters of the equation of state for symmetric nuclear matter. These values were obtained earlier from a simultaneous analysis of the values of the ‘‘neutron skin’’ Δ Rnp of ^208 Pb and ^48 Ca nuclei from the PREX-II and CREX experiments, from the results of ab initio calculations of equations of state and ground-state properties of nuclei, and from astrophysical observations and data on the discovery of gravitational waves from the merger of binary neutron stars by the LIGO-Virgo Collaboration in 2017.

An effective approximation to a fully self-consistent global description of the total force function of b decay within the framework of the theory of finite Fermi systems is presented, based on the calculation of ground states within the framework of the modified energy density functional of Fayans et al. (DF3-f) and the continuum quasiparticle random phase approximation (CQRPA). The isovector parameter ℎ2− of the volume part of the functional has been refined, the permissible range of which was determined earlier by us from restrictions on the parameters of the equation of state for nuclear matter—the symmetry energy and its derivative at equilibrium density, obtained from a joint analysis of the value of the ‘‘neutron skin’’ ΔRnp of the nuclei 208Pb and 48Ca, found in the PREX-II and CREX experiments, results of ab initio calculations of the properties of the ground states of nuclei with the interaction of N3LO and systematics of data on the masses of neutron stars from astrophysical observations. New calculations of the Gamow–Teller strength functions for the reference doubly magic nuclei 208Pb and 132Sn, as well as for the nucleus 130Sn with developed neutron pairing have been carried out. In the proposed model, the global DF3-a + CQRPA calculations of beta-decay half-lives of heavy (quasi)spherical nuclei with Z = 81–83 and T1/2 240 s are conducted. Experimental lifetimes are described with accuracy up to factor 5.

The probabilities of the E1 transition between the first $${{2}^{ + }}$$ and $${{3}^{ - }}$$ excited levels in nuclei with pairing have been calculated within the self-consistent many-body nuclear theory and Green’s function method. Calculations for a long chain of even–even tin isotopes have been performed for the first time. The known Fayans energy density functional has been used to calculate the characteristics of phonons and E1 transitions between excited states. A good description has been achieved for existing experimental data for the reduced probabilities of E1 transitions between the first one-phonon states for the 116–124Sn isotopes but not for the 112Sn and 114Sn isotopes. Possible reasons for this discrepancy have been discussed; the most probable reason is the deformation in the ground or excited states. It has been shown that new dynamical three-quasiparticle correlations in the ground state should be taken into account to explain the experimental data for 116–124Sn.

Fully self-consistent study of the charge radii in Ca region is exemplified by the calculation in the long chains of K isotopes. The neutron-deficient and neutron-rich nuclei with pairing in both neutron and proton sectors, as well as the (semi-) magic nuclei around the closed neutron shells at N = 20, 28, 32 are treated within the Energy Density Functional (EDF) approach with the Fayans functional DF3-a. The performance of the DF3-a is analysed in describing the odd-even staggering effects found both in previous and in more recent CERN-ISOLDE experiments for 36–52 K isotopes.

Self-consistent calculations of potential surfaces, quadrupole moments, and charge radii of the mercury isotopes ^178-208 Hg are calculated within the approach based on the Fayans energy-density functional. The existence of weakly oblate and strongly prolate isomeric states is shown. The charge radii are predicted to a typical precision of 0.01 fm for all isotopes, with the exception of three particular cases of ^181,183,185 Hg.

For the first time, a self-consistent method for studying second-order anharmonic effects within quantum many-body theory is applied to calculating probabilities for transitions between low-lying one-phonon states in nuclei where there is pairing. The approach used here takes into account (i) self-consistency between the effective nuclear field and effective interaction owing to the use of the method of the energy density functional with recommended parameters of the DF3-a Fayans functional, (ii) three-quasiparticle ground-state correlations, and (iii) nuclear-polarizability effects. The present study addresses E1 transitions between 3(1)(-) and 2(1)(+) one-phonon states in the semimagic tin isotopes Sn118-124 . Good agreement with experimental data is attained. It is shown that three-quasiparticle ground-state correlations make a significant contribution to the quantity being considered. Special features that the problem under study has in nuclei with pairing are examined, and effects of the spin components of the phonon-creation amplitude are also considered.

For neutron-rich O and F isotopes in the region of the so-called oxygen anomaly, the one- and two-neutron separation energies, charge and matter radii are calculated within the Fayans energy density functional DF3-a. The beta-decay half-lives and delayed multi-neutron emission branchings are treated in the Continuum Quasiparticle Random Phase approximation (DF3-a $$+$$ CQRPA). We discuss the applicability limits of the global approaches for the ground state and integral $$\beta$$ -decay properties of light nuclei. These characteristics calculated within the DF3-a $$+$$ CQRPA and relativistic RHB $$+$$ RQRPA are compared for oxygen and fluorine isotopic chains.

For the first time, a self-consistent method for studying second-order anharmonic effects within quantum many-body theory is applied to calculating probabilities for transitions between low-lying one-phonon states in nuclei where there is pairing. The approach used here takes into account (i) self-consistency between the effective nuclear field and effective interaction owing to the use of the method of the energy density functional with recommended parameters of the DF3-a Fayans functional, (ii) three-quasiparticle ground-state correlations, and (iii) nuclear-polarizability effects. The present study addresses E 1 transitions between 3_1^- and 2_1^+ one-phonon states in the semimagic tin isotopes ^118-124 Sn. Good agreement with experimental data is attained. It is shown that three-quasiparticle ground-state correlations make a significant contribution to the quantity being considered. Special features that the problem under study has in nuclei with pairing are examined, and effects of the spin components of the phonon-creation amplitude are also considered.

For the first time, a self-consistent method for studying second-order anharmonic effects within quantum many-body theory is applied to calculating probabilities for transitions between low-lying one-phonon states in nuclei where there is pairing. The approach used here takes into account (i) self-consistency between the effective nuclear field and effective interaction owing to the use of the method of the energy density functional with recommended parameters of the DF3-a Fayans functional, (ii) three-quasiparticle ground-state correlations, and (iii) nuclear-polarizability effects. The present study addresses $$E$$ 1 transitions between $$3_{1}^{-}$$ and $$2_{1}^{+}$$ one-phonon states in the semimagic tin isotopes $${}^{118{-}124}$$ Sn. Good agreement with experimental data is attained. It is shown that three-quasiparticle ground-state correlations make a significant contribution to the quantity being considered. Special features that the problem under study has in nuclei with pairing are examined, and effects of the spin components of the phonon-creation amplitude are also considered.

Fully self-consistent study of the charge radii in the long chains of isotopes from Ar to Ti is presented. The neutron-deficient and neutron-rich nuclei with pairing in both neutron and proton sectors, as well as the (semi-) magic nuclei around the closed neutron shells at $$N=20$$ , 28, 32 are treated within the Energy Density Functional (EDF) approach with the Fayans functional DF3-a. The performance of the DF3-a and its recent option Fy( $$\Delta r$$ , HFB) is analyzed in describing the absolute and differential rms radii. The scale of odd–even staggering is compared with one found in the CERN-CRIS experiments for $${}^{36{-}52}$$ Ca, $${}^{36{-}52}$$ K isotopes. The DF3-a calculations are consistent with magic behavior of charge radii in K isotopes at $$N=32$$ . A non-regular $$A$$ -dependent contribution due to the quasiparticle–phonon coupling is responsible for the universal increase of the charge radii after crossing the neutron shell at $$N=28$$ . Possible effects of deformation and higher power density gradient terms in the surface and pairing parts of the functional are mentioned.

The isobaric-analog resonancesfor nuclei around the neutron shell closures at N = 20, 50, 82 are treated in thefullyself-consistentDensityFunctionalplusContinuumQuasiparticleRandomPhaseApproximation (DF+CQRPA).The aim is to check how the self-consistency is preserved in the calculations for long isotopic chains. The beta-decay half-lives and delayed multi-neutron emission branchingare calculated for the reference Ni isotopic chain. The relative contributions of the GT and first-forbidden transitions are compared with that of the relativistic QRPA and Finite Amplitude Method. The accuracy of the global beta decay calculations performed within FRDM+RPA, DF+CQRPA and RHB+QRPA models are analysed.