Theory Of Finite Fermi Systems Research Articles

Charge radii of thallium isotopes near the N=126 shell closure

The changes in the mean-squared charge radius of Tlg209 (N=128) and Tlm207 (N=126) relative to Tl205 have been measured for the first time using the in-source laser resonance-ionization spectroscopy technique with the Laser Ion Source and Trap (LIST) at ISOLDE (CERN). The application of the LIST suppresses the dominant background from isobaric francium isotopes and allows access to thallium nuclides with A⩾207. The characteristic kink in the charge radii at the N=126 neutron shell closure, as well as the odd-even effect similar to that in the adjacent bismuth, lead, and mercury isotopic chains, have been observed. The self-consistent theory of finite Fermi systems based on the energy density functional by Fayans reproduces the behavior of charge radii in these isotopic chains near N=126. The comparison with calculations in the framework of the relativistic mean field (RMF) approach is also presented. In the case of the Fayans functional it is a specific form of pairing interaction with the dependence on the density gradient that is essential to provide agreement with the experimental charge radii. In particular, the kink is reproduced without the inversion of g9/2 and i11/2 neutron single-particle states, which is a prerequisite to correctly describe the kink in the RMF models. Published by the American Physical Society 2024

Magnetic moments of thallium isotopes in the vicinity of magic N = 126

The magnetic dipole moments (μ) of 209Tlg (N=128) and 207Tlm (N=126) have been measured for the first time using the in-source laser resonance-ionization spectroscopy technique with the Laser Ion Source and Trap (LIST) at ISOLDE (CERN). The application of the LIST suppresses the usually overwhelming background of the isobaric francium isotopes and allows access to heavy thallium isotopes with A⩾207. The self-consistent theory of finite Fermi systems based on the energy density functional by Fayans et al. well describes the N dependence of μ for 1/2+ thallium ground states, as well as μ for the 11/2− isomeric states in europium, gold and thallium isotopes. The inclusion of particle-vibration coupling leads to a better agreement between the theory and experiment for μ(Tlg, Iπ=1/2+). It is shown that beyond mean-field contributions to μ cannot be neglected at least for thallium isotopes with Iπ=1/2+.

Nuclear Spin-Isospin Response within the Fayans Functional

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.

Interaction of Solar Neutrinos with {}^{98}mathrm{Mo} and {}^{100}mathrm{Mo} Nuclei

The process of neutrino interaction with {}^{98}mathrm{Mo} and {}^{100}mathrm{Mo} nuclei is studied with allowance for the effect of charge-exchange resonances. The results obtained by calculating the cross section for solar-neutrino capture by the isotopes {}^{98}Mo and {}^{100}Mo, sigma(E_{nu}), are presented. Use is made of both experimental data obtained for the strength functions S(E) in (p,n) and ({}^{3}He, t) charge-exchange reactions and the strength functions S(E) calculated within the theory of finite Fermi systems. The effect of the resonance structure of S(E) on the calculated cross sections for solar-neutrino capture is studied, and the contribution of each high-lying resonance to the capture cross section sigma(E_{nu}) is isolated. The contributions of all components of the solar neutrino spectrum are calculated. The contribution of background solar neutrinos to the double-beta decay of {}^{100}Mo nuclei is estimated.

New prospects for iodine detector and Solar neutrinos registration

The neutrino capture cross section σ(E) by 127I nucleus is studied with proper consideration of the nuclear strength function S(E) and its resonance structure. The calculations of giant Gamow-Teller, analog and pigmy resonances are realized based on the framework of the self-consistent finite Fermi systems theory. The results are compared with known experimental (p,n) reaction data that confirmed the significant influence of high-lying resonances on the cross section values. In the case when the energy of incident neutrino is higher than the sum of neutron emission threshold Sn and reaction threshold the 126Xe isotope is produced. Comparison of experimental yields for 127Xe and 126Xe isotopes can give the sensitive indicator of the metallicity for different Solar models. The results allow to confirm the advantages of the iodine detector for detecting hard astrophysical and accelerator neutrinos.

New Equation for the Vertex of Theory of Finite Fermi-Systems: Accounting for Phonon Coupling

New Equation for the Vertex of Theory of Finite Fermi-Systems: Accounting for Phonon Coupling

Microscopic Model to Take into Account Complex Configurations for Pygmy and Giant Resonances

A microscopic model for taking into account quasiparticle–phonon interaction in magic nuclei is considered within nuclear quantum many-body theory. This model is of interest for constructing a microscopic theory of pygmy and giant multipole resonances—first of all, a description of their fine structure. This article reports on a continuation and development of our earlier study [1]. Basic physics results of that study are confirmed here, and new results are obtained: (i) exact (not approximate, as in [1]) expressions for the first and second variations of the vertex in the phonon field are found and employed; (ii) a new equation involving, in addition to the known effective interaction, the total amplitude for particle–hole interaction is derived for the vertex, which is the main ingredient in the theory of finite Fermi systems; (iii) the required two-phonon configurations are obtained owing to the last result. The new equation for the vertex now contains complex configurations such as 1p1hotimestextrm{phonon} and two-phonon ones, along with numerous ground-state correlations.

Self-Consistent Calculation of the Charge Radii in a Long $${}^{\mathbf{58{-}82}}$$Cu Isotopic Chain

The charge radii are calculated in long chain of copper isotopes that includes the $${}^{58,79}$$ Cu exotic nuclei, which are close to the doubly magic nuclei of $${}^{58,78}$$ Ni, and the nuclei featuring the $$N=32$$ , $$34$$ , and $$40$$ magic subshells. Use is made of the self-consistent theory of finite Fermi systems and the family of energy density functionals proposed by Fayans and his coauthors (DF3, DF3-a, …). The results are compared with experimental data and with the results of the calculations based on self-consistent models that employ new versions of the Fayans functional—Fy(std) and Fy(HFB, $$\nabla r$$ ), whose parameters were obtained by means of an extended optimization protocol—as well as with the results of ab-initio calculations performed on the basis of the renormalization-group model and with the results of the calculation with a density-dependent spin–orbit interaction stemming from three-nucleon forces. The weakening of odd–even staggering of radii of nuclei in the ISOLDE-CERN experiments as the nuclei approach the $$N=50$$ closed neutron shell is analyzed, and the possible mechanisms behind this weakening are considered. It is shown that the isotopic dependences of the charge radii and the total beta-decay energies are correlated.

Microscopic theory of pygmy- and giant resonances: accounting for complex 1p1h$$\otimes $$phonon configurations

The Green function formalism with a consistent account for phonon coupling (PC), based on the self-consistent theory of finite Fermi systems, is applied for pygmy- and giant multipole resonances in magic nuclei with the aim to consider particle–hole (ph) and complex 1p1h $$\otimes $$ phonon configurations. A new equation for the effective field, which describes nuclear polarizability, is obtained. It contains new PC contributions, which are of interest in the energy region under consideration. They are due to: (1) the tadpole effect in the standard ph-propagator, (2) two new induced interactions (caused by the exchange of the ph-phonon) in the second ph-channel and in the particle–particle channels, and (3) the first and second variations of the effective interaction in the phonon field. The general expressions for energies and probabilities of transitions between the ground and excited states are obtained. The qualitative analysis and discussion of the new terms are performed.

Global Calculations of Beta-Decay Properties Based on the Fayans Functional

An effective approximation to a fully self-consistent global description of beta-decay properties of nuclei within the theory of finite Fermi systems is presented. It is based on describing the ground state properties within the energy density functional proposed by Fayans and coauthors (DF3) and on the continuum quasiparticle random-phase approximation (CQRPA). The accuracy of global DF3 $$+$$ CQRPA calculations is analyzed. For more than 200 (quasi)spherical nuclei with $$Z=18$$ to 51 having half-lives in the range of $$T_{1/2}<5$$ s, the experimental half-lives and delayed neutrons emission probabilities are described within a factor of two and three, respectively. A comparison is performed with the results of similar calculations based on state-of-the-art self-consistent models : the relativistic spherical RHB $$+$$ RQRPA approach and deformed finite-amplitude method (FAM) and HFB $$+$$ QRPA approaches, as well as the interacting shell model. A detailed analysis of beta-decay properties in the nickel isotopic chain that were obtained in various calculations allows us for determining basic mechanisms responsible for the sudden shortening of the half-lives that was found experimentally at RIKEN for isotopes heavier than the doubly magic $${}^{78}$$ Ni nucleus. These are the contributions of first-forbidden (FF) transitions and multiphonon configurations and spin inversion of the respective ground states. The acceleration effect in question is highly sensitive to the balance of the contributions of Gamow–Teller (GT) and FF transitions to the total beta-decay rate. It is shown that, in nickel isotopes, the ratio of these contributions takes different values before and after the neutron-shell crossing at $$N=50$$ .

Nuclear Resonances and the Interaction between Neutrinos and a Ga–Ge System

Calculations are presented for cross section σ(Eν) of solar neutrino capture by 71Ga nuclei. The calculations are based on experimental data on force function S(E) obtained in charge-exchange reactions 71Ga(p, n)71Ge and 71Ga(3He, t)71Ge. Charge-exchange force function S(E) for 71Ga is calculated using the self-consistent theory of finite Fermi systems. The effect the resonance structure of S(E) has on calculated cross section σ(Eν) is studied. It is shown that the resonance part adds about 5% to the rate of the reaction estimated with only discrete states.

Effect of High-Lying Resonances on Cross Sections for Solar-Neutrino Capture by $${}^{\mathbf{127}}$$I Nuclei

The resonance structure of the charge-exchange strength function $$S(E)$$ and its effect on the cross sections for solar-neutrino capture by $${}^{127}$$ I nuclei are analyzed. Three types of isobaric resonances are studied within the self-consistent theory of finite Fermi systems. These are the giant Gamow–Teller resonance; the analog resonance; and the pygmy resonances, which lie lower. The capture cross section $$\sigma(E)$$ for solar neutrinos incident to $${}^{127}$$ I nuclei is calculated with allowance for the resonance structure of the strength function $$S(E)$$ , and the effect of each resonance on the energy dependence $$\sigma(E)$$ is analyzed. It is shown that all high-lying charge-exchange resonances should be taken into account in calculating the cross section $$\sigma(E)$$ . The contributions of neutrinos of different origin to the structure of the cross section $$\sigma(E)$$ are analyzed. In particular, the contribution of energetic neutrinos to the ratio of the $${}^{127}$$ Xe and $${}^{126}$$ Xe production rates is considered. The $${}^{126}$$ Xe $$/^{127}$$ Xe isotope ratio is an indicator of hard boron neutrinos in the solar spectrum.

Anharmonic Effects in the Theory of Finite Fermi Systems

Some results obtained by E.E. Saperstein and his coauthors in the theory of the ground state and low-lying excited states of magic and semimagic nuclei are discussed briefly. Corrections to the creation amplitude $$g$$ for one low-lying phonon are considered for the first time. These corrections, treated on the basis of the existence of a small parameter, include the tadpole-induced coupling of the amplitudes for the creation of one and two phonons.

Charge-Exchange Isobaric Resonances and Local-Interaction Parameters

Three types of isobaric resonances—giant Gamow–Teller, analog, and pygmy resonances (GTR, AR, and PR, resonances)—are studied within the microscopic theory of finite Fermi systems and its model approximation. The calculated GTR, AR, and PR energies agree well with experimental data. The parameters of local Landau–Migdal isospin–isospin and spin–isospin interactions are determined from a comparison of the calculated GTR, AR, and PR energies with experimental data. A comparison of the values obtained for these parameters with their counterparts deduced by other others from experimental data on charge–exchange reactions demonstrates agreement within the errors in the majority of cases.

Restoration of Wigner’s Sypersymmetry in Heavy and Superheavy Nuclei

Various aspects of restoration of Wigner’s supersymmetry [SU(4) symmetry] in heavy and superheavy nuclei are analyzed by comparing the results of calculations with experimental data. The energy differences between the giant Gamow–Teller and analog resonances ($$E_{\mathrm{G}}$$ and $$E_{\mathrm{A}}$$) are given according to calculations within the theory of finite Fermi systems for 34 nuclei for which experimental data are known. The calculated energy differences $$\Delta E_{\mathrm{G{-}A}}$$ of $$E_{\mathrm{G}}$$ and $$E_{\mathrm{A}}$$ tend to zero in heavier nuclei, demonstrating the restoration of Wigner’s SU(4) symmetry. Also, the isotopic dependence of the Coulomb energy difference between neighboring nuclear isobars is analyzed within the SU(4) approach for more than 400 nuclei in the mass-number range of $$A=5{-}244$$. The restoration of Wigner’s SU(4) symmetry in heavy nuclei is confirmed. It is shown that the restoration of Wigner’s SU(4) symmetry is compatible with the possible existence of an island of stability in the region of superheavy nuclei.

The effective single particle potential and the tadpole

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.

Resonance Structure of the Charge-Exchange Strength Function

The resonance structure of the charge-exchange strength function S(E) is studied. Three types of isobaric resonances are considered within the self-consistent theory of finite Fermi systems and within its model approximation. These are giant Gamow-Teller, analog, and pygmy resonances (GTR, AR, and PR, respectively). The energies calculated for GTR, AR and three PRs agree well with experimental data. In heavy nuclei, the energy difference ΔEG-A = EGTR — EAR tends to zero, which corresponds to restoration of Wigner’s SU(4) symmetry. The average deviation of the calculated values of ΔEG-A from known experimental data for 33 nuclei is 0.30 MeV. The root-mean-square deviations of the calculated energies of pygmy resonances from experimental data are also moderately small, δE < 0.40 MeV. The strength function S(E) is calculated for the isotopes 71Ga, 98Mo, 118Sn, and 127I. The calculated values of the resonance energies and resonance-peak parameters are close to their experimental counterparts. A strong effect of charge-exchange resonances on neutrino-capture cross sections, including those for solar neutrinos, is demonstrated.

Cross Sections of Solar Neutrino Capture by Nuclei and Charge-Exchange Resonances

The resonance structure of charge-exchange strength function S(E) and its effect on the cross sections of neutrino capture by 71Ga, 98Mo, and 127I were examined using the self-consistent theory of finite Fermi systems. Gamow–Teller, analog, and lower-lying pygmy resonances are considered in calculating strength function S(E). Cross sections σ(E) of solar neutrino capture are calculated for the above three isotopes with the resonance structure of strength function S(E) factored in, and the influence of each resonance on energy dependence σ(E) is analyzed. It is found that all charge-exchange resonances in strength function S(E) must be considered in calculating cross section σ(E). Even if just the high-lying resonances are neglected, cross section σ(E) can be underestimated, and this could affect the interpretation of experimental data.

Resonance Structure of the Charge-Exchange Strength Function and Neutrino-Capture Cross Sections for the Isotopes 71Ga, 98Mo, and 127I

A resonance structure of the charge-exchange strength function S(E) and its effect on the neutrino-capture cross sections for the isotopes 71Ga, 98Mo, and 127I are studied within the self-consistent theory of finite Fermi systems. The calculation of the strength function S(E) takes into account Gamow–Teller, analog, and so-called lower lying pygmy resonances. The neutrino-capture cross sections σ(E) for the above three isotopes are calculated with allowance for the resonance structure of the strength function S(E), and the effect of each resonance on the energy dependence σ(E) is analyzed. It is found that all charge-exchange resonances in the strength function S(E) should be taken into account in calculating the neutrino-capture cross section σ(E) for the isotopes 71Ga, 98Mo, and 127I. The disregard of even highlying resonances leads to a substantial underestimation of the cross section σ(E), and this may affect the interpretation of respective experimental data.

Charge-exchange Resonances of Tin Isotopes in Sn(3He,t)Sb Reaction

Charge-exchange resonances: the giant Gamow–Teller, analog and the so-called “pygmy” resonances have been studied in the self-consistent theory of finite Fermi systems. Microscopic and semi-classical calculations are presented for nine tin isotopes with known experimental data 112,114,116,117,118,119,120,122,124Sn. These data is from Sn(3He,t)Sb charge-exchange reaction at the energy (3He) = 200 MeV. The average standard deviation for GTR and AR energies is δE ≤ 0.30 MeV that is close to the experimental E