Theory Of Finite Fermi Systems Research Articles

Nucleosynthesis of Heavy Elements in Thermonuclear Explosions 'Mike', 'Par' and 'Barbell'

The formation of transuranium nuclides in pulsed neutron fluxes of thermo-nuclear explosions is investigated in the kinetic model of the astrophysical r-process, taking into account time dependence of the external parameters and including the processes accompanying the β-decay of neutron-rich nuclei. Time-dependent neutron fluxes in the interval ∼ 10−6 s were modeled within the developed adiabatic binary model. Probabilities of β-delayed processes were calculated using the microsco-pic theory of finite Fermi systems. Calculations of the yields of transuranium nuclides Y(A) are made for three experimental USA thermonuclear explosions ”Mike” (Y

Production of Transuranium Nuclides in Pulsed Neutron Fluxes from Thermonuclear Explosions

The production of transuranium nuclides in pulsed neutron fluxes from thermonuclear explosions has been studied within the kinetic model of the astrophysical r-process taking into account the time dependence of external parameters and processes accompanying the beta decay of neutron-rich nuclei. Neutron fluxes depending on the time in the range of ~10–6 s have been simulated within the developed adiabatic binary model. The probabilities of beta-delayed processes have been calculated within the microscopic theory of finite Fermi systems. The yields of transuranium nuclides Y(A) have been calculated for three experimental thermonuclear explosions Mike (YM), Par (YP), and Barbel (YB) (United States). The rms deviations of the calculations from experimental data are 91, 33, and 29% for YM, YP, and YB, respectively. These deviations are much smaller than those for other known calculations and are comparable with the proposed exponential approximation ensuring rms deviations of 56, 86.8, and 60.2% for YM, YP, and YB, respectively. The even–odd anomaly in the observed yields of heavy nuclei is explained by the dominant effect of processes accompanying the beta decay of heavy neutron-rich isotopes.

Charge-exchange isobaric resonances

Three types of the charge-exchange isobaric resonances - giant Gamow-Teller (GTR), the analog (AR) and pygmy (PR) ones are investigated using the microscopic theory of finite Fermi systems and its approximated version. The calculated energies of GTR, AR and three PR’s are in good agreement with the experimental data. Calculated differences ΔEG-A=EGTR-EAR go to zero in heavier nuclei indicating the restoration of Wigner SU(4)-symmetry. The average deviation for ΔEG-A is 0.30 MeV for the 33 considered nuclei where experimental data are available. The comparison of calculations with experimental data on the energies of charge-exchange pygmy resonances gives the standard deviation δE<0:40 MeV. Strength functions for the 118Sn, 71Ga, 98Mo and 127I isotopes are calculated and the calculated resonance energies and amplitudes of the resonance peaks are close to the experimental values. Strong influence of the charge-exchange resonances on neutrino capturing cross sections is demonstrated.

Self-consistent account for phonon induced corrections to quadrupole moments of odd nuclei. Pole and non-pole diagrams.

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.

Beta-decay half-lives for short neutron rich nuclei involved into the r-process

The beta-strength function model based on Finite Fermi-Systems Theory is applied for calculations of the beta-decay half-lives for short neutron rich nuclei involved into the r- process. It is shown that the accuracy of beta-decay half-lives of short-lived neutron-rich nuclei is improving with increasing neutron excess and can be used for modeling of nucleosynthesis of heavy nuclei in the r-process.

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

The Nozieres–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.

Charge-exchange pigmy resonances of tin isotopes

Charge-exchange states, the so-called “pigmy” resonances, which are below the giant Gamow–Teller resonance, have been studied in the self-consistent theory of finite Fermi systems. Microscopic numerical calculations and semiclassical calculations are presented for nine tin isotopes with the mass numbers A =112, 114, 116, 117, 118, 119, 120, 122, and 124, for which experimental data exist. These data have been obtained in the Sn(3He,t)Sb charge-exchange reaction at the energy E(3He) = 200 MeV. The comparison of calculations with experimental data on the energies of charge-exchange resonances gives the standard deviation δE < 0.40 MeV for microscopic numerical calculations and δE < 0.55 MeV for calculations by semiclassical formulas, which are comparable with experimental errors. The strength function for the 118Sn isotope has been calculated. It has been shown that the calculated resonance energies are close to the experimental values; the calculated and experimental relations between heights of pygmy resonance peaks are also close to each other.

The first self-consistent calculation of quadrupole moments of odd semi-magic nuclei accounting for phonon-induced corrections

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 gL2, where gL 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 phonon is taken into account in which the 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 strongly cancel each other, leaving room for other ‘small’ corrections, so that the resulting PC correction is much lower than the absolute values of each of the two main ones. However, it remains noticeable, making the overall agreement with the data significantly better.

Hyperfine structure of electronic levels and the first measurement of the nuclear magnetic moment of 63Ni

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.

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.

Charge-exchange resonances and restoration of Wigner’s supersymmetry in heavy and superheavy nuclei

Various facets of the question of whether Wigner’s supersymmetry [SU(4) symmetry] may be restored in heavy and superheavy nuclei are analyzed on the basis of a comparison of the results of calculations with experimental data. The energy difference between the giant Gamow–Teller resonance and the analog resonance (the difference of E G and E A) according to calculations based on the theory of finite Fermi systems is presented for the case of 33 nuclei for which experimental data are available. The calculated difference ΔE G–A of E G and E A tends to zero in heavier nuclei, showing evidence of the restoration of Wigner’s SU(4) symmetry. Also, the isotopic dependence of the Coulomb energy difference between neighboring isobaric nuclei 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 SU(4) symmetry is compatible with the possible existence of the stability island in the region of superheavy nuclei.

E2 transitions between excited single-phonon states: Role of ground-state correlations

The probabilities for E2 transitions between low-lying excited 3− and 5− single-phonon states in the 208Pb and 132Sn magic nuclei are estimated on the basis of the theory of finite Fermi systems. The approach used involves a new type of ground-state correlations, that which originates from integration of three (rather than two, as in the random-phase approximation) single-particle Green’s functions. These correlations are shown to make a significant contribution to the probabilities for the aforementioned transitions.

On the anomalous A 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.

On microscopic theory of radiative nuclear reaction characteristics

A survey of some results in the modern microscopic theory of properties of nuclear reactions with gamma-rays is given. First of all, we discuss the impact of phonon coupling (PC) on the photon strength function (PSF) because it represents the most natural physical source of additional strength found for Sn isotopes in recent experiments that could not be explained within the stan- dard HFB+QRPA approach. The self-consistent version of the Extended Theory of Finite Fermi Systems in the Quasiparticle Time Blocking Approximation, or simply QTBA, is applied. It uses the HFB mean field and includes both the QRPA and PC effects on the basis of the SLy4 Skyrme force. With our microscopic E1 PSFs, the following properties have been calculated for many stable and unstable even-even semi-magic Sn and Ni isotopes as well as for double-magic 132Sn and 208Pb using the reaction codes EMPIRE and TALYS with several nuclear level density (NLD) models: 1) the neutron capture cross sections, 2) the corresponding neutron capture gamma spectra, 3) the av- erage radiative widths of neutron resonances. In all the properties considered, the PC contribution turned out to be significant, as compared with the standard QRPA one, and necessary to explain the available experimental data. The results with the phenomenological so-called generalized super- fluid NLD model turned out to be worse, on the whole, than those obtained with the microscopic HFB+combinatorial NLD model. Finally, we also discuss the modern microscopic NLD models based on the self-consistent HFB method and show their relevance to explain experimental data as compared with the phenomeno- logical models. The use of these self-consistent microscopic approaches is of particular relevance for nuclear astrophysics, but also for the study of double-magic nuclei.

Self-consistent theory of finite Fermi systems vs Skyrme–Hartree–Fock method. Spherical nuclei

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 so-called tadpole term.

Microscopic calculations of the characteristics of radiative nuclear reactions for double-magic nuclei

The neutron capture cross sections and average radiative widths of neutron resonances for two double-magic nuclei 132Sn and 208Pb have been calculated using the microscopic photon strength functions, which were obtained within the microscopic self-consistent version of the extended theory of finite Fermi systems in the time blocking approximation. For the first time, the microscopic PSFs have been obtained within the fully self-consistent approach with exact accounting for the single particle continuum (for 208Pb). The approach includes phonon coupling effects in addition to the standard RPA approach. The known Skyrme force has been used. The calculations of nuclear reaction characteristics have been performed with the EMPIRE 3.1 nuclear reaction code. Here, three nuclear level density (NLD) models have been used: the so-called phenomenological GSM, the EMPIRE specific (or Enhanced GSM) and the microscopical combinatorial HFB NLD models. For both considered characteristics we found a significant disagreement between the results obtained with the GSM and HFB NLD models. For 208Pb, a reasonable agreement has been found with systematics for the average radiative widths values with HFB NLD and with the experimental data for the HFB NLD average resonance spacing D0, while for these two quantities the differences between the values obtained with GSM and HFB NLD are of several orders of magnitude. The discrepancies between the results with the phenomenological EGLO PSF and microscopic RPA or TBA are much less for the same NLD model.

Impact of phonon coupling on the radiative nuclear reaction characteristics

The pygmy dipole resonance and photon strength functions (PSF) in stable and unstable Ni and Sn isotopes are calculated within the microscopic self-consistent version of the extended theory of finite fermi systems in the quasiparticle time blocking approximation. The approach includes phonon coupling (PC) effects in addition to the standard QRPA approach. The Skyrme force SLy4 is used. A pygmy dipole resonance in 72Ni is predicted at the mean energy of 12.4 MeV exhausting 25.7% of the total energy-weighted sum rule. With our microscopic E1 PSFs in the EMPIRE 3.1 code, the following radiative nuclear reaction characteristics have been calculated for several stable and unstable even-even Sn and Ni isotopes: 1) neutron capture cross sections, 2) corresponding neutron capture gamma-spectra, 3) average radiative widths of neutron resonances. Here, three variants of the microscopic nuclear level density models have been used and a comparison with the phenomenological generalized superfluid model (GSM) has been performed. In all the considered properties, including the recent experimental data for PSF in Sn isotopes, the PC contributions turned out to be significant, as compared with the QRPA one, and necessary to explain the available experimental data. The phenomenological GSM NLD model used in EMPIRE3.1 gives, on the whole, the worse results than the microscopic HFB plus combinatorial NLD model.

Beta-decay half-lives for the r-process nuclei

For nucleosynthesis calculations of the r-process it is important to know beta-decay half-lives of short-lived neutron-rich nuclei. In the present paper these characteristics are calculated for an extended number of neutron-rich nuclei, important for the r-process. In our calculations the model description of beta-strength functions based on Finite Fermi-Systems Theory is used. The comparison with other predictions and experimental data is done. It is shown that the accuracy of beta-decay half-lives of short-lived neutron-rich nuclei is increasing with increasing neutron excess and can be used for modeling of nucleosynthesis of heavy nuclei in the r-process. For nuclei heavier than lead the half-lives of neutron-rich nuclei are on average 10 times smaller, than proposed of other predictions.

Electric quadrupole and magnetic dipole moments of odd nuclei near the magic ones in a self-consistent approach

We present a model which describes the properties of odd-even nuclei with one nucleon more, or less, with respect to the magic number. In addition to the effects related to the unpaired nucleon, we consider those produced by the excitation of the closed shell core. By using a single particle basis generated with Hartree-Fock calculations, we describe the polarization of the doubly magic-core with Random Phase Approximation collective wave functions. In every step of the calculation, and for all the nuclei considered, we use the same finite-range nucleon-nucleon interaction. We apply our model to the evaluation of electric quadrupole and magnetic dipole moments of odd-even nuclei around oxygen, calcium, zirconium, tin and lead isotopes. Our Random Phase Approximation description of the polarization of the core improves the agreement with experimental data with respect to the predictions of the independent particle model. We compare our results with those obtained in first-order perturbation theory, with those produced by Hartree-Fock-Bogolioubov calculations and with those generated within the Landau-Migdal theory of finite Fermi systems. The results of our universal, self-consistent, and parameter free approach have the same quality of those obtained with phenomenological approaches where the various terms of the nucleon-nucleon interaction are adapted to reproduce some specific experimental data. A critical discussion on the validity of the model is presented.

Restoration of Wigner supersymmetry in heavy and superheavy nuclei

The possibility of the restoration of Wigner supersymmetry (SU(4) symmetry) in heavy and superheavy nuclei has been analyzed by comparing the calculations with experimental data. The differences between the energies of the giant Gamow–Teller resonance (EG) and analog resonance (EA) calculated within the finite Fermi system theory for 33 nuclei for which experimental data exist are presented. The energy differences ΔEG–A between EG and EA tend to zero in heavier nuclei, demonstrating the restoration of Wigner SU(4) symmetry. The energy differences ΔEG–A have also been calculated for heavy and superheavy nuclei located on the betastability line in the mass number range of A = 140–290. In the SU(4) approach, the isotopic dependence of the difference between the Coulomb energies of neighboring isobar nuclei has been analyzed for more than 400 nuclei in the mass number range of A = 3–244. The restoration of Wigner SU(4) symmetry in heavy and superheavy nuclei has been confirmed. It has been shown that the restoration of SU(4) symmetry does not contradict the possibility of the existence of the “island of stability” in the region of superheavy nuclei.