Theory Of Finite Fermi Systems Research Articles

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.

Existence of nuclei with unusual neutron excess?

A realistic model is suggested based on the quasiparticle Lagrange version of the self-consistent Finite Fermi Systems theory supplemented with the microscopically calculated surface parameters of the Landau–Migdal interaction amplitude. The latter are expressed in terms of the off-shell T-matrix of free NN-scattering and show a strong dependence on the chemical potential of a nucleus under consideration in the drip line vicinity. This effect could result in shifting the neutron drip line position to very large values of the neutron excess.

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.

Simple microscopic model for the scalar-isoscalar component of the Landau-Migdal amplitude

A simple microscopic model is proposed that describes the coordinate dependence of the zeroth harmonic f0(r) of the scalar-isoscalar component of the Landau-Migdal amplitude. In the theory of finite Fermi systems due to Migdal, such a dependence was introduced phenomenologically. The model presented in this study is based on a previous analysis of the Brueckner G matrix for a planar slab of nuclear matter; it expresses the function f0(r) in terms of the off-mass-shell T matrix for free nucleon-nucleon scattering. The result involves the T matrix taken at the negative energy value equal to the doubled chemical potential μ of the nucleus being considered. The amplitude f0(r) found in this way is substituted into the condition that, in the theory of finite Fermi systems, ensures consistency of the self-energy operator, effective quasiparticle interaction, and the density distribution. The calculated isoscalar component of the mean nuclear field V(r) agrees fairly well with a phenomenological nuclear potential. Owing to a strong E dependence of the T matrix at low energies, the potential-well depth V(0) depends sharply on μ, increasing as |μ| is reduced. This effect must additionally stabilize nuclei near the nucleon drip line, where μ vanishes.

Structure and direct protonic decay of isobaric analogous and isovector monopole giant resonances

A description of the partial protonic widths of isobaric analogous resonances is proposed on the basis of the continuum random-phase approximation and a partly self-consistent phenomenological version of the theory of finite Fermi systems. The results of the calculations performed for spherical nuclei over a wide interval of atomic-mass values are in satisfactory agreement with the corresponding experimental widths. The probability of the direct protonic decay of an isovector monopole giant resonance in the β− channel is estimated in connection with some recent experiments.

Statistical theory of finite Fermi systems with chaotic excited eigenstates

Statistical theory of finite Fermi systems with chaotic excited eigenstates

Statistical theory of finite Fermi systems with chaotic excited eigenstates

Abstract A theory of strongly interacting Fermi systems of a few particles is developed. At high excitation energies (a few times the single-particle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-particle basis states by the residual two-body interaction. This regime can be described as many-body quantum chaos. Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy. Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g. rare earths) and multicharged ions, molecules, clusters and quantum dots in solids. The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-particle basis states (determinants) constructed using the shell-model orbital basis. A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without d...

Statistical theory of finite Fermi systems based on the structure of chaotic eigenstates

An approach is developed for the description of isolated Fermi systems with finite numbers of particles, such as complex atoms, nuclei, atomic clusters, etc. It is based on statistical properties of chaotic excited states which are formed by the interaction between particles. A type of ``microcanonical'' partition function is introduced and expressed in terms of the average shape of eigenstates ${F(E}_{k},E),$ where $E$ is the total energy of the system. This partition function plays the same role as the canonical expression $\mathrm{exp}(\ensuremath{-}{E}^{(i)}/T)$ for open systems in a thermal bath. The approach allows one to calculate mean values and nondiagonal matrix elements of different operators. In particular, the following problems have been considered: the distribution of occupation numbers and its relevance to the canonical and Fermi-Dirac distributions; criteria of equilibrium and thermalization; the thermodynamical equation of state and the meaning of temperature, entropy and heat capacity; and the increase of effective temperature due to the interaction. The problems of spreading widths and the shape of the eigenstates are also studied.

Microscopic calculations of β-decay characteristics near the A=130 r-process peak

The β-decay half-lives of r-process nuclides near Z=50, N=82 shell closures are calculated within the finite Fermi-system theory. To describe the ground state properties, the ETFSI approximation has been used. Comparison is made with exact self-consistent calculations, previous large-scale predictions and experimental data.

Towards a statistical theory of finite Fermi systems and compound states: Random two-body interaction approach.

The model of Fermi particles with random two-body interaction is investigated. This model allows to study the origin and accuracy of statistical laws in few-body systems, the role of interaction and chaos in thermalization, Fermi-Dirac distribution for quasi-particles with spreading widths, matrix elements of external field and enhancement of weak perturbation in chaotic compound states.

Microscopic description of the excitation of some states in the 90,92,94,96Zr isotopes

We describe the application of a realistic self-consistent theory of finite Fermi systems to the ground and low excited states of the 90,92,94,96 Zr isotopes. Results were obtained for the ground, 2 1 + and 3 1 − states in each nucleus, and for the lowest 4 + , 5 − , 6 + and 8 + states in 90 Zr. Transition densities were generated for the excitation of each of these states and their properties examined. Transition potentials for their excitation by hadronic inelastic scattering were constructed by folding with appropriate interactions between the projectile and each target nucleon. The calculated inelastic scattering cross sections are compared in detail with experimental results, particularly those for alpha particles at 35.4 MeV and 6 Li at 70 MeV. The implications of any discrepancies found are discussed. In addition, the theoretical results were used as “experimental” data in order to test the validity of using various simple models for the analysis of data.

Spin observables for the isovector spin-dipole resonance seen in [formula omitted

We describe how polarization-transfer data can be used to identify J π = 0 −, 1 −and 2 − components of the ΔT = 1, ΔL = 1, ΔS = 1 isovector “spin-dipole” resonance seen in charge-exchange reactions at medium energies. Data for 40Ca(p,n) are compared with distorted-wave impulse approximation (DWIA) calculations with theory of finite Fermi systems (TFFS) wave functions.

Ground state properties and β-decay half-lives near 132Sn in a self-consistent theory

The self-consistent finite Fermi-system theory with three different parameter sets is used to calculate decay energies and Gamow-Teller strength distributions of neutron-rich short-lived nuclides near shell closures Z=50, N=82. Among the parameters, the role of a strong surface neutronproton attraction and an isovector spin-orbit force is discussed. The obtained β-decay half-lives are compared with large-scale calculation results and with available experimental data. Some predictions for the ground state properties of other unstable closed-shell nuclei are presented.

Gamow-Teller strength functions of superfluid odd- A nuclei and neutrino capture reactions

The charge-exchange excitations of superfluid odd- A nuclei are studied within the framework of the self-consistent finite Fermi-system theory. The pairing blocking effects due to the odd quasiparticle, the effective NN-interactions both in the particle-hole (ph) and particle-particle (pp) channel, and also the ph-continuum are taken into account. Gamow-Teller strength functions of 71Ga, 115In and 19F nuclei are calculated and compared with those extracted from experimental spectra of (p,n) reactions. The total capture cross sections of the reactor electron antineutrinos are calculated (assuming complete ν e → ν e conversion), as well as the solar-neutrino capture rates for the 71Ga and 115In+ 19F detectors. Uncertainties regarding nuclear-structure information involved in these calculations are discussed.

Influence of effective spin-orbit interaction on the collective states of nuclei

A self-consistent approach to the description of collective states in nuclei is developed. It is based on a new form of density functional and quasiparticle RPA-type equations of the theory of finite Fermi systems solved in coordinate representation with exact allowance for both central and spin-orbit effective interactions. Within this approach the low-lying natural-parity states and octupole electric strength functions for the 16O, 40Ca, 48Ca and 208Pb nuclei are calculated. It is shown that by incorporating the spin-orbit interaction self-consistently the admixture of the isoscalar 1 − spurious state is avoided and the agreement with experimental data on both excitation energies and reduced probabilities of collective transitions is improved as a rule.

Quenching of the spin-dependent scattering of weakly interacting massive particles on heavy nuclei

We present calculations of the quenching of the spin-dependent elastic scattering cross section for dark matter WIMPs on heavy nuclei. The theory of finite Fermi systems was used to describe the behavior of the nuclear spin matrix elements in the nuclear medium. The results of the calculations for planned dark matter detector nuclei are not only always smaller than corresponding single particle estimations but in some cases also differ from the ones obtained by using measured nuclear magnetic moments.

Effects of nuclear structure in the spin-dependent scattering of weakly interacting massive particles

We present calculations of the nuclear from factors for spin-dependent elastic scattering of dark matter WIMPs from123Te and131Xe isotopes, proposed to be used for dark matter detection. A method based on the theory of finite Fermi systems was used to describe the reduction of the single-particle spin-dependent matrix elements in the nuclear medium. Nucleon single-particle states were calculated in a realistic shell model potential; pairing effects were treated within the BCS model. The coupling of the lowest single-particle levels in123Te to collective 2+ excitations of the core was taken into account phenomenologically. The calculated nuclear form factors are considerably less then the single-particle ones for low momentum transfer. At high momentum transfer some dynamical amplification takes place due to the pion exchange term in the effective nuclear interaction. But as the momentum transfer increases, the difference disappears, the momentum transfer increases and the quenching effect disappears. The shape of the nuclear form factor for the131Xe isotope differs from the one obtained using an oscillator basis.

Ground-state magnetization density of 89Y.

Elastic electron scattering cross sections have been measured for [sup 89]Y at 180[degree] for 0.72[lt][ital q][lt]2.67 fm[sup [minus]1]. The [ital M]1 form factor has been extracted and a Fourier-Bessel analysis performed to obtain the ground-state magnetization density. Calculations including effects of core polarization have been performed within the framework of the finite Fermi system theory. These show a weakening of the strong repulsion in the spin-isospin channel and are in overall agreement with the data.

Giant dipole resonance in small metal clusters

The problem of giant dipole resonance in small metal clusters is considered. By using the finite Fermi system theory the description of the photoabsorption cross section is given. The effect of spillout of valence electrons is disregarded. It is shown that there exist two types of valence electron vibrations: giant dipole resonance and surface plasmons. The energies of the giant dipole and the plasmon resonances are calculated. The values of the maximum cross section for the two types of resonances are estimated. A comparison of theoretical results with experimental data is also given.

Many-particle effects in nucleus-nucleus collisions

Migdal's theory of finite Fermi systems is applied for the description of nucleus-nucleus collisions at laboratory energies less than a few GeV A . It is taken into account that the pionic degree of freedom softens in nuclear matter. Free paths of nucléon and pion quasiparticles are calculated. Compact formulas are written for pion, nucleon- and photon-production cross sections. In addenda, the main formulas are presented for the NN-interaction amplitude and pion polarization operator in non-equilibrium and heated equilibrium nuclear matter.