Finite Fermi systems theory and self-consistency relations

The self-consistent theory of the finite Fermi systems is outlined. This approach is based on the same Fermi liquid theory principles as the familiar theory for finite Fermi systems (FFS) by Migdal. We show that the basic Fermi system properties can be evaluated in terms of the quasiparticle Lagrangian L_q which incorporates the energy dependency effects. This Lagrangian is defined so that the corresponding Lagrange equations should coincide with the FFS theory equations of motion of the quasiparticles. The quasiparticle energy E_q defined in the terms of t he quasiparticle Lagrangian L_q according to the usual canonical rules is shown to be equal to the binding energy E_o of the system. For a given Lagrangian L_q the particle densities in nuclei, the nuclear single-particle spectra, the low-lying collective states (LCS) properties, and the amplitude of the interquasiparticle interaction are also evaluated. The suggested approach is compared with the Hartree-Fock theory with effective forces.     

The nucleus 60Fe from 58Fe(t,p)60Fe

The ⁵⁸Fe(t, p)⁶⁰Fe reaction has been studied at an incident energy of 15 MeV. Angular distributions have been measured for 29 states up to E_x = 5.2MeV. Comparison of the data with DWBA calculations, using pure configurations for the transfer amplitudes, has enabled the L-transfer (and hence J^π value) to be determined for all the states investigated. Twenty-three new J^π assignments have been made. The trend in the ground-state strength for the ^54,56,58Fe(t, p)^56,58,60Fe reactions has been reproduced, using a simple model in which the two-neutron transfer amplitudes are calculated in the quasiparticle limit. Finally the distribution of transition strength among the excited states of the three reactions is discussed.     

Forward peaking of near Coulomb energy protons in (n,p) reactions at 14.1 MeV

We apply a modified statistical model of compound nucleus reactions to analyse low energy proton angular distributions from the ⁹³Nb(n, p), ^natAg(n, p) and ^natIn(n, p) reactions at E_n=14.1 MeV. The forward peaking at the maximum of the proton evaporation spectrum at E _p = 6–8 MeV is reproduced and interpreted as an indication of the decay of thermalized-nonequilibrated nuclear states.     

Quantum and classical relativistic energy states in stationary geometries

The positive and negative root states (E⁺, E^?) for a particle moving along a geodesic in a stationary background, introduced by Christodoulou and Ruffini, are here interpreted in the framework of a relativistic quantum field theory. It is shown how E⁺ and E^? have to be considered as the classical correspondent of the positive and negative energy states of a quantized field. It is explicitly shown that crossing between the states E⁺ and E^? can occur and consequently the necessary condition for particle creation as given by Klein, Sauter, Heisenberg and Euler can be encountered.     

QRPA coordinate space calculations of 2<Superscript>+</Superscript> states in <Emphasis Type="Italic">N</Emphasis>=20 isotones

The first 2⁺ states in N=20 isotones are studied within the self-consistent quasiparticle random phase approximation based on the Green’s function method. The residual interaction between quasiparticles with full velocity dependence is consistently derived from the Skyrme interaction plus pairing interaction energy density functional. The B(E2, 0 ₁ ⁺ → 2 ₁ ⁺ ) transition probabilities and the excitation energies of the first 2⁺ states are well described within a single framework. We discuss mainly the microscopic origin of the anomalously large B(E2) value and the very low excitation energy in ³²Mg.     

Spectral functions and hole nuclear states

An explicit expression for the spectral function of hole nuclear states is given in the framework of the coherent fluctuation model. It is shown that the spectral function and single-particle width, centroid energy, quasiparticle effective mass, etc., are functionals of the ground-state nucleon density distribution. Calculation of the spectral functions for⁵⁸Ni,⁴⁰Ca,²⁸Si is carried out and the results are compared with the experimental data.     

The statistical theory of multi-step compound and direct reactions

The theory of nuclear reactions is extended so as to include a statistical treatment of multi-step processes. Two types are distinguished, the multi-step compound and the multi-step direct. The wave functions for the system are grouped according to their complexity. The multi-step direct process involves explicitly those states which are open, while the multi-step compound involves those which are bound. In addition to the random phase assumption which is applied differently to the multi-step direct and to the multi-step compound cross-sections, it is assumed that the residual interaction will have non-vanishing matrix elements between states whose complexities differ by at most one unit. This is referred to as the chaining hypothesis. Explicit expressions for the double differential cross-section giving the angular distribution and energy spectrum are obtained for both reaction types. The statistical multi-step compound cross-sections are symmetric about 90°. The classical statistical theory of nuclear reactions is a special limiting case. The cross-section for the statistical multi-step direct reaction consists of a set of convolutions of single-step direct cross-sections. For the many step case it is possible to derive a diffusion equation in momentum space. Application is made to the reaction ¹⁸¹Ta(p, n)¹⁸¹W using the statistical multi-step compound formalism.     

Excitation spectrum of a paramagnetic-superconducting contact

A calculation of the bound states in a paramagnetic-superconducting contact, valid at any temperature belowT _c, is performed by using a recently developed method of solving the Bogoliubov equations. The problem of self-consistency of the pair-potentialΔ(x) is being avoided by leaving open the detailed form ofΔ(z), introducing instead the characteristic lenghth for the spatial variation of the pair-potential,d=_O∫ ^D (1?Δ(z)/Δ)dz, as a fit parameter. The energies, the quasiparticle wave-functions and the density of the bound states are calculated for negligible impurity scattering. The energy gap of the excitation spectrum reduces from about one third of its bulk value to practically zero as the thicknessa of the normal film increases froma?d toa?d.     

Neutronh 11/2 alignments in the triaxial nucleus133La

High spin states have been studied in¹³³La via the¹²²Sn (¹⁵N, 4ny) fusion evaporation reaction. Bands build on low lying h_11/2,g_7/2 and d_5/2 proton states have been identified. At higher spin a h_11/2 neutron alignment is observed. The softness with respect to the triaxial deformation makes the nuclear shape sensitive to the quasiparticle configurations and coexistence between states withy ≈ + 30°,y ≈ ? 30° andy ≦ ? 60° was found. The results have been interpreted using total routhian surface (TRS) model calculations.     

The 18O(p, α)15N reaction at stellar energies

The ¹⁸O(p, α)¹⁵N reaction has been investigated in the energy range E_p = 72–935 keV. The three known resonances above E_p = 620 keV have been confirmed and four new resonances have been found below E_p = 340 keV. All observed resonances correspond to known compound states in ¹⁹F. Information on resonance energies, total widths and ωγ values is reported. The low-energy resonances are superimposed on a non-resonant reaction yield, which varies smoothly with beam energy and which exhibits pronounced α-particle angular distributions asymmetric around 90°. The explanation of these data requires either interferring amplitudes of broad resonances with differing parities or a direct (p, α) reaction mechanism. The investigated energy range corresponds to the important temperature range of T = (0.05–2.5) × 10⁹ K. The energy averaged astrophysical reaction rates are compared with predictions.     

Structure of excited states in100Mo and102Mo from spectroscopy using18O induced reactions

The lifetimes have been determined for the 2⁺, 0^+～ and 4⁺ states in¹⁰⁰Mo and¹⁰²Mo using the recoil-distance Doppler-shift method. The states have been excited in¹⁰⁰Mo by Coulomb excitation and in¹⁰²Mo by the two-neutron transfer reaction induced by¹⁸O ions on a¹⁰⁰Mo target. The study of the excitation function for the elastic and inelastic scattering on the ground and first excited 2⁺ state in¹⁰⁰Mo at beam energies between 20 and 61 MeV shows that 40 MeV is the highest incident energy for pure Coulomb excitation. Above this energy nuclear absorption sets in and nuclear scattering contributes to the excitation of the 2⁺ state of¹⁰⁰Mo. From the lifetimes of the 2⁺ and 4⁺ states deformation parameters of ¦β¦= 0.21 and ¦β¦=0.31 for¹⁰⁰Mo and¹⁰²Mo respectively were deduced. The 0^+′ levels are not shape isomeric states, as suggested earlier, but they decay by enhancedE2 transitions to the first 2⁺ states. From a comparison with similar states in other transitional nuclei it is suggested that they are band heads forβ vibrational bands.     

Deformation properties of the neutron-deficient odd-A Pt and Hg nuclei

Nuclear and atomic spectroscopy measurements have provided a great number of data on the neutron-deficient Pt and Hg nuclei. The odd-A Pt and Hg with A<186 have a prolate shape, and the even-even isotopes have a triaxial shape, while the nuclear shape of the odd-A Pt and Hg with A>186 is still an open question. The energy of the low-lying levels and the nuclear moments have been calculated in the framework of a semimicroscopic “axial-rotor + 1 quasiparticle” coupling model. The predictions are compared with the experimental data and discussed. The results strongly suggest a prolate shape for the negative-parity low-lying states of the odd-A ^187–191Pt and ^187–193Hg isotopes.     

Properties of the low-lying excited states in even-even nuclei around the closed shell N=82

The properties of low-lying states in ¹³⁶Ba and ¹⁴⁴Nd are calculated within the quasiparticle phonon model. It is shown that the strong quadrupole interaction in the particle-particle channel leads to the appearance of low-lying isovector excitations. Due to this reason, there are two branches in the lowlying part of the spectrum, an isoscalar and an isovector one. Both branches show peculiar regularities of E2 and M1 transitions.     

Microscopic study of positive-parity yrast bands of 224−234Th isotopes

The positive-parity bands in ^224???234Th are studied using the projected shell model (PSM) approach. The energy levels, deformation systematics, B(E2) transition probabilities and nuclear g-factors are calculated and compared with the experimental data. The calculation reproduces the observed positive-parity yrast bands and B(E2) transition probabilities. Measurement of B(E2) transition probabilities for higher spins and g-factors would be a stringent test for our predictions. The results of theoretical calculations indicate that the deformation systematics in ^224???234Th isotopes depend on the occupation of low k components of high j orbits in the valence space and the deformation producing tendency of the neutron–proton interaction operating between spin orbit partner (SOP) orbits, the [(2g_9/2) _π –(2g_7/2) _ν ] and [(1i_13/2) _π –(1i_11/2) _ν ] SOP orbits in the present context. In addition, the deformation systematics also depend on the polarization of (1h_11/2) _π orbit. The low-lying states of yrast spectra are found to arise from 0-quasiparticle (qp) intrinsic states whereas the high-spin states turn out to possess composite structure.     

The fission processes 236U(α, α′f) at Eα = 50 MeV and 235U(d,pf) at Ed = 23 MeV and the total kinetic energy release in fission of excited nuclei

The fissioning nucleus ²³⁶U was investigated by two different reactions. Total kinetic energies (TKE) as function of the excitation energy above the highest fission threshold are shown to have different behaviour for E_X below the two quasiparticle threshold 2Δ and above. A strong dependence on the mass splitting is observed.     

Measurement ofg-factors in160Yb by aγ-γ coincidence technique

Aγ-γ coincidence technique has been developed forg-factor measurements of short-lived nuclear states. The method involvesγ-detection in 4π geometry as well as transient magnetic fields and the recoil-distance technique. A first experiment was performed for the isotope¹⁶⁰Yb produced in the reaction⁶⁴Ni(¹⁰⁰Mo, 4n) at 430 MeV beam energy. The valueg=? 0.23(31) of the 14⁺ yrast state, which is compatible with zero, establishes thevi _13/2 quasiparticle structure to be responsible for the first backbend. A meang-factor for low spin states around the 4⁺ state,g=+0.48(26) was also derived as well as lifetimes for yrast states up toI ^π=8⁺.     

Statistical theory of nuclear neutrino capture: (II). Inclusion of first-forbidden transitions

The statistical theory of nuclear neutrino capture is extended to include first-forbidden transitions. A comparison with the theory of Bahcall and Frautschi is made. It is found that the present theory predicts neutrino capture cross sections which are smaller than those of Bahcall and Frautschi by a factor 2–3 for neutrino energies less than 50 MeV when first-forbidden transitions are dominant. Calculation of the cross section is made for the process in which ³⁷Cl nuclei capture electron neutrinos that are emitted in muon decay. The present calculation gives a cross section which is around one half of that of Donnelly and Haxton. Finally the contributions of the highly excited states in ³⁷Ar to the neutrino capture cross section are evaluated. It is shown that the contributions from the highly excited states (E > 6.02 MeV) to the neutrino capture cross section amount to 60% for E_v = 50 MeV.     

Fine Structure and Collectivity of the Levels of the Pygmy Dipole Resonance in <Superscript>208</Superscript>Pb in a Self-Consistent Model

A novel fully self-consistent microscopic approach based on the energy density functional method is employed to calculate the fine structure of the pygmy dipole resonance in ²⁰⁸Pb, i.e., the energies and reduced probabilities of E1 transitions for the states with energies below 10 MeV. The approach includes the random-phase approximation, quasiparticle–phonon interaction and the single-particle continuum. The theoretical results are compared to the available high-resolution data and found to agree with measured integral characteristics of the pygmy dipole resonance at energies above 5.7 MeV. Residual spin–spin forces are quantified, and their contribution is found to be significant at both low and high energies. A recently proposed criterion is employed to analyze the collectivity of the 1^–states in ²⁰⁸Pb.