Self-consistent medium polarization in RPA

The standard random-phase approximation for finite systems is extended by including the effect of the exchange of the RPA phonons in the residual interaction selfconsistently. It is shown that this particle-hole interaction is strongly energy dependent due to the presence of poles corresponding to 2p2h (and more complex) excitations. The RPA eigenvalue problem with this energy-dependent residual interaction also provides solutions for these predominantly 2p2h-like states. In addition a modified normalization condition is obtained.This new scheme is applied to ⁵⁶Ni (⁵⁶Co) in a large (up to 7ħω) configuration space using a residual interaction of G-matrix type. It is shown that the lowest 2⁺ eigenvalue, which in the standard RPA becomes imaginary, is stabilized when the selfconsistent screening is taken into account. Another feature observed is the splitting of the M1 strength as an example of 1p1h and 2p2h mixing.     

Exciton level densities with spin and parity based on random matrix model

Level densities for fixedJ ^π and the exciton number are evaluated for closed shell nuclei⁴⁰Ca and²⁰⁸Pb. The single particle spectra and wave functions are generated by Woods-Saxon potentials. The effects of the residual interaction are taken into account statistically by the method of generating function and Grassmann integral. The matrix elements for the residual interaction are assumed to be random variables with Gaussian distributions whose second moments are calculated by using a zero range interaction. The second moments are evaluated for fixedJ ^π by ignoring the Pauli principle between active nucleons and the spectator. This approximation is shown numerically to be very good. The partial level densities are calculated using the second moments as well as independent particle model spectra. The resulting level densities spread over wider energy ranges, have a smoother energy dependence and are enhanced at low energies compared with the independent particle model densities, although the total level densities do not differ by much.     

Microscopic description of the E0, E2 and E1 giant resonances in 40Ca, 48Ca and 56Ni

The isovector E1 as well as the isoscalar, isovector and full electromagnetic E2 and E0 strength distributions for ⁴⁰Ca, ⁴⁸Ca and ⁵⁶Ni have been calculated in a large energy range up to 50 MeV of excitation. The microscopic model used includes the continuum RPA, 1p1h⊗phonon configurations and ground state correlations induced by these configurations. It is shown that the latter effect gives an increase of the energy weighted sum rules of 4–7%. In all these nuclei the isoscalar E0 and E2 resonances are spread out over the broad energy region. We obtained a reasonable good agreement with the available experimental data including the recent ones for the isoscalar E0 resonance in ⁴⁰Ca. The theoretical transition densities show a rather strong dependence on the excitation energy.     

Many-body corrections to the nuclear anapole moment

The many body contributions to the nuclear anapole moment of ¹³³Cs, ²⁰⁵TI, ^207,209Pb and ²⁰⁹Bi are calculated in the random-phase approximation with the effective residual interaction. A strong reduction of a valence nucleon contribution was found, caused by the core polarization effects. The new type of contribution to the anapole moment from the core particles due to the induced weak interaction was calculated. The last contribution compensates the former reduction to large extent. The compensation is complete in the leading approximation if the proton-neutron residual forces are absent.     

(d, 6Li) reactions on intermediate mass nuclei

(d, ⁶Li) reactions have been studied at 28 and 36 MeV on ^{40, 42}Ca, ⁵⁶Fe, ⁵⁸Ni and ¹¹⁴Sn. In most reactions levels were identified up to 3–4 MeV. A DWBA analysis has been carried out in the zero-range approximation, assuming simple configurations for the final state. The spectroscopic factors for the ground-state transitions remain fairly constant from ⁴⁰Ca to ¹¹⁴Sn. Transitions leading to excited states are discussed.     

Deformation effects in the 28Si+12C and 28Si+28Si reactions

The possible occurrence of highly deformed configurations is investigated in the ⁴⁰Ca and ⁵⁶Ni di-nuclear systems as formed in the ²⁸Si + ¹²C, ²⁸Si reactions by using the properties of emitted light charged particles. Inclusive as well as exclusive data of the heavy fragments and their associated light charged particles have been collected by using the ICARE charged particle multidetector array. The data are analysed by Monte Carlo CASCADE statistical-model calculations using a consistent set of parameters with spin-dependent level densities. Significant deformation effects at high spin are observed as well as an unexpected large ⁸Be cluster emission of a binary nature.     

An analysis of some proton-nucleus scattering data at 1 GeV

The elastic and inelastic scattering data of 1 GeV protons on ¹²C, ³⁹K,^{40, 48}Ca, ⁵⁸Ni and ²⁰⁸Pb are analysed within the framework of Glauber theory. The collective excitations to one-phonon levels are treated using the Tassie model under the adiabatic approximation. Effects of both the coupling between the elastic and the inelastic channels and the two-body correlation in the intrinsic state are considered. The ground state and transition densities for the protons are taken from electron scattering experiments and appropriate assumptions for the neutron densities are made. In most of the cases, better agreement with the experimental data than reported in earlier analyses is obtained. The effects of the coupling and the pair correlation seem to be important only for ¹²C. The elastic data strongly indicate that the density distributions for protons and neutrons in ⁴⁸Ca and ²⁰⁸Pb are different. In ⁴⁸Ca, the surface envelope of the neutron distribution is found to be the same as for the proton distribution but is placed at a larger radius. On the other hand, the neutron distribution in ²⁰⁸Pb seems to be relatively much more diffuse.     

Temperature dependence of collective states in the random-phase approximation

We investigate the temperature dependence of collective states in the framework of the random-phase approximation at finite temperature. We show that sum rules can be extended to collective energies at finite temperature. Numerical methods are developed to solve the RPA equations at finite temperature. Results are presented and discussed in the case of ⁴⁰Ca for isovector dipole and isoscalar octupole vibrations, using oscillator wave functions and a zero-range force. We show that the broadening of giant dipole resonances observed experimentally, appears as a natural consequence of the structure of the RPA equations. Comparison is made with the schematic model for which the temperature dependence of collective states can be worked out analytically.     

Microscopic calculation of the surface absorption in the optical potential

We calculated the contributions of the two-particle one-hole (2p-1h) and the one-particle two-hole (1p-1h) excitations to the imaginary partW(E, R) of then-⁴⁰Ca optical potential. The bound single particle states and energies of the⁴⁰Ca nucleus are calculated quantum mechanically by solving the Schrödinger equation with a Woods-Saxon potential. For the excited states in the continuum we use the Thomas-Fermi approximation. Different forms of contact residual interactions have been tested. A combination of aδ-force and a smeared SDI can fit the phenomenologicalW(E, R).     

Implication of proton-nucleus scattering for density distributions of unstable nuclei

The use of elastic proton scattering at intermediate and high energies to obtain information about the density distributions of unstable nuclei is investigated. A comparison between the relativistic impulse approximation (RIA) and Glauber model for proton scattering from ¹⁶O, ⁴⁰Ca, ⁴⁴Ca and ⁴⁸Ca at medium energies is performed. We used density distributions derived from the relativistic mean-field theory, employing the recent relativistic force NL-RA1, as well as experimental and phenomenological densities. It is found that the eikonal approximation can describe the cross-section only at small scattering angles and is weakly sensitive to the density distributions, while the RIA nicely produced the experimental cross-sections, even at medium and larger angles, and was very sensitive to the nuclear densities. Furthermore, the RIA better describes the isospin dependence of the cross-section. We used the RIA to investigate the density distribution of ⁵⁸Ca for proton scattering at different energies. It is found that the cross-section strongly depends on the parameters of the density distribution even at a small scattering angle. These results are important in extracting information about the structure of unstable nuclei. We also investigated the RIA and its sensitivity in describing halo nuclei such as ⁶He. We used for ⁶He a no-halo Gaussian density and a realistic-halo density that derived in the cluster orbital shell model approximation and contains the extended distribution of the valence nucleons. Comparison with the recent experimental data at GSI at 717 MeV/nucleon shows that the RIA successfully described the data at all considered range of the momentum transfer and on the other hand favor the halo structure of ⁶He. Received: 1 December 2001 / Accepted: 31 July 2002 / Published online: 11 February 2003 RID="a" ID="a"e-mail: mrashdan@hotmail.com Communicated by P. Schuck     

Calculations of the β-decay half-lives of neutron-deficient nuclei

In this work,β~+/EC decays of some medium-mass nuclei are investigated within the extended quasiparticle random-phase approximation(QRPA),where neutron-neutron,proton-proton and neutron-proton(np) pairing correlations are taken into consideration in the specialized Hartree-Fock-Bogoliubov(HFB) transformation.In addition to the pairing interaction,the Br¨uckner G-matrix obtained with the charge-dependent Bonn nucleon-nucleon force is used for the residual particle-particle and particle-hole interactions.Calculations are performed for even-even proton-rich isotopes ranging from Z =24 to Z =34.It is found that the np pairing interaction plays a significant role inβ-decay for some nuclei far from stability.Compared with other theoretical calculations,our calculations show good agreement with the available experimental data.Predictions of β-decay half-lives for some very neutron-deficient nuclei are made for reference.     

Microscopic analysis of the breathing mode in 40Ca and 58Ni

Recent experimental studies of the giant electric resonance region in ⁵⁸Ni and ⁴⁰Ca with inelastically scattered α-particles of energy E_α= 240 MeV are analyzed within a microscopic nuclear structure model. The model includes the continuum RPA and more complex 1p1h⊗phonon configurations. By superimposing the contributions of different multipoles up to L = 4 we obtain good agreement with the newest (reanalyzed) data for the isoscalar monopole strength and for the total (α,α′) cross section in ⁵⁸Ni. Agreement with experiment for the isoscalar monopole resonance in ⁴⁰Ca is obtained too. We emphasize the necessity of using microscopic transition densities and discuss consequences for the analyses of such experiments in light and medium mass nuclei. It is shown that the gross structure of the isoscalar monopole resonance in ⁴⁰Ca is caused by the 1p1h⊗phonon configurations. Received: 23 December 1999 / Revised version: 28 February 2000     

Properties of finite nuclei in a relativistic quantum field theory

A renormalizable relativistic quantum field theory is used to study finite nuclei in the mean-field Thomas-Fermi approximation. Mass formula parameters are calculated and proton densities illustrated for ⁴⁰Ca and ²⁰⁸Pb. The Dirac equation is solved to determine single-particle spectra.     

DWBA approach to inelastic scattering at medium energies

Medium energy proton elastic and inelastic scattering to states of ⁵⁸Ni and ²⁰⁸Pb, and ⁴He elastic and inelastic scattering to states of ⁴⁰Ca, are analyzed using the partial wave approach, by solving the Schrödinger equation with relativistic kinematics and using the distorted wave Born approximation. Our results can be compared with results of several previous analyses of the nucleon inelastic data using the Glauber approximation. Our calculations are absolute, using nuclear collective parameters obtained from a survey of a large number of low-energy analyses of inelastic scattering of electrons, nucleons and nuclei from ⁴⁰Ca, ⁵⁸Ni and ²⁰⁸Pb.     

Gamma-ray spectroscopy of the doubly magic nucleus 56Ni

The doubly magic N = Z nucleus ⁵⁶Ni has been investigated with two fusion-evaporation reactions; ⁴⁰Ca(²⁸Si, 3α)⁵⁶Ni at a beam energy of 122MeV and ²⁸Si(³²S, 2p2n)⁵⁶Ni at 130MeV. To detect γ-rays in coincidence with evaporated particles the Ge-detector array Gammasphere was used in conjunction with the charged-particle detector system, Microball and a 1π neutron detector array. Results include a significantly extended level scheme of ⁵⁶Ni, which is compared to large-scale shell model calculations in the fp shell. The experimental and theoretical results agree to a large extent, with one notable exception; the theoretical model fails to predict the proper sequence of the yrast and yrare 8⁺ states.     

On the energy spectra of single-particle states in nuclei

The single-particle spectra of ¹⁶O, ⁴⁰Ca, ⁴⁸Ca and ⁵⁶Ni have been studied using self- consistent field methods and a quadratically velocity-dependent two-nucleon effective (reaction- matrix) interaction. The self-consistent field equations are derived in some detail for the spin- independent interaction which is used. A one-body spin-orbit interaction of the Thomas form is added.     

RPA calculations with Gaussian expansion method

The Gaussian expansion method (GEM) is applied to calculations of the nuclear excitations in the random-phase approximation (RPA). We adopt the mass-independent basis-set that is successful in the mean-field calculations. The RPA results obtained by the GEM are compared with those obtained by several other available methods in Ca isotopes, by using a density-dependent contact interaction along with the Woods–Saxon single-particle states. It is confirmed that energies, transition strengths and widths of their distribution are described by the GEM with good precision, for the 1⁻, 2⁺ and 3⁻ collective states. The GEM is then applied to the self-consistent RPA calculations with the finite-range Gogny D1S interaction. The spurious center-of-mass motion is well separated from the physical states in the E1 response, and the energy-weighted sum rules for the isoscalar transitions are fulfilled reasonably well. Properties of low-energy transitions in ⁶⁰Ca are investigated in some detail.     

The quasiparticle rpa as a model for gamow-teller ß-decay

The validity of the quasiparticle random-phase approximation is studied by comparing it with full shell-model calculations in the sd-shell. Phenomenological interactions relevant for the sd-shell have been applied, and Gamow-Teller ß⁺ strengths are calculated. It is found that in the QRPA, the ß⁺ strength is a factor of two higher than the shell-model result. The shell-model results are less sensitive to the particle-particle interaction strength than the QRPA. With u, v factors from the shell-model wavefunctions, the ß⁺ strength in the QRPA reproduces the shell-model result. This suggests that the QRPA does not contain enough ground-state correlations.