Particle–particle Tamm–Dancoff approximation and particle–particle random phase approximation calculations for 18O and 18F nuclei

The nuclear structures of ¹⁸O and ¹⁸F nuclei are studied using particle–particle Tamm–Dancoff approximation (pp TDA) and particle–particle random phase approximation (pp RPA). All possible single-particle states of the allowed angular momenta are considered in the 0p and 1s–0d shells. The Hamiltonian is diagonalized in the presence of Warburton and Brown interactions. The results containing energy-level schemes and transition strength B(E2) are compared with the available experimental data.     

Structure of unstable nuclei near proton drip line

Gamov-Teller (GT) states in nuclei near the proton drip line are studied by using a microscopic Hartree-Fock (H-F) + Tamm-Dancoff approximation (TDA) (or random phase approximation (RPA)). The calculations predict that giant Gamow-Teller (GT) β-decays are possible for N=Z nuclei heavier than ₂₈⁵⁶Ni₂₈, carrying most of the sum rule strength. The amplitude of isospin T=1 admixed to the T=0 ground state in N=Z nuclei is also discussed in relation with Fermi β-decay sum rule. Finally, the shapes of unstable nuclei near the proton drip line are studied by using the finite-range droplet model (FRDM).     

Study of the Gamow-Teller resonance in 90Nb and 208Bi

An approach is proposed for studying the spreading properties of the Gamow-Teller resonance (GTR) in heavy nuclei including the coupling to 2p2h configurations and the ground-state correlations beyond RPA. The GTR is generated by a proton p-neutron h (πp-νh) phonon within the renormalized RPA. The second-order configuration mixing beyond RPA is realized by constructing two-phonon configurations, in which one of two intermediate phonon states is a πp-νh phonon. The numerical calculations are performed in the parent nuclei ⁹⁰Zr and ²⁰⁸Pb making use of M3Y nucleon-nucleon interaction and the single-particle wave functions obtained in the standard harmonic oscillator potential. The single-particle energies around the Fermi surface are substituted with the empirical values or those given by a Woods-Saxon potential. The results obtained provide a reasonable account for recent experimental findings on the GTR in these nuclei. The extension of the present approach to highly excited (hot) nuclei is also provided. The GTR is found to be stable against temperatures up to T = 6 MeV.     

Calculations of the giant dipole resonance for sd-shell nuclei in the open-shell random phase approximation

The systematics of the giant dipole resonance have been calculated in the open-shell RPA for all the self-conjugate sd-shell nuclei, using (i) a phenomenological Rosenfeld interaction, (ii) Barret, Hewitt and McCarthy G-matrix elements and (iii) Kuo G-matrix elements. The excitations are based on shell model ground states for all nuclei except ²⁸Si for which a projected Hartree-Fock ground state was used.     

ENERGY DEPENDENCE OF G MATRIX AND RPA

The effect of energy dependence (ED) of the G matrix on RPA is investigated. Using the Hamada-Johnston potential, we calculate the 1p-1h TDA spectra of ¹⁶O. The following four cases are considered: (1) every G matrix element is approximated by its on shell value, (2) ED of G is taken intoaccount rigorously, (3) the effect of self-screening (SC) is considered, but the G matrix elements are assumed on the energy shell, (4) both SC and ED of G are taken into account. It is found that ED of G indeed causes a substantial damping effect on the backward-propagating bubbles of RPA as suggested by Wu. Further, ED of G and SC work in the same direction to diminish the difference between the energy spectra calculated by TDA and RPA.     

Contribution of particle-particle,hole-hole and particle-hole ring diagrams to the binding energies of finite nuclei

Two classes of diagrams, namely particle-particle, hole-hole (pp, hh) and particle-hole (ph) ring diagrams are summed for the nuclei ¹⁶O and ⁴⁰Ca, and their contributions to the ground-state energy shift ΔE of these nuclei is calculated. We find that hh and mixed diagrams (involving both pp and hh interactions) are not less important than the usual pp ladder diagrams which are summed in the standard Brueckner approach. We also study the convergence of these two classes of diagrams as the dimension of the model space involved is increased, and as a function of the residual interaction used. In evaluating these diagrams a transition-amplitude method is used. This is compared to the quasi-boson correlation expression for the ground-state energy due to particle-hole excitations and to an analogous correlation expression resulting from particle-particle and hole-hole excitations. Additionally we derive expressions for, and evaluate a subclass of these diagrams namely “TDA” ring diagrams, where unlike the usual pp, hh and ph diagrams, backward-folding graphs are excluded. We find that the backward-folding graphs are negligible for pp, hh ring diagrams and small for ph graphs. In the smallest model space considered for ⁴⁰Ca we also obtained the TDA ring diagram contributions via matrix inversion techniques which additionally allow us to study the relative importance of ph exchange graphs neglected in the ring-diagram formalism, and of cross TDA diagrams (i.e. TDA ring diagrams where both pp, hh, and ph interactions are allowed). Finally we study the uncertainties spurious effects introduce in ring-diagram calculations.     

Self-screening of the particle-hole interaction and core polarization of the effective two-particle interaction

The diagrams of the Tamm-Dancoff and random-phase approximations (TDA and RPA) have been summed to calculate the core polarization of the effective interaction between two nucleons in the 1s0d and Ip0f shells. The large core-polarization corrections obtained in the TDA and particularly the RPA are strongly reduced when the self-screening corrections to the particle-hole and ground-state correlation vertices are included. The screening corrections serve to suppress the collectivity of the core phonons and in particular stabilize the isoscalar monopole phonon in ⁴⁰Ca against collapse. When screening is included the TDA and RPA give core-polarization corrections which are similar in magnitude and in many cases lead to good agreement with experiment. Because of neglected effects and other uncertainties the qualitative rather than the quantitative features of the results are stressed.     

Particle-hole calculations in4He and16O with centre of mass subtracted kinetic energy

It is found that in light nuclei it is very important to use a relative kinetic energy operator. This kinetic energy is mass number dependent and contributes in all odd parity (J*,T) channels. In particular it is seen to produce the spurious state exactly at zero energy in the (1⁻, 0) channel in TDA both in⁴He and¹⁶O. The effect of the relative KE is to decrease the central force attraction and increase the relative importance of the tensor force. The latter is important in RPA. Sussex matrix elements without the hard core are used.     

Nuclear compression modulus and isotope shifts of Pb nuclei

Isotope shifts of Pb nuclei are studied by taking into account giant monopole and quadrupole resonance by a perturbative method. Giant monopole states are calculated by the HF + RPA response function method using three parameter sets of the Skyrme interactions SGI, SGII and SIII which give the compression moduli K_∞ = 269 MeV, 217 MeV and 356 MeV, respectively. Our calculations reproduce the kink of the observed isotope shifts at ²⁰⁸Pb, while the second-order effect due to the giant quadrupole resonances is not enough to explain the observed odd-even staggering. The Skyrme force SGII having K_∞ = 217 MeV shows the best quantitative agreement among three forces in comparison with the experimental data of the isotope shifts of Pb nuclei. The effect of the effective mass is also discussed.     

Proton and neutron contributions to the charge longitudinal response

The charge longitudinal response of nuclei, as measured by inclusive inelastic electron scattering, is investigated in the semiclassical RPA framework. The proton and neutron contributions to the total response are explicitly separated out. It is found that a sizable neutron ejection can be induced by RPA correlations, particularly at low momentum and energy transfer. A comparison of our theory with the experimental data is presented, also in the case of asymmetric nuclei (N ≠ Z). In particular, the differences in the neutron contributions between ³⁰Ca and ⁴⁸Ca are discussed.     

Core polarization effects on transition densities in medium-heavy nuclei

We propose a microscopic model to study the core-polarization effects of giant resonances on the transition densities of open-shell nuclei. We use the Hartree-Fock-RPA method for the calculation of the single-particle wave functions and the response function of the giant resonances. Particle-vibration coupling is applied to take into account the core polarization effect on the valence many-body wave functions. We apply our model to the quadrupole transitions in the several medium-heavy nuclei. Valence many-body wave functions are calculated with the generalized seniority scheme and with the shell model. Results for the proton and neutron effective charges and the Coulomb form factors for the N = 82 isotones and for ¹¹⁶Sn and ¹¹⁰Pd are presented and discussed. The effective coupling hamiltonian is determined by the Skyrme interaction SGII which is used also in the HF and RPA calculations. The calculated core polarization charges show some state dependences. The average theoretical values are δe_p = 0.4–0.5 and δe_n = 0.6–0.7 compared to typical empirical values of δe_p = 0.6 and δe_n = 1.2.     

Microscopic description of collective states near the yrast line of nuclei with stable octupole deformation

Collective states near the yrast line in nuclei with stable octupole deformation are discussed in the framework of the random phase approximation (RPA) based on the cranking model. These vibrational states are characterized by the quantum number of generalized signature (eigenvalue of the operator S_x = PR_x^?1(π)). In the zero-octupole deformation limit the RPA equations of motion are reduced to the well-known ones characterized by both values of parity and signature, respectively. The connection of the translational and rotational symmetry of the model hamiltonian with the spurious solutions of the RPA equation of motion is discussed. Expressions for the reduced probabilities B(E1), B(E2) and B(E3) are obtained. These expressions confirm the conclusions of phenomenological models for the strong E1 and E3 intraband transitions in nuclei with stable octupole deformation.     

M1 resonances in unstable magic nuclei

Within a microscopic approach which takes into account RPA configurations, the single-particle continuum and more complex 1p 1 h?phonon configurations isoscalar and isovector M1 excitations for the unstable nuclei^56,78Ni and^100,132Sn are calculated. For comparison, the experimentally known Ml excitations in⁴⁰Ca and²⁰⁸Pb have also been calculated. In the latter nuclei good agreement in the centroid energy, the total transition strength and the resonance width is obtained. With the same parameters we predict the magnetic excitations for the unstable nuclei. The strength is sufficiently concentrated to be measurable in radioactive beam experiments. New features are found for the very neutron rich nucleus⁷⁸Ni and the neutron deficient nucleus¹⁰⁰Sn.     

The isospin mixing and the superallowed Fermi beta decay

In the present work, the isospin admixtures in the nuclear ground states of the parent nuclei and isospin structure of the isobar analog resonance (IAR) states have been investigated by studying the 0^?+???0^?+? superallowed Fermi ?? decays using Pyatov??s restoration method. Within the random phase approximation (RPA), in this method, the effect of isospin breaking due to the Coulomb forces has been evaluated, taking into account the effect of pairing correlations between nucleons.     

Equations for O+ states in deformed nuclei

The quasiparticle-phonon nuclear model equations are derived for describing theKπ=O⁺ states in doubly even deformed nuclei taking account of particle-hole and particle-particle interactions between quasiparticles. Inclusion of particle-particle interactions complicates the RPA equations. Equations for the functions of monopole and quadrupole pairing are derived from the condition of eliminating spurious RPA solutions. In the QPNM, inclusion of a particle-particle interaction does not lead to very complicated calculations. The obtained equations can serve as a basis for calculating characteristics of the O⁺ excited states of doubly even deformed nuclei.     

Continuum RPA correlations in quasielastic electron scattering from 12C decay on (e,e'p) and (e,e'n) reaction channels

We investigate the rôle of RPA correlations in longitudinal and transverse response functions for inelastic electron scattering from ¹²C at momentum transfers ranging between 200 MeV/c and 550 MeV/c. We refer to a continuum self-consistent RPA theory with a SK3 interaction. Electromagnetic operators are taken for uncorrelated nucléons. The partial response on (e, e'p) and (e, e'n) reaction channels is also calculated. Since energy-weighted sum rules are conserved, we can control the effect of the Hartree-Fock non-locality expressed by the SK3 nucleon effective mass as well as the action of creation and descruction of 1p 1h pairs on the true ground state induced by the RPA residual interaction.     

Coulomb displacement energies in nuclei: A new approach

In the present work the positions of the isobaric analog resonances (IAR) are calculated using the HF-TDA theory with a complete proton particle-neutron hole basis. The important feature of this approach is the fact that the HF potential and the particle-hole interaction used in the TDA are derived from the same two-body interaction. In this theory all the higher order effects are taken into account in one consistent framework. The calculations are performed for several N > Z, closed shell nuclei. For these nuclei good agreement between the experimental and theoretical excitation energies of the IAR is obtained.     

The surface delta interaction in the transuranic nuclei

The Surface Delta Interaction (SDI) is employed to calculate the ernergy of gamma-vibrational and theK=0, 1, 2, and 3 Octupole vibrational band heads in the even-mass Transuranic nuclei. The quasi-particle Random Phase (RPA) and the quasi-particle Tamm Dancov approximations (TDA) are utilized to solve the Hamiltonian. The resulting energies and gamma transitions are compared with the Pairing plus Quadrupole (PQF) or Octupole (POF) force model and the available experimental data. The agreement between theory and experiment is satisfatory. Only theK=0, 1, and 2 Octupole bands are collective. TheK=3 negative parity state is practicaly a pure two quasi-particle state.     

A new boson expansion for the solution of the n-fermion problem with an application to 4He

A new approximation method for the n-fermion problem is developed and tested within the exactly solvable model of Lipkin, Meshkov and Glick. Results are compared with the exact solutions and RPA. Applying the method to the ⁴He nucleus, excitation energies, total binding energy and the ground-state energies of ³He and ⁵He are calculated.