The isospin forbidden 1− → 0+ transition in 40Ca

The isospin forbidden transition 1^? (6.95 MeV) → 0⁺ (g.s.) in ⁴⁰Ca is explained within a model that mixes isospin through single-particle energy differences and the two-body Coulomb interaction. There is no need to introduce an isospin non-conserving part of the nucleon-nucleon interaction to explain this anomalously fast transition.     

One- and two-body dissipation in heavy-ion collisions

A microscopic theory has been formulated for one- and two-body dissipation in collisions between two heavy nuclei. With a nucleon-nucleon interaction as the basic perturbation in a density matrix approach with “linear response” approximations, the one- and two-body nuclear friction coefficients for the ⁴⁰Ca + ⁴⁰Ca system have been calculated and their dependence on relative kinetic energy and smearing of nuclear single-particle states was obtained. The results of our calculation show that: (a) the combined one- and two-body friction coefficients compare favourably with phenomenological values, (b) the one-body dissipation is more effective than two-body in kinetic energy damping, while both the mechanisms are comparable for the damping of relative angular momentum, (c) the importance of the two-body friction compared to one-body increases at higher relative kinetic energies and (d) the effect of introducing a smearing in nuclear levels appears as a lowering of nuclear friction.     

A microscopic,but not self-consistent approach to nuclear binding and deformation energies

Using various versions of the Skyrme force and Negele's interaction, we calculate deformation energies of nuclei by evaluating the expectation value of the many-body Hamiltonian in wave functions taken to be antisymmetrized products of single-particle functions. These single-particle functions are eigenfunctions of a phenomenological potential, here taken to be a deformed Woods-Saxon well. The method can be thought of as an extension of the Strutinsky shell-correction method, to make the connection with the two-body interaction. The method employed here is checked by comparison with Hartree-Fock (HF) results; our method is, however, much faster than the HF method, and, therefore, suitable for a wide range of problems where one tests the sensitivity of results to changes in the two-body interaction. A fairly good agreement with the HF method is obtained for ground-state energies, radii and deformations, as well as for deformations of shape isomers. The main discrepancy is that our energies tend to increase slightly too rapidly with deformation, indicating that we may not have chosen the best phenomenological well. Two-dimensional energy surfaces, which agree quite well with those from the Strutinsky method, are found for ²⁴⁰Pu.     

On high-energy elastic scattering of protons by nuclei

The two coupled channel formalism for high energy elastic scattering [1] is extended to include spin and isospin effects. For a spin and isospin zero nucleus these manifest themselves by additional spin-orbit terms in the potentials. Explicit formulas for these potentials are obtained in terms of the fully spin and isospin dependent nucleon-nucleon scattering amplitude, the ground state nuclear form factor and the state dependent correlation functions. The coupling potential except for a small term arising from double spin and isospin flip process involving nuclear excitation depends only upon the pair correlations.Numerical calculations are performed for the elastic scattering of 1 GeV protons incident on ⁴He. Various phenomenological dynamical two-body correlations as well as correlations generated from the Reid soft-core and Tabakin potentials in an approximate Brueckner-Hartree-Fock calculation are considered. The angular distribution beyond its first diffraction minimum as well as the polarization in the same angular range are shown to be sensitive to these correlations. However, the present accuracy of the experimental data and the lack of knowledge of the nucleon-nucleon scattering amplitude prevent any definitive conclusion about their nature.     

Nuclear matter spectral function in the Bethe-Brueckner-Goldstone approach

The microscopic many-body theory of the Nuclear Equation of State is discussed in the framework of the Bethe-Brueckner-Goldstone method. The expansion is extended up to the three hole-line diagrams contribution. Within the same scheme, the hole spectral function is calculated in nuclear matter to assess the relevance of nucleon-nucleon short-range correlations. The calculation is carried out by using several nucleon-nucleon realistic interactions. Results are compared with other approaches based on variational methods and transport theory. Discrepancies appear in the high-energy region, which is sensitive to short-range correlations, and are due to the different many-body treatment more than to the specific NN interaction used. Both nuclear matter Equation of State and spectral function appear to be dominated by two-body correlations.Received: 1 November 2002, Published online: 15 July 2003PACS: 21.65.+f Nuclear matter - 21.10.Pc Single-particle levels and strength functions     

A simplified approach to three-body correlations in nuclear matter through a non-zero particle spectrum

Self-consistent nuclear-matter calculations are presented which take into account Dahlblom's results for the contribution to the binding energy due to three-body correlations. We propose a justified parametrization of the single-particle potential for particle states, the energy contribution of which cancels approximately the energy from certain three-body correlations. Indications are given of how to fix this particle-state potential for a given two-body interaction. Two nucleon-nucleon potentials are used: the Reid soft-core potential and a fully momentum-dependent one-boson-exchange potential similar to the form proposed by Ingber and Potenza. The mechanism of the increase in the total wound due to three-body correlations is investigated and reasons are given why this does not prevent the saturation densities from moving to higher values. Due to three-body correlations and with self-consistency on the hole spectrum, the increase in nuclear-matter binding energy is 0.60 MeV/A for the Reid soft-core interaction and 0.68 Mev/A for the OBEP. The saturation momentum is shifted from 1.42 fm^?1 to 1.44 fm^?1 for the Reid potential and from 1.58 fm^?1 to 1.62 fm^?1 for the OBEP.     

A model for short range correlation in the three-body system

A method by means of which the two-body short-range correlations in the nucleon-nucleon interaction are taken accurately into account in three-body bound-state calculations is described. The method is independent of the nucleon-nucleon interaction. We employ our method to calculate meson-exchange corrections to the magnetic moments of ³H and ³He and the Coulomb energy of ³He.     

Quenching of spectroscopic factors for proton removal in oxygen isotopes

We present microscopic coupled-cluster calculations of the spectroscopic factors for proton removal from the closed-shell oxygen isotopes (14,16,22,24,28)O with a chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order. We include coupling-to-continuum degrees of freedom by using a Hartree-Fock basis built from a Woods-Saxon single-particle basis. This basis treats bound and continuum states on an equal footing. We find a significant quenching of spectroscopic factors in the neutron-rich oxygen isotopes, pointing to enhanced many-body correlations induced by strong coupling to the scattering continuum above the neutron emission thresholds.     

The Lorentz-Lorenz correction

The Ericson-Ericson Lorentz-Lorenz correction in the propagation of pions in matter is derived in a relativistic theory for general pion frequency and wave vector, in terms of the nucleon-nucleon pair correlation function. The relation to the electromagnetic Lorentz-Lorenz correction is described. It is shown that ρ-meson exchange between nucleons can be expected to give contributions to the Lorentz-Lorenz correction comparable to those from π-mesons. The precise magnitude of the ρ-contributions depends sensitively on the detailed behaviour of the two-body correlation function, since the range of the interaction through ρ-exchange is comparable to that of the repulsive correlations.     

Microscopic theory of multiple scattering for open-shell nuclei

We consider the scattering of a distinguishable projectile from a nucleus assuming that the underlying interaction Hamiltonian is a sum of two-body potentials. We show that the effective interaction of the projectile with the nucleus in a truncated nuclear model space can be calculated as a linked-cluster expansion. The rules for evaluating this expansion are given in terms of the nucleon-nucleon and projectile-nucleon potentials and the exact eigenstates of the (effective) shell-model interaction. The shell-model interaction is required to be an energy-independent, Hermitian potential; its expression in terms of the underlying two-body potential is given by folded diagrams. The terms in the expansion of the effective projectile-nucleus interaction must also contain folded diagrams but, unlike the shell-model potential, these are energy-dependent in order to describe the singularities associated with the crossing of the scattering thresholds as the projectile energy is varied. Once the effective interaction is known, elastic and inelastic scatterings may be evaluated numerically by solving a finite-dimensional coupled-channel equation.     

Dynamical Study of Tensor Observables in the Energy Range of 80 keV to 95 MeV: Tests of Effective Two-Body Models

 Realistic interactions are used to study tensor observables in the energy range of 80 keV to 95 MeV deuteron laboratory energy, as well as the differential cross section for the two-body photodisintegration of . The Siegert form of the E1 multipole operator in the long-wavelength limit is taken as the sole component of the electromagnetic interaction. The three-body Faddeev equations for the bound-state and continuum wave functions are solved using the Paris, Argonne V14, Bonn-A, and Bonn-B potentials. The corresponding nucleon-nucleon t-matrices are represented in a separable form using the Ernst-Shakin-Thaler representation. The Coulomb force between protons is neglected and no three-nucleon force is included. The contribution of nucleon-nucleon P-wave components to the observables is carefully studied, not only in the angular distribution of the observables, but also as a function of the deuteron laboratory energy for fixed centre-of-mass angle. Comparison with data is shown wherever it exists. Results with simple Yamaguchi-type interactions with variable %D-state in the deuteron are compared with realistic interactions and one of these model potentials is used to study the results in terms of contributions from specific wave-function components or terms in the electromagnetic operator. Effective two-body models are examined by means of a derivation that is consistent with the underlying three-body calculation and that leads to an effective two-body t-matrix for neutron-deuteron elastic scattering carrying the same on-shell amplitudes as the original three-body equations. Received September 21, 1999; revised December 23, 1999; accepted February 9, 2000     

Universality of Short-Range Nucleon-Nucleon Correlations in Nuclei

We investigate the short-range correlations in light nuclei. The highly correlated many-body states are obtained with an explicitly correlated basis which enables us to get a precise solution of a many-body Schrödinger equation for a realistic interaction. We show two-body density distributions for the different spin-isospin channels calculated from three- and four-body states to investigate the short-range correlations between nucleon pairs. At distances below 1 fm a universal behavior is found which does not depend on the many-body states. The universality is also seen in high momentum components of the two-body momentum distributions.     

A correlated-basis-functions approach to realistic nuclear matter

The method of correlated basis functions is adapted to the nuclear-matter problem with two-nucleon potentials containing tensor as well as central components. Procedures are described for evaluating through three-body cluster order the energy expectation value with respect to a constrained trial ground-state wave function incorporating tensor and central correlations, and for calculating in two-body cluster approximation the second-order perturbation correction in a basis of likewise-correlated functions. Results for the 5100, 5200, Gammel-Christian-Thaler and Hamada-Johnston potentials are presented and dissected.     

Mean single-particle potentials and single-particle energies in a microscopic model of the nucleus

A method for calculating mean single-particle potentials and the corresponding single-particle energy levels in nuclei is presented. Specific formulas for these quantities are written for Slater determinant wave functions in the case of polarized orbitals and a central exchange nucleon-nucleon potential featuring a Gaussian radial dependence. The resulting theoretical estimates of single-particle properties of the nuclei considered in the present study are in satisfactory agreement with relevant experimental data.     

A unitary model for three-body collisions

A connected 3 → 3 formalism for three-body collision processes is reduced to a hierarchy of three on-energy-shell integral equations and one off-energy-shell integral equation. Only the on-energy-shell equations, which involve only on-energy-shell three-body and two-body amplitudes, need be solved exactly in order to obtain elastic and break-up amplitudes satisfying the unitarity constraints exactly. Applied to n-d break-up, the on-energy-shell equations ensure that the n-d initial-state interaction, the nucleon-nucleon final-state interactions, and more complicated 3 → 3 processes are correctly described. After angular momentum analysis the on-energy-shell equations are one-dimensional integral equations, even in the case of local two-body potentials. This unitary model provides a practical scheme for calculating approximate three-body elastic and break-up amplitudes when two-body local potentials are used to describe the two-body subsystems.     

Nucleon-nucleon correlations and the Coulomb Displacement Energy

Coulomb Displacement Energies (CDE) are accurately known for a wide range of nuclear masses. Assuming isospin independence in the nuclear Hamiltonian, the CDE can in first instance be interpreted as the Coulomb interaction energy between the density of the excess neutrons and the proton charge density in the parent nucleus. However, when using reasonable meanfield models for the proton and neutron density one underestimates the CDE by about 8% on average. This discrepancy is known as the Nolen-Shiffer anomaly, and various explanations have been put forward in the past. In this work we reexamine the role of nucleon-nucleon correlations. We present calculations for the pair density functions in various nuclei. Preliminary results suggest that the modifications to the mean-field pair density functions cause an enhancement of the CDE in the order of 4%, which is ratherA-independent.     

Restoration of rotational symmetry in deformed relativistic mean-field theory

We report on a very recently developed three-dimensional angular momentum projected relativistic mean-field theory with point-coupling interaction (3DAMP+RMF-PC). Using this approach the same effective nucleon-nucleon interaction is adopted to describe both the single-particle and collective motions in nuclei. Collective states with good quantum angular momentum are built projecting out the intrinsic deformed mean-field states. Results for ²⁴Mg are shown as an illustrative application.