Oblique-basis shell-model calculations

A one-dimensional harmonic oscillator in a box is used to introduce the oblique-basis concept. The method is extended to the nuclear shell model by combining traditional spherical shell model states, which yield a diagonal representation of the usual single-particle interaction, with SU(3) shell model collective configurations that track deformation. An application to ²⁴Mg, using the realistic two-body interaction of Wildenthal, is used to explore the validity of this mixed-mode shell-model scheme. The theory is also applied to lower pf-shell nuclei, ^44–48Ti and ⁴⁸Cr, using the Kuo-Brown-3 interaction. These nuclei show strong SU(3) symmetry breaking due mainly to the single-particle spin-orbit splitting. Nevertheless, the results also show that yrast band B(E2) values are insensitive to fragmentation of SU(3) symmetry. Specifically, the quadrupole collectivity as measured by B(E2) strengths remains high even though the SU(3) symmetry is rather badly broken. The results suggest that an oblique-basis mixed-mode shell-model theory may be useful in situations where competing degrees of freedom dominate the dynamics.     

Effective operators in shell-model calculations

After a brief review of the properties of the nucleon-nucleon interaction and of basic shell-model theory, the microscopic theory for determining effective interactions and operators for use in shell-model calculations is given. Difficulties in applying the usual formalism are discussed. Finally, a new large-basis, no-core shell-model approach is presented, which is able to handle these difficulties. Supported in part by NSF grant No. PHY96-05192. Lectures given at the 10th Indian Summer School of Nuclear Physics: “Theory of Many-Fermion Systems”, Prague, September 8–12, 1997.     

Electronic structure calculations and strong correlations: A model study

Metals with strong correlations are a major challenge for realistic electronic structure calculations. The complexity of the systems under consideration precludes a direct fully microscopic treatment by means of the theoretical and computational methods available at present. The present paper analyzes the applicability and restrictions of common approximation schemes by comparing their predictions for a model pertinent to heavy fermion metals to the exact solution. The criteria chosen for the assessment are the density distribution in the ground state as well as the energy scale for low-lying excitations.     

Asymptotic equations for two-body correlations

An asymptotic equation for two-body correlations is proposed for a large number of particles in the framework of the integro-differential equation approach. The quality of this equation is discussed with examples.     

Exact shell-model and projected Hartree-Fock calculations for Mg

The results of a projected Hartree-Fock calculation are compared with those of an exact shell-model calculation for states of J ? 6 in the nucleus ²⁴Mg. The realistic Kuo interaction is used, and gives reasonable agreement with experiment.     

A numerical approach to nuclear shell-model calculations

An application of the Lanczos algorithm for the matrix eigenproblem to nuclear shell-model calculations is described. The method has many advantages over conventional shell-model techniques, one of the most important being a very much slower growth of computation time with increasing dimensionality of the shell-model basis.     

Effective shell-model transition operators for muon-capture calculations

Recently many shell-model calculations have been performed in order to extract the value of the ratio C _P /C _A in light nuclei. Most of these calculations fail to reproduce the value given by the partially conserved axial vector hypothesis, roughly 7. We show that, with the effective transition operators calculated by the perturbative techniques, this discrepancy can be, at least partly, solved. New angular correlation data for ²⁸Si are used for the extraction of C _P /C _A . In the case of ²⁰Ne, the capture rate data are used for the extraction.     

Electric-dipole sum rule and two-body correlations in nuclei

The enhancement factor κ in the electric dipole sum rule is calculated using the linked diagram perturbation theory for the effective operator and the Reid nucleon-nucleon potential. Results are in good agreement with the recent experimental values for ¹⁶O and ⁴⁰Ca, namely κ is around 1.0. There is, however, a large discrepancy between theory and experiment for ⁴He. The two-body correlations, especially those induced by the tensor force, are found to be extremely important for the enhancement factor.     

Rearrangement effects in shell-model calculations using density-dependent interactions

A general method is developed to treat density-dependent effective nucleon-nucleon interactions in shell-model calculations. A trial function is introduced, that can generate any excitation mode of the nucleus. The method is based on the evaluation of the expectation value of the full Hamiltonian with respect to this generating Slater determinant wave function. Rearrangement effects, due to the density-dependence of the interaction are systematically included. The proposed formalism is applied in first instance to simplified excitation modes, such as two-quasiparticle and particle-hole configurations. A detailed study on the importance of the various types of rearrngement terms is carried out. A more specific application of the general formalism is presented in carrying out an extended shell-model calculation on ¹¹⁶Sn, including, apart from the neutron 2qp-excitations, proton 1p-1h excitations and coupled excitations of the type (1p-1h) ⊗ (2qp).     

Detection of multipartite entanglement with two-body correlations

We show how to detect entanglement with criteria built from simple two-body correlation terms. Since many natural Hamiltonians are sums of such correlation terms, our ideas can be used to detect entanglement by energy measurement. Our criteria can straightforwardly be applied for detecting different forms of multipartite entanglement in familiar spin models in thermal equilibrium. PACS 03.65.Ud; 03.67.Mn; 05.50.+q     

Residual two-body matrix elements for pre-equilibrium calculations

The effective matrix elements which appear in pre-equilibrium calculations in the rate expressions for the residual two-body interactions have been evaluated from analyses of emitted particle energy spectra. Probably because of details in the model formulation, the results are found to depend on the nature of the projectile. They are, however, of reasonable magnitude and show a mass number and excitation energy dependence consistent with predictions based on calculations of mean free paths in nuclear matter. The square of the empirical effective matrix element is found to approximately obey the relation M² = K_aA⁻³E⁻¹ with the values of K_a = 95 MeV³ and 725 MeV³ applying to proton and α-particle induced reactions respectively. The quantities A and E are the mass number and excitation energy of the system respectively.     

Event rates for CDM detectors from large-scale shell-model calculations

We investigate the scattering of the CDM candidate LSP (Lightest Supersymmetric Particle) off nuclei. We have computed the associated event rates and annual modulation signals for the ²³Na, ⁷¹Ga, ⁷³Ge and ¹²⁷I CDM detectors by using the nuclear shell model in realistic model spaces and exploiting microscopic effective two-body interactions. Large-scale computations had to be performed in order to achieve convergence of the results. We have tabulated the associated nuclear-structure coefficients for several LSP masses enabling easy interpolation of our results for any other mass. The relevance of the spin-dependent and coherent channels for the event rates is discussed, from both the nuclear-structure and the SUSY-model viewpoints.     

The applicability of nuclear field theory to shell-model calculations

Previous NFT calculations of the four-particle spectrum reached different conclusions concerning the applicability of the lowest-order Rayleigh-Schroedinger perturbation expansion. In the present paper, we show that the inclusion of second-order diagrams and/or diagonalization procedures yields satisfactory results both for the energies and for the transfer matrix elements even for j-shells as small as the $\text{j =}\text{7}\text{2}$ and $\text{j =}\text{11}\text{2}$ shells.     

Symplectic shell-model calculations for 20Ne with horizontal configuration mixing

The symplectie shell model, which incorporates vertical $\text{(2n}\text{h}\text{?}\text{ω; n = 1, 2…)}$ major shell configuration mixing as dictated by a quadrupole interaction, is augmented with horizontal (0?ω) mixing induced by realistic single-particle energies and a monopole-pairing interaction. The excitation spectrum and B(E2) rates of the ²⁰Ne ground band are accurately reproduced without the use of an effective charge. The degree of horizontal and vertical mixing is found to be on the order of 20% in the ground state and up to as much as 50% for the 8⁺ level.     

Structure of two-body correlations in high energy hadron production

Experimental information on diffraction is used to estimate long range effects in multiparticle production. Diffractively produced secondaries are found to produce a plateau in the central region. Diffraction accounts for 30% of the observed correlations and the remainder, consistent with being short range, corresponds to a cluster size of 2.4 charged particles.     

Extended shell-model calculations for the A = 6 nuclei

Extended shell-model calculations for the A = 6 nuclei using the Sussex matrix elements and the Gogny et al. potential are presented. The results are discussed in connection with those obtained in the framework of the lowest order shell-model configurations.     

Three-nucleon calculations without the explicit use of two-body potentials

Using as two-nucleon interaction input the ³S₁-³D₁ and ¹S₀ partial waves, the Faddeev equations are solved for the three-nucleon bound state. The ³S₁³D₁T-matrix is calculated from the Reid potential. Avoiding the usual potential fit, the ¹S₀T-matrix is directly continued off-shell and is constructed consistent with the ¹S₀ phase shift of elastic two-nucleon scattering. The off-shell part of the ¹S₀T-matrix is parametrized and with this parametrization the dependence of the three-nucleon bound-state properties is studied. As a result it is found that the binding energy varies only between 6.2 MeV and 6.8 MeV, while the minimum in the charge form factor for electron scattering from ³He lies between 12.9 fm^?2 and 18.7 fm^?2. The larger (smaller) ³He binding energy is accompanied by a ³He charge form factor whose minimum is at larger (smaller) momentum transfers.     

Supernova inelastic neutrino-nucleus cross sections from high-resolution electron scattering experiments and shell-model calculations

Highly precise data on the magnetic dipole strength distributions from the Darmstadt electron linear accelerator for the nuclei 50Ti, 52Cr, and 54Fe are dominated by isovector Gamow-Teller-like contributions and can therefore be translated into inelastic total and differential neutral-current neutrino-nucleus cross sections at supernova neutrino energies. The results agree well with large-scale shell-model calculations, validating this model.