Matrix Elements Of Effective Interaction Research Articles

Proton-neutron multiplets in exoticSb134: Testing the shell-model effective interaction

The experimental level structure of 134Sb is compared with the results of a shell-model calculation in which the two-body matrix elements of the effective interaction have been derived from the CD-Bonn nucleon-nucleon potential. The experimental data, including the very low-lying first-excited 1- state, are remarkably well reproduced by the theory. The results of this paper complement those of our previous studies on 135Sb and 134Sn, showing that our effective interaction is well suited to describe 132Sn neighbors beyond N=82. The various terms which contribute to the matrix elements of the proton-neutron effective interaction are examined and their relative importance is evidenced.

Proton particle-neutron hole states in132Sbwith a realistic interaction

The structure of the particle-hole nucleus ${}^{132}\mathrm{Sb}$ provides a direct source of information on the effective neutron-proton interaction in the ${}^{132}\mathrm{Sn}$ region. We have performed a shell-model calculation for this nucleus using a realistic effective interaction derived from the Bonn A nucleon-nucleon potential. The results are in very good agreement with the experimental data evidencing the reliability of our effective interaction matrix elements both with isospin $T=1$ and $T=0.$

Bonn potential and sd-shell nuclei.

Using a G-matrix folded diagram method and the Bonn nucleon-nucleon potential, the s-d shell effective interaction is derived and applied to evaluate the spectra of some light sd-shell nuclei. Due to the relatively weak tensor-force characteristic for the Bonn potential, the effective interaction matrix elements, particularly those with isospin T=0, come out generally more attractive than in earlier derivations in which local, strong tensor-force potentials were used. As a consequence of this, our results for the effective interaction and the spectra are in considerably better agreement with empirical determinations and experimental data. The sensitivity of the above nuclear structure calculations to the strength of the nuclear tensor force is demonstrated systematically and the dependence of the s-d shell matrix elements on the nuclear mass number is studied.

Coupled cluster approaches with an approximate account of triexcitations and the optimized inner projection technique

A general orthogonally spin-adapted formalism for coupled cluster (CC) approaches, with an approximate account of triexcited configurations, and for optimized inner projection (OIP) technique is described. Modifying the linear part of the CC equations for pair clusters (CCD) we obtain the orthogonally spin-adapted, non-iterative version of the CCDT-1 method of Bartlett et al. [J. Chem. Phys. 80, 4371 (1984), 81, 5906 (1984), 82, 5761 (1985)]. Similar modification of an approximate coupled pair theory corrected for connected quadruply excited clusters (ACPQ) yields a new approach called ACPTQ. Both the CCDT-1 and ACPTQ methods can be formulated in terms of effective interaction matrix elements between the orthogonally spin-adapted biexcited singlet configurations. The same matrix elements also appear in the orthogonally spin-adapted form of the CCD + T(CCD) perturbative estimate of triply excited contributions due to Raghavachari [J. Chem. Phys. 82, 4607 (1985)] and Urban et al. [J. Chem. Phys. 83, 4041 (1985)], and in the OIP method when applied to the Pariser-Parr-Pople (PPP) model Hamiltonians. We use the diagrammatic approach based on the graphical methods of spin algebras to derive the explicit form of these interaction matrix elements. Finally, the relationship between different diagrammatic spin-adaptation procedures and their relative advantages are discussed in detail.

Strength of tensor force and s-d-shell effective interactions.

The {ital s}-{ital d}-shell effective interaction is derived from the Bonn {ital NN} potential, using a {ital G}-matrix folded-diagram method. It is found that due to the relatively weak-tensor-force characteristic for the Bonn potential, the effective interaction matrix elements, particularly those with isospin {ital T}=0, come out generally more attractive than in previous derivations which were based on conventional local strong-tensor-force {ital NN} potentials. This renders the results obtained with the Bonn potential in considerably better agreement with the recent {ital s}-{ital d}-shell matrix elements of Wildenthal.

Λ and Σ hypernuclei

The present status of structure calculations for p-shell Λ hypernuclei, including the phenomenological determination of ΛN effective interaction matrix elements, is briefly reviewed. For Σ hypernuclei the Nijmegen potential model D is used for guidance in constructing ΣN effective interactions. The structure of Σ 12Be and Σ 12C, including isospin mixing in the latter case, is discussed, and a comparison is made with experimental data.

Higher-order approximations for the particle-particle propagator

A new type of approximations for many-body Green's functions proposed recently is applied to the particle-particle (pp) propagator for anN-particle fermion system. The new approach which is referred to as the algebraic diagrammatic construction (ADC) is based on an exact resummation of the perturbation series for the pp-propagator in terms of a simple algebraic form introducing energy-independent effective interaction matrix elements and transition amplitudes. These effective quantities are represented by perturbation expansions and can be determined consistently through a given ordern of perturbation theory by comparing the algebraic form with the diagrammatic perturbation series of the pp-propagator through ordern. By this procedure one obtaines a systematic set of approximation schemes (ADC(n)) that represent infinite partial summations for the pp-propagator being complete throughnth order of perturbation theory. The explicit ADC equations forn=1 and 2 are presented and discussed. Comparison is made with the particle-particle random phase approximation (RPA). It is demonstrated that the second-order ADC scheme constitutes an essential step beyond the RPA which is consistent only through first order.

Microscopic versus empirical effective interactions in a singlejshell

Effective-interaction matrix elements within a single j shell can be determined directly from experimental data. Such matrix elements have been found to be much different from those calculated microscopically within a complete major shell. The recent work of Moszkowski et al. showed that this difference is at least partially due to the severe truncation to a single j shell. We have constructed the microscopic effective interaction for a single j shell using two different methods: (1) simple perturbation theory and (2) explicit projection from the full major shell to a single j shell. We conclude that the empirical matrix elements and the full major-shell matrix elements should not agree, since the model spaces are different. On top of this the empirical values and the microscopic results for a single j shell would be expected to be similar only when the configurations vertical-bar ( j/sup 2/) JT> are very pure.

Structure calculations for40Ca with the supersoft-core potential

The ground-state properties of40Ca are studied by using the Hartree-Fock approximation and an effective interaction calculated by means of the supersoft-core potential. Shell model spaces of various sizes are used. The effective interaction matrix elements used in the Hartree-Fock procedure, the ground-state binding energy and the r.m.s. radius obtained with the supersoft-core potential are compared with the results obtained with realistic hard-core potentials.

Spin-tensor decomposition of nuclear effective interactions

A simple technique is decribed for extracting from two-body effective interaction matrix elements the separate contributions of the parts of the effective interaction of tensor rank zero, one and two in spin space. Some minor applications are presented to illustrate the method.

Shell-Model Calculations forV51andCr52

Employing ${\mathrm{Ca}}^{48}$ as the core and the reaction matrix elements of Kuo and Brown for the residual interaction among the three valence protons, the nuclear energy levels of ${\mathrm{V}}^{51}$ are calculated within the spherical shell-model framework. All the $0f\ensuremath{-}1p$ configurations are included. The wave functions obtained on diagonalizing the Hamiltonian matrices are used to calculate the transition rates and spectroscopic factors for the reaction ${\mathrm{Ti}}^{50}({\mathrm{He}}^{3},d){\mathrm{V}}^{51}$. Good agreement with experiments is found suggesting that it is not necessary to include deformation in ${\mathrm{V}}^{51}$ as in the papers of Scholz and Malik. The consequences of mixing effective interaction matrix elements of Lips and McEllistrem and realistic Kuo-Brown matrix elements are studied and it is pointed out that such a mixture does not yield a successful effective interaction model. Our results are further supported by similar calculations on ${\mathrm{Cr}}^{52}$.

Estimate of the binding energy of 16O with matrix elements of effective interaction

An estimate of the binding energy of 16O nucleus is given using matrix elements of effective interaction determined by means of a variational method with a “healing condition”. A “minimum condition” is also derived for these matrix elements.