Nonlocal Separable Potential Research Articles

Pairing correlations: I. The ground-state coupled-cluster formalism as a unifying approach

the general problem of pairing correlations within a many-fermion system of identical particles is discussed at some length. We show in this first work in a series how the ground-state version of the [exp(S) or] coupled-cluster formalism (CCF) of quantum many-body theory may be rather generally applied to this problem, and how it thereby provides a very powerful and unifying approach to it. At the so-called SUB2 level of truncation, which is the lowest natural level of approximation for homogeneous systems, the CCF may be cast as a nonlinear integral equation for a four-point correlation function,S 2, which provides a measure of the two-particle/two-hole component in the true “ground-state” wavefunction. This approximation couples the particle-particle, hole-hole and particle-hole correlations simultaneously, and treats them all on an equal footing. In the present work we concentrate particular attention on particle-particle and hole-hole correlations by focussing on the formulation of generalised ladder approximations within the CCF. These are therefore likely to be physically applicable in the low-density regime. In particular, we show that the well-known Galitskii approximation may be formulated within the CCF as that drastic sub-approximation to the full SUB2 equation which keeps only the so-called complete ladder (CLAD) terms, which we describe. A second paper applies the CCF to the particular case of a general (non-local) separable potential, and obtains exact analytic solutions within the CLAD approximation for the corresponding wavefunctions of the simultaneous particle-particle and hole-hole substructures within the many-fermion system.

The Study of Hypertriton with Three-Body Integral Equation

From a Faddeev-type integral equation for three-body bound state, the hypertriton binding energy is calculated by using the nonlocal two-body separable potential with the parameters taken from the scattering data of meson theoretical potential. The effects of and interactions in three-body bound state are studied and the meson theoretical potentials of Refs.[1-3] are examined. The calculated results are reasonably close to the experimental values. The comparisons of our results with others are made.

Green’s function for motion in Coulomb-modified separable nonlocal potentials

A closed form expression is derived for the outgoing wave radial Green’s function 𝒢(+)l (r,r′) for motion in the Coulomb plus rank one separable nonlocal potential with form factor vl(r)=2−l ×(l!)−1 rle−βlr. Some possible applications of the result are discussed.

On the Lippmann-Schwinger equation off the energy shell

Dolinszky has observed (ibid., vol.10, p.1639, 1984) that off-shell T matrix elements can be expressed in terms of simple quadratures involving solutions of the radial Schrodinger equation. It is pointed out that this is not true in general for the K matrix. The K matrix equation for separable non-local potentials, however, can be treated by an approach similar to that of Dolinszky.

Equivalent local potentials from nonlocal separable ones.

A method is presented for the explicit construction of a family of equivalent local potentials from a given nonlocal separable potential. This procedure can be also applied in the case when a Coulomb potential is added to the separable short range interaction.

On the localisation of separable non-local potentials

The work of McTavish (1982) on the localisation of separable non-local potentials is formulated in terms of the regular boundary condition. As expected, the result for the equivalent local potential thus obtained is in exact agreement with that of McTavish, who used a standing-wave boundary condition for his construction procedure. The work of McKellar and May (1965) for writing the phase equation for such potentials is reviewed briefly. An ansatz is introduced for the phase equation which, on the one hand, yields the equation of McKellar and May and, on the other hand, permits a simple off-energy-shell generalisation of the phase method for energy-momentum-dependent potentials. An equation is derived for the interpolating quasi-phase function. It is shown that the off-shell extension function can also be calculated within the framework of this approach. A case study is presented to judge the quality of equivalent potentials. The authors' results indicate that the potential obtained in the approach of McTavish reproduces exactly the on- and off-shell properties of the parent non-local potential while the Taylor expansion provides an equivalent potential which works only at low energies and in a narrow range of off-shell momenta.

The phase equation for non-local separable potentials

The recent work of McTavish (1982) on the momentum and energy dependence of non-local separable potentials is improved to ensure that the equivalent potentials are not singular. The improvement provides a basis for a phase equation. This phase equation is a first-order nonlinear ordinary differential equation similar to that for local potentials. It is a great simplification on the integro-differential equation obtained by Calogero (1967).

A class of one-dimensional relativistic band models

The solution to the Dirac equation is worked out for a nonlocal separable periodic potential which varies in one direction. The relativistic version of the Kronig–Penney model is obtained as a special case.

Форм-факторы дейтрона и наблюдения e-d поляризации для потенциалов Парижа и Граца—II

Elastic e-d scattering is studied by using the meson-theoretical Paris potential and the nonlocal separable Graz-II potential. Electric and magnetic form factors are calculated with inclusion of meson exchange currents and compared to existing experimental data. Deuteron vector and tensor polarizations and predicted and discussed in relation to the deuteron wave functions of the potential models considered. Thereby the off-shell behaviour of the Graz-II interaction is found to be close to the one of the Paris potential over the most important domain of low and moderate off-shell momenta.

Influence of the Coulomb-distortion effect on proton-proton observables

The effect of the Coulomb distortion of the strong interaction is studied on the basis of nucleon-nucleon observables. In particular, cross sections, polarizations, spin-correlation parameters, and spin-transfer coefficients are considered for proton-proton as well as neutron-neutron scattering at laboratory kinetic energies ${E}_{\mathrm{lab}}=10,20, \mathrm{and} 50$ MeV. The calculations are performed for the meson-theoretical Paris potential, the nonlocal separable Graz potential, and also using the Arndt-Hackman-Roper parametrization of proton-proton scattering phase shifts.NUCLEAR REACTIONS $N\ensuremath{-}N$ interaction; Coulomb corrections in polarization observables.

Quantum statistical theory of adsorption and desorption of a gas at a solid surface

The non-equilibrium initial value problem of phonon-mediated adsorption and desorption of a gas at a solid surface is formulated explicitly in a quantum-statistical theory and adsorption, flash desorption and isothermal desorption times are calculated using a non-local separable surface potential. We find that the flash desorption time is a function of both initial and final temperatures T g and T s and can, for fixed T g, be approximated by Frenkel's formula over a limited range of flash temperatures T s. We fit our theory to flash desorption data for He desorbing from Constantan and find excellent agreement. Predictions are given for the H/NaCl system. Isothermal and flash desorption times are correlated, and experiments are suggested to demonstrate the differences.

Non-local potentials and positive energy bound states

For a non-local separable potential it is shown that, in general, a positive energy bound state cannot be interpreted as a zero-width resonance.

Neutron-proton transfer reactions leading toT=1 particle-hole states of56Co

Zero range DWBA analysis for two-particle (neutron and proton) transfer reactions is carried out, using simple shell model structure wave functions for54Fe,56Co and58Ni, with56Ni inert core. In this structure calculation, a microscopic set of two-body interaction matrix elements derived from the non-local separable potential of Tabakin are employed. These matrix elements include in the perturbation theory two corrections (i) the second-order Born term and (ii) the appropriate core excitations. Unlike the situation in many two-particle transfer reactions, the fragmentation of the reaction strengths to the excited states with respect to the lowest states of same spin and parity in the above transfer processes is satisfactorily borne out from this analysis.

T-matrix for the mongan potential

The Jost functions and the T-matrix outside an energy surface are obtained by applying the method of van Leeuwen and Reiner to scattering by a nonlocal separable potential.

Quantum statistical theory of flash desorption

The nonequilibrium initial value problem of phonon-mediated flash desorption of a gas from a solid surface is formulated explicitly and flash desorption times td=td(Tg, Ts) are calculated, using a nonlocal separable surface potential, as a function of both initial and final temperatures Tg and Ts, respectively. We find that for fixed Tg, td can be approximated by Frenkel’s formula over a limited range of flash temperatures Ts. We fit our theory to flash desorption data for He desorbing from Constantan and find excellent agreement. Predictions on 4He (H or D) desorbing from LiF (NaF) are given. Our theory is formulated both in one and three dimensions and it is shown by numerical examples that the theory of flash desorption works equally well in either case.

Wave functions from an off-energy-shell generalisation of the Gordon’s method

An ansatz is introduced in the Gordon’s method for nonlocal separable potentials to construct expressions for off-shell wave functions associated with the physical, regular and standing wave boundary conditions. This method has certain calculational advantages and is particularly suitable for dealing with potentials of higher rank. Results obtained for the Mongan case IV potential agree with those derived by the complicated techniques.

Energy per particle, effective mass and magnetic susceptibility in neutron matter

Relations for energy per particle, effective mass and magnetic susceptibility in neutron matter are derived using a simple three-parameter density-dependent effective interaction constructed in an earlier work (see ibid., vol.5, no.1, p.85 (1979). The effective mass M*/M, which has a value 0.985 at kn=0.5 fm-1, decreases steadily with increase in density. The ratio chi F/ chi of the magnetic susceptibility of a Fermi gas of non-interacting neutrons to that of neutron matter increases with density up to kn=1.4 fm-1 and then decreases. The results of Haensel (1975) calculated with the Mongan nonlocal separable potential show a similar trend where chi F/ chi decreases beyond knp2.4 fm-1. As chi F/ chi is quite sensitive to the odd-state interaction energy, which is usually negligible up to a density corresponding to kn=2 fm-1, the results of magnetic susceptibility obtained with the simple effective interaction mentioned above acting in even states only are expected to be reliable only below this region of density.

Faddeev equations for the nuclear break-up process

The nuclear break-up process is reconsidered on the basis of a three-body problem. The nuclear reactions with an initial state of two interacting particles leading to a final state of three free particles are considered. Faddeev equations are given for this kind of nuclear break-up processes. Nonlocal separable (NLS) potentials are used for the two-body interactions. The NLS potentials used in this work are of the Yamaguchi, Gaussian and Tabakin potential forms. Different types of nuclear break-up processes are considered. Different nuclear reactions are considered such that the two initially different interacting particles lead to a final state of three free particles which are one of the unbound states of one of the nuclei6Li,9Be or12C. By solving the Faddeev equations, numerical calculations for the nuclear break-up processes are performed for the resulting integral equations.

Model nuclear matter calculations in several Brueckner and Green's function theories

Model nuclear matter calculations are performed using two versions of the Brueckner theory (standard lowest order theory and a version with self-consistent “physical” onshell insertions in particle lines) and three Green's function theories (Λ00,Λ10 and Galitskii's ladder approximation). Ground state properties are derived using a strongs-wave nonlocal separable nucleon-nucleon potential. We investigate the differences between the results obtained using different theories, stemming from different treatment of the exclusion principle and of dispersive effects of the medium. The effect of the off-shell self-consistency in theΛ10 theory is found to be important.

Nuclear optical model potential in the Λ10 approximation

The complex mass operator is calculated in the framework of the Λ 10 theory using a nonlocal separable central potential. The imaginary part of the on-shell and of the off-shell mass operators is found to be sensitive to off-shell effects and to differ from those derived from the Λ 00 approximation.