Jost function for coupled channels

Recently, we proposed an exact method for direct calculation of the Jost function for central potentials (which may have Coulombic tails) and the Jost matrix for non-central short range potentials. This method works for all real or complex momenta of physical interest, including the spectral points corresponding to bound and Siegert states. In this work we extend it for potentials which couple channels with different thresholds. The proposed method is based on simple differential equations of the first order, which can be easily solved numerically. Thus, the spectrum generated by any given potential can be thoroughly investigated. At the same time the physical wave function can be obtained having the correct asymptotic behaviour.Comment: 5 pages, latex, no figures, talk given at XVI European Conference on Few-Body Problems in Physics, Autrans, June 1998, to appear in Few-Body Systems Supp

Exact method for locating potential resonances and Regge trajectories

We propose an exact method for locating the zeros of the Jost function for analytic potentials in the complex momentum--plane. We further extend the method to the complex angular--momentum plane to provide the Regge trajectories. It is shown, by using several examples, that highly accurate results for extremely wide as well as for extremely narrow resonances with or without the presence of the Coulomb interaction can be obtained.Comment: RevTeX, 19 pages, 3 figures, submitted to J.Phys.

The in-medium few-body problem

We are concerned with few-particle correlations in a fermionic system at finite temperature and density. Within the many-body Green functions formalism the description of correlations is provided by the Dyson equation approach that leads to effective few-body equations. They contain the dominant medium effects, which are self energy corrections and the Pauli blocking. Hence the effective two-body interactions between quasiparticles are momentum/energy-dependent and therefore they can be usesed in the medium modified, momentum space, integral AGS equations for three- and four-body systems. To investigate correlations and clusters beyond four-body, we employ, instead, the configuration space two-variable integro-differential equations (IDEA) for $A$-body bound systems which are based on Hyperspherical Harmonics and the Faddeev decomposition of the wave function in two-body amplitudes. This requires the transformation of the energy dependent two-body interactions to equivalent local, energy independent, ones. To achieve this we use inverse scattering techniques the resulting interactions being, on-- and (to all practical purposes) off--shell equivalent to the energy dependent potentials. In this way we obtain binding energy results for the 2--, 3--, 4--, and 16--particle in a medium at a finite temperature and various densities. Several aspects of the problem are discussed and the behavior of the potential surfaces obtained in the extreme adiabatic approximation, below and above the Mott transition, is investigated.Comment: 16 pages, 7 figures, uses balkan.st

Eta-meson light nucleus scattering and Charge Symmetry Breaking

The \eta-meson collision with light nuclei, ^2H, ^3H, ^3He, and ^4He, is considered on the basis of a microscopic approach which utilises Faddeev type and Lippmann-Schwinger equations. The nuclear hamiltonian is approximated by the finite rank approximation which amounts to the coherent approximation. The \eta-nucleus scattering length and the resonance and bound--state poles of the amplitude describing elastic scattering of \eta-meson by these nuclei are obtained. For each of the nuclei considered, the minimal factor enhancing the \eta N--attraction that moves the poles to the quasi--bound state area of the complex k--plane, is determined. It is shown that within the existing uncertainties in the elementary \eta N iteraction all these nuclei can support a quasi--bound state which can result in a formation of an eta-mesic nucleus. Various aspects of the eta-nucleus physics are discussed with specific emphasis given to the \eta--nucleus effective interaction in configuration space (constructed via the Marchenko inverse scattering method), to the Okubo--Zweig--Iizuka (OZI) rule, and to the charge symmetry breaking problem.Comment: 6 pages, latex, no PS-figures, Talk given at the International Workshop on Exciting Physics with New Accelerators Facilities (EXPAF97), SPring8, Aioi, Japan, March 11-13, 199

p-3^3He Effective Potentials based on the Pauli Corrected Resonating Group Method

Effective interactions that fit the low energy p-$^3$He experimental data have been constructed. They are based on the Resonating Group Method and a modified Orthogonality Condition Model in which Pauli and partly Pauli forbidden states are removed from the spectrum. Partial waves up to L=3 have been considered. The LS force acting between the proton and $^3$He has been included phenomenologically, while the Coulomb interaction has been incorporated using a renormalization technique for a screened Coulomb interaction. The potentials are also given in a separable momentum space form, obtained using the Ernst-Shakin-Thaler (EST) method. In all cases the potentials generate phase shifts that fit well the low energy experimental data.Comment: 47 pages, 19 figures, 29 tables, Submitted to Physical Review

A METHOD OF CALCULATING THE JOST FUNCTION FOR ANALYTIC POTENTIALS

A combination of the variable-constant and complex coordinate rotation methods is used to solve the two-body Schr\"odinger equation. The latter is replaced by a system of linear first-order differential equations, which enables one to perform direct calculation of the Jost function for all complex momenta of physical interest, including the spectral points corresponding to bound and resonance states. Explicit forms of the equations, appropriate for central, noncentral, and Coulomb-tailed potentials are given. Within the proposed method, the scattering, bound, virtual, and resonance state problems can be treated in a unified way. The effectiveness of the method is demonstrated by a numerical example.Comment: LaTex, 63K, 20 page

Bound State Calculations for Three Atoms Without Explicit Partial Wave Decomposition

A method to calculate the bound states of three-atoms without resorting to an explicit partial wave decomposition is presented. The differential form of the Faddeev equations in the total angular momentum representation is used for this purpose. The method utilizes Cartesian coordinates combined with the tensor-trick preconditioning for large linear systems and Arnoldi's algorithm for eigenanalysis. As an example, we consider the He$_3$ system in which the interatomic force has a very strong repulsive core that makes the three-body calculations with standard methods tedious and cumbersome requiring the inclusion of a large number of partial waves. The results obtained compare favorably with other results in the field.Comment: 18 pages, 3 figures, 9 tables, revtex

Integral Equation Results for the 4He(e,e'p)3H Reaction at High Missing Momenta

The two-fragment electrodisintegration of 4He into proton and triton is calculated in Plane Wave Impulse Approximation (PWIA). The three- and four-nucleon wave functions involved are obtained by solving the Alt-Grassberger-Sandhas (AGS) integral equations, with the Malfliet-Tjon potential as the underlying NN-interaction. Our results are in remarkable agreement with the experimental data and, in contrast to alternative approaches, do not exhibit any dip in the five-fold differential cross section at a missing momentum of ~ 450 MeV/c.Comment: 4 pages, RevTeX, 3 Postscript figures, to be publishe

Light Nuclei within Nuclear Matter

We investigate the properties of 3He, 4He, 6He, 7Li and 16O nuclei in nuclear matter of finite temperature and density. A Dyson expansion of the many-body Green function leads to few-body equations that are solved using the ntegro-Differential Equation Approach (IDEA) and the Antisymmetrized Molecular Dynamics (AMD) methods. The use of the latter method allows us to trace the individual movement of the wave packet for each nucleon and the formation and disintegration of quasi-nuclei in a changing thermodynamical nuclear matter environment.Comment: 12 pages, 5 figure

On the possibility of an eta-meson light nucleus bound state formation

The resonance and bound--state poles of the amplitude describing elastic scattering of $\eta$-meson off the light nuclei $^2H$,\,$^3H$,\, $^3He$, and $^4He$ are calculated in the framework of a microscopic approach based on few--body equations. For each of the nuclei, the two--body parameters that enhance the $\eta N$--attraction which generate quasi--bound states, are also determined.Comment: 23K, RevTeX, 8 pages, no figures, to appear in FBS Supp