S. A. Sofianos

Binding energies and scattering observables in the 4He3 atomic system

Abstract:The 4He3 system is investigated using a hard-core version of the Faddeev differential equations. Realistic 4He-4He interactions are employed, among them the LM2M2 potential by Aziz and Slaman and the recent TTY potential by Tang, Toennies and Yiu. We calculate the binding energies of the 4He trimer, but concentrate in particular on scattering observables. The scattering lengths and the atom-diatom phase shifts are calculated for center of mass energies up to 2.45 mK. It is found that the LM2M2 and TTY potentials, although of quite different structure, give practically the same bound-state and scattering results.

Three-body configuration space calculations with hard-core potentials

We present a mathematically rigorous method suitable for solving three-body bound-state and scattering problems when the inter-particle interaction is of a hard-core nature. The proposed method is a variant of the boundary condition model and it has been employed to calculate the binding energies for a system consisting of three atoms. Two realistic He-He interactions of Aziz and collaborators have been used for this purpose. The results obtained compare favourably with those previously obtained by other methods. We further used the model to calculate, for the first time, the ultralow-energy scattering phase shifts. This study revealed that our method is ideally suited for three-body molecular calculations where the practically hard-core of the inter-atomic potential gives rise to strong numerical inaccuracies that make calculations for these molecules cumbersome.

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.

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Abstract Among the light nuclear clusters the α -particle is by far the strongest bound system and therefore expected to play a significant role in the dynamics of nuclei and the phases of nuclear matter. To systematically study the properties of the α -particle we have derived an effective four-body equation of the Alt–Grassberger–Sandhas (AGS) type that includes the dominant medium effects, i.e. self energy corrections and Pauli-blocking in a consistent way. The equation is solved utilizing the energy dependent pole expansion for the subsystem amplitudes. We find that the Mott transition of an α -particle at rest differs from that expected from perturbation theory and occurs at approximately 1/10 of nuclear matter densities.

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SummaryA combination of the variable-constant and complex coordinate rotation methods is used to solve the two-body Schrödinger 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 short-range and Coulombtailed 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.

-particle in nuclear matter

An exact method for direct calculation of the Jost functions and Jost solutions for non-central analytic potentials which couple partial waves of different angular momenta is presented. A combination of the variable-constant method with the complex coordinate rotation is used to replace the matrix Schrodinger equation by an equivalent system of linear first-order differential equations. Solving these equations numerically, the Jost functions can be obtained to any desired accuracy for all complex momenta of physical interest, including the spectral points corresponding to bound and resonant states. The effectiveness of the method is demonstrated using the Reid soft-core and Moscow nucleon-nucleon potentials which involve tensor forces.

A method for calculating the Jost function for analytic potentials

Abstract A method is proposed for solving the phase problem in specular neutron reflection. A differential equation for the reflection phase is derived and solved in terms of the reflectivity and the dwell time. This opens the possibility of determining surface profiles from measured quantities by inversion. A schematic example is presented.

Jost function for coupled partial waves

It is shown that the spectral points (bound states and resonances) generated by a central potential of a single-channel problem, can be found using rational parametrization of the S-matrix. To achieve this, one only needs values of the S-matrix along the real positive energy axis. No calculations of the S-matrix at complex energies or a complex rotation are necessary. The proposed method is therefore universal in that it is applicable to any potential (local, non-local, discontinuous, etc) provided that there is a way of obtaining the S-matrix (or scattering phase shifts) at real collision energies. Besides this, combined with any method that extracts the phase shifts from the scattering data, the proposed rational parametrization technique would be able to do the spectral analysis using the experimental data.

A proposal for the determination of the phases in specular neutron reflection

The scattering length for the eta-meson collision with deuteron is calculated on the basis of rigorous few-body equations (AGS) for various eta-N input. The results obtained strongly support the existence of a resonance or quasi-bound state close to the eta-d threshold.

Padé approximation of the S-matrix as a way of locating quantum resonances and bound states

Abstract We present a method based on hyperspherical harmonics to solve the nuclear many-body problem. It is an extension of accurate methods used for studying few-body systems to many bodies and is based on the assumption that nucleons in nuclei interact mainly via pairwise forces. This leads to a two-variable integro-differential equation which is easy to solve. Unlike methods that utilize effective interactions, the present one employs directly nucleon–nucleon potentials and therefore nuclear correlations are included in an unambiguous way. Three body forces can also be included in the formalism. Details on how to obtain the various ingredients entering into the equation for the A -body system are given. Employing our formalism we calculated the binding energies for closed and open shell nuclei with central forces where the bound states are defined by a single hyperspherical harmonic. The results found are in agreement with those obtained by other methods.