S.A. Rakityansky

Faddeev type calculation of eta d threshold scattering

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.

Jost function for singular potentials

An exact method for direct calculation of the Jost function and Jost solutions for a repulsive singular potential is presented. Within this method the Schrodinger equation is replaced by an equivalent system of linear first-order differential equations, which after complex rotation, can easily be solved numerically. The Jost function 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 method can also be used in the complex angular-momentum plane to calculate the Regge trajectories. The effectiveness of the method is demonstrated using the Lennard-Jones (12,6) potential. The spectral properties of the realistic inter-atomic He4-He4 potentials HFDHE2 and HFD-B of Aziz and collaborators are also investigated.

Jost function for coupled channels

Almost any textbook on the scattering theory has a chapter devoted to the Jost function, but none of them gives a practical recipe for its calculation. Thus one usually gets a feeling that the Jost function is a pure mathematical object, elegant and useful in formal theory, but impractical in computations. This is even more so in the case of multi-channel problems, where the Jost function is, in fact, a matrix. Recently, we proposed an exact method for direct calcu- lation of the Jost function for central potentials (which may have Coulombic tails) [1, 2] and the Jost matrix for non-central short range potentials [3]. 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.

Low-energy ηd-resonance

Abstract: Elastic ηd-scattering is considered within the Alt-Grassberger-Sandhas (AGS) formalism for various ηN input data. A three-body resonant state is found close to the ηd threshold. This resonance is sustained for different choices of the two-body ηN-scattering length aηN. The position of the resonance moves towards the ηd threshold when ReaηN is increased, and turns into a quasi-bound state at ReaηN∼ 0.7-0.8 fm depending on the choice of ImaηN.

Low-energy eta d resonance

Abstract: Elastic ηd-scattering is considered within the Alt-Grassberger-Sandhas (AGS) formalism for various ηN input data. A three-body resonant state is found close to the ηd threshold. This resonance is sustained for different choices of the two-body ηN-scattering length aηN. The position of the resonance moves towards the ηd threshold when ReaηN is increased, and turns into a quasi-bound state at ReaηN∼ 0.7-0.8 fm depending on the choice of ImaηN.

Threshold scattering of the η-meson off light nuclei

The scattering lengths of eta-meson collisions with light nuclei d,t,3He, and 4He are calculated on the basis of few-body equations in coherent approximation. It is found that the eta-nucleus scattering length depends strongly on the number of nucleons and the potential-range parameter. By taking into account the off-shell behavior of the eta-N amplitude, the eta-4He scattering length increases considerably.Abstract The scattering lengths of η-meson collisions with light nuclei 2H, 3H, 3He, and 4He are calculated on the basis of few-body equations in coherent approximation. It is found that the η-nucleus scattering length depends strongly on the number of nucleons and the range parameter. By taking into account the off-shell behavior of the ηN amplitude, the ηα scattering length increases considerably.

Interaction of η-Meson with Light Nuclei

A microscopic treatment of η-nucleus scattering is presented. When applying the underlying exact integral equations, excitations of the target are neglected, and an input ηN amplitude is chosen which reproduces the S11(1535) resonance. It is shown that the η-nucleus scattering lengths are quite sensitive to the ηN parameters and the nuclear wave functions. For a special choice of these parameters an η 4 He quasi-bound state occurs.

Coherent photoproduction of η-mesons on three-nucleon systems

Abstract A microscopic few-body description of near-threshold coherent photoproduction of the η meson on tritium and 3 He targets is given. The photoproduction cross section is calculated using the Finite Rank Approximation (FRA) of the nuclear Hamiltonian. The results indicate a strong final state interaction of the η meson with the residual nucleus. Sensitivity of the results to the choice of the ηN T -matrix is investigated.

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

The resonance and bound-state poles of the amplitude describing elastic scattering of η-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 necessary two-body ηN-input allowing appearance of quasi-bound η-nucleus state, are also determined.

Triple collisions e− p 7Be in solar plasma

Abstract Several nuclear reactions involving the 7 Be nucleus, not included into the standard model of the pp -chain, are discussed. A qualitative analysis of their possible influence on the fate of the 7 Be in solar plasma and of their role in the interpretation of the solar neutrino experiments is given. As an example, the reaction rate of the non-radiative production of 8 B in the triple collision p + e − + 7 Be → 8 B + e − is estimated in the framework of the adiabatic approximation. For the solar interior conditions the triple collision reaction rate is approximately 10 −4 of that for the binary process p + 7 Be → 8 B + γ .