M. Braun

Multichannel inverse scattering problem in one dimension: Thresholds and bound states

We consider the multichannel inverse scattering problem in one dimension in the presence of thresholds and bound states for a potential of finite support. Utilizing the Levin representation, we derive the general Marchenko integral equation for N-coupled channels and show that, unlike the case of the radial inverse scattering problem, the information on the bound-state energies and asymptotic normalization constants can be inferred from the reflection coefficient matrix alone. Thus, given this matrix, the Marchenko inverse scattering procedure can provide us with a unique multichannel potential. The relationship with supersymmetric partner potentials as well as possible applications are discussed. The integral equation has been implemented numerically and has been applied to several schematic examples showing the characteristic features of multichannel systems. A possible application of the formalism to technological problems is briefly discussed.

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.

Nonradiative proton-deuteron fusion in stellar plasma

Abstract The nuclear reaction e + p + d → 3 He + e is considered at thermonuclear energies. The motion of the electron is treated within the adiabatic approximation and the pd scattering state is constructed in the form of an antisymmetrised product of the bound-state wave function of the deuteron and of the wave function of the pd relative motion. The latter is calculated using an effective pd potential constructed via the Marchenko inverse scattering method. The bound-state wave function of 3He is obtained using Faddeev-type integrodifferential equations. The reaction rate thus obtained for the solar interior conditions is approximately 10−4 of the corresponding rate for the radiative capture pd → 3 He γ .

The φ-NN and φφ-NN mesic nuclear systems

We present a two-variable integro-differential equation describing bound systems of unequal mass particles. The method is based on an extension of the two-variable integro-differential equations in the D = 3(A − 1)-dimensional space, known as IDEA, describing the bound states of A-body systems. This method has been successfully applied in the past to few-body systems with the results obtained being in good agreement to those of competing methods. In the present work we investigate whether the same is true for unequal mass particles. Therefore, we first employ the formalism to obtain binding energies for Λ- and ΛΛ-nuclear systems and compare the results with some other results in the field. Secondly, we apply it to the - and -nuclear systems. Using –nucleon and – interactions, available in the literature, we found that mesic–nuclear systems could exist.

Nuclear fusion via triple collisions in solar plasma

Abstract We consider several nuclear fusion reactions that can take place at the center of the sun, which are omitted in the standard pp-chain model. More specifically the reaction rates of the nonradiative production of 3 He, 7 Be, and 8 B nuclei in triple collisions involving electrons are estimated within the framework of the adiabatic approximation. These rates are compared with those of the corresponding binary fusion reactions.

Momentum Dependent Nucleon-Nucleon Potentials and the Off-Shell Dependence of the Triton Binding Energy

An inverse scattering scheme for nucleon-nucleon potentials in coupled channels is presented which includes a term proportional to the square of the momentum. The method is used to construct a set of fully phase equivalent potentials having a different momentum dependence. A characteristic dependence of the triton binding energy on the off-shell behaviour of these potentials is found.

NN potentials with explicit momentum dependence obtained from generalized darboux transformations

Using recently developed inversion techniques based on generalized Darboux transformations we constructed, in uncoupled channels, momentum dependent potentials having a momentum independent term and one term linear in the square of the momentum. Varying the momentum dependent term of these potentials we created via inversion sets of potentials that are phase equivalent up to at least 2 GeV to the commonly used Nijmegen and Paris nucleon-nucleon potentials. These sets of potentials offer us the possibility to study the sensitivity of the triton binding energy on the momentum dependence of the NN-force.

Momentum dependent nucleon-nucleon potentials via inverse scattering techniques

Abstract Inverse scattering methods based on exactly solvable models have been used to determine specific momentum dependent nucleon-nucleon potentials from nucleon-nucleon phase shifts in uncoupled partial waves. The novel method has been applied to the 1 S 0 channel. The explicit momentum dependencies considered are restricted to those of the well known parametrisations of the Paris and the Nijmegen potentials which consist of a momentum independent term and one linear in the square of the momentum. The interplay between momentum dependent and independent parts is demonstrated, generating phase equivalent potentials to the Paris potential with different momentum dependencies. Furthermore the sensitivity of the triton binding energy on the momentum dependence has been studied.