arXiv subjects

Jean-Marc Sparenberg

Publications and source records attributed to Jean-Marc Sparenberg.

25 records · Page 2Linked to original sources

arXiv2008

Coupling between scattering channels with SUSY transformations for equal thresholds

Supersymmetric (SUSY) transformations of the multi-channel Schrödinger equation with equal thresholds and arbitrary partial waves in all channels are studied. The structures of the transformation function and the superpotential are analyzed. Relations between Jost and scattering matrices of superpartner potentials are obtained. In particular, we show that a special type of SUSY transformation allows us to introduce a coupling between scattering channels starting from a potential with an uncoupled scattering matrix. The possibility for this coupling to be trivial is discussed. We show that the transformation introduces bound and virtual states with a definite degeneracy at the factorization energy. A detailed study of the potential and scattering matrices is given for the $2\times 2$ case. The possibility of inverting coupled-channel scattering data by such a SUSY transformation is demonstrated by several examples ($s-s$, $s-p$ and $s-d$ partial waves).

quant-ph↗

arXiv2007

Exactly-solvable coupled-channel potential models of atom-atom magnetic Feshbach resonances from supersymmetric quantum mechanics

Starting from a system of $N$ radial Schrödinger equations with a vanishing potential and finite threshold differences between the channels, a coupled $N \times N$ exactly-solvable potential model is obtained with the help of a single non-conservative supersymmetric transformation. The obtained potential matrix, which subsumes a result obtained in the literature, has a compact analytical form, as well as its Jost matrix. It depends on $N (N+1)/2$ unconstrained parameters and on one upper-bounded parameter, the factorization energy. A detailed study of the model is done for the $2\times 2$ case: a geometrical analysis of the zeros of the Jost-matrix determinant shows that the model has 0, 1 or 2 bound states, and 0 or 1 resonance; the potential parameters are explicitly expressed in terms of its bound-state energies, of its resonance energy and width, or of the open-channel scattering length, which solves schematic inverse problems. As a first physical application, exactly-solvable $2\times 2$ atom-atom interaction potentials are constructed, for cases where a magnetic Feshbach resonance interplays with a bound or virtual state close to threshold, which results in a large background scattering length.

quant-ph↗

arXiv2007

Supersymmetric transformations for coupled channels with threshold differences

The asymptotic behaviour of the superpotential of general SUSY transformations for a coupled-channel Hamiltonian with different thresholds is analyzed. It is shown that asymptotically the superpotential can tend to a diagonal matrix with an arbitrary number of positive and negative entries depending on the choice of the factorization solution. The transformation of the Jost matrix is generalized to "non-conservative" SUSY transformations introduced in Sparenberg et al (2006 J. Phys. A: Math. Gen. 39 L639). Applied to the zero initial potential the method permits to construct superpartners with a nontrivially coupled Jost-matrix. Illustrations are given for two- and three-channel cases.

math-ph↗

arXiv2004

Hybrid potential/R-matrix models for the 12C + alpha system

I present ongoing developments on hybrid models which combine the potential model, for the description of the background, with the R-matrix model, for the description of discrete states. Physical parameters of discrete states are converted into formal R-matrix parameters, taking into account the potential background. The nuclear part of this potential is constructed by a new variant of an inversion method based on supersymmetric quantum mechanics. The method is illustrated on 12C + alpha S-wave elastic phase shifts.

nucl-th↗

arXiv2004

On the practical interest of one-body overlap functions

Two types of one-body functions extracted from microscpic models of the 8B ground state are compared with one another and with a potential-model wave function. The one-body overlap function seems to have the strongest physical meaning.

nucl-th↗

arXiv2004

Deducing the asymptotic normalization constant of the 2+ subthreshold state in 16O from 12C + alpha elastic scattering

R-matrix analyses of the 12C + alpha elastic-scattering phase shifts deduced from a recent high-precision measurement of the differential cross sections are performed. The l=0 phase shifts constrain the R-matrix radius a around 5.85 fm, while the l=2 phase shifts lead to a strong constrain neither on a nor on the asymptotic normalization constant C of the 2+ subthreshold state (except for a loose upper limit). This contradicts previous R-matrix analyses of the 12C + alpha elastic scattering and explains the incompatibility between values of C obtained in these analyses.

nucl-th↗

arXiv2003

Many-body approach to proton emission and the role of spectroscopic factors

The process of proton emission from nuclei is studied by utilizing the two-potential approach of Gurvitz and Kalbermann in the context of the full many-body problem. A time-dependent approach is used for calculating the decay width. Starting from an initial many-body quasi-stationary state, we employ the Feshbach projection operator approach and reduce the formalism to an effective one-body problem. We show that the decay width can be expressed in terms of a one-body matrix element multiplied by a normalization factor. We demonstrate that the traditional interpretation of this normalization as the square root of a spectroscopic factor is only valid for one particular choice of projection operator. This causes no problem for the calculation of the decay width in a consistent microscopic approach, but it leads to ambiguities in the interpretation of experimental results. In particular, spectroscopic factors extracted from a comparison of the measured decay width with a calculated single-particle width may be affected.

nucl-th↗