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The interaction of a quantum particle with a gaseous detector is studied in the quantum-mechanical state space of the particle-detector system by means of a simple stationary scattering 3D model. The particle is assumed to interact with N two-level point-like scatterers depicting the atoms of the detector. Due to the contact interaction, the particle scatters off the atoms in isotropic spherical waves. Remarkably, the Lippmann–Schwinger equation of this multiple scattering problem can be exactly solved in a nonperturbative way. The aim is to analyze the influence of the initial microstate of the detector on the observed outcome, and to understand the mechanism of track formation in gaseous detectors. It is shown that the differential cross-section of excitation must be large enough in the forward direction to get the formation of tracks. In addition, the relatively small influence of atomic positions is highlighted. These results are explained through a perturbative calculation. [ABSTRACT FROM AUTHOR]

Starting from a system of N radial Schrödinger equations with a vanishing potential and finite threshold differences between the channels, a coupled N × 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. For N = 2, previous results are reviewed, in particular regarding the number of bound states and resonances of the potential. A schematic inverse problem with one resonance is considered. [ABSTRACT FROM AUTHOR]