Low-lying spectra in anharmonic three-body oscillators with a strong short-range repulsion

Three-body Schroedinger equation is studied in one dimension. Its two-body interactions are assumed composed of the long-range attraction (dominated by the L-th-power potential) in superposition with a short-range repulsion (dominated by the (-K)-th-power core) plus further subdominant power-law components if necessary. This unsolvable and non-separable generalization of Calogero model (which is a separable and solvable exception at L = K = 2) is presented in polar Jacobi coordinates. We derive a set of trigonometric identities for the potentials which generalizes the well known K=2 identity of Calogero to all integers. This enables us to write down the related partial differential Schroedinger equation in an amazingly compact form. As a consequence, we are able to show that all these models become separable and solvable in the limit of strong repulsion.Comment: 18 pages plus 6 pages of appendices with new auxiliary identitie

Strangeness Electromagnetic Production on Nucleons and Nuclei

Isobar models for the electromagnetic production of kaons are discussed with emphasis on the K^+ photoproduction at very small kaon angles and K^0 photoproduction on deuteron. Distorted-wave impuls approximation calculations of the cross sections for the electroproduction of hypernuclei are presented on the case of the ^{12}B_\Lambda production.Comment: 9 pages, 7 figures, talk presented at the 10th Int. Conference on Hypernuclear and Strange Particle Physics, Tokai, Japan, Sept. 14 - 18, 200

PT symmetric models in more dimensions and solvable square-well versions of their angular Schroedinger equations

For any central potential V in D dimensions, the angular Schroedinger equation remains the same and defines the so called hyperspherical harmonics. For non-central models, the situation is more complicated. We contemplate two examples in the plane: (1) the partial differential Calogero's three-body model (without centre of mass and with an impenetrable core in the two-body interaction), and (2) the Smorodinsky-Winternitz' superintegrable harmonic oscillator (with one or two impenetrable barriers). These examples are solvable due to the presence of the barriers. We contemplate a small complex shift of the angle. This creates a problem: the barriers become "translucent" and the angular potentials cease to be solvable, having the sextuple-well form for Calogero model and the quadruple or double well form otherwise. We mimic the effect of these potentials on the spectrum by the multiple, purely imaginary square wells and tabulate and discuss the result in the first nontrivial double-well case.Comment: 21 pages, 5 figures (see version 1), amendment (a single comment added on p. 7