Search for long-lived states in antiprotonic lithium

The spectrum of the (L_i^3 + p-bar + 2e) four-body system was calculated in an adiabatic approach. The two-electron energies were approximated by a sum of two single-electron effective charge two-center energies as suggested in [6]. While the structure of the spectrum does not exclude the existence of long-lived states, their experimental observability is still to be clarified

Formulae for partial widths derived from the Lindblad equation

A method for calculating partial widths of auto-ionizing states is proposed. It combines either a complex absorbing potential or exterior complex scaling with the Lindblad equation. The corresponding classical rate equations are reproduced, and the trace conservation inherent in the Lindblad equation ensures that the partial widths sums up to the total width of the initial auto-ionizing state

Analytic structure and power series expansion of the Jost function for the two-dimensional problem

For a two-dimensional quantum-mechanical problem, we obtain a generalized power series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similar to the standard effective-range expansion. In order to do this, we consider the Jost function and analytically factorize its momentum dependence that causes the Jost function to be a multivalued function. The remaining single-valued function of the energy is then expanded in the power series near an arbitrary point in the complex energy plane. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This makes it possible to obtain a semi-analytic expression for the Jost function (and therefore for the S-matrix) near an arbitrary point on the Riemann surface and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles. The method is applied to a model similar to those used in the theory of quantum dots.http://www.iop.org/EJ/journal/JPhysAnf201

A method for extracting the resonance parameters from experimental cross-sections

Within the proposed method, a set of experimental data points are fitted using a multi-channel S-matrix. Then the resonance parameters are located as its poles on an appropriate sheet of the Riemann surface of the energy. The main advantage of the method is that the S-matrix is constructed in such a way that it has proper analytic structure, i.e. for any number of two-body channels, the branching at all the channel thresholds is represented via exact analytic expressions in terms of the channel momenta. The way the S-matrix is constructed makes it possible not only to locate multi-channel resonances but also to extract their partial widths as well as to obtain the scattering cross-section in the channels for which no data are available. The efficiency of the method is demonstrated by two model examples of a single-channel and a two-channel problems, where known resonance parameters are rather accurately reproduced by fitting the pseudo-data artificially generated using the corresponding potentials.http://www.worldscinet.com/ijmpehb201