Exact method for locating potential resonances and Regge trajectories

Abstract

We propose an exact method for locating the zeros of the Jost function for analytic potentials in the complex momentum-plane. We further extend the method to the complex angular-momentum plane to provide the Regge trajectories. It is shown, by using several examples, that highly accurate results for extremely wide as well as for extremely narrow resonances with or without the presence of the Coulomb interaction can be obtained.

S matrix poles and the second virial coefficient

“…An expansion in 1/k up to the 4 th order yields the results in table 3. We see that we are able to reproduce the exact results, for the higher poles, to 5 digits.…”

Global minimization in few-body systems

“…In the absence of Coulomb forces (η = 0) we obtain, with N = 5, the energy eigenvaluesvalues 3.023634509 and 1.329872790 that differ in the 9th significant digit from those found in [5].…”

“…The required boundary conditions for the solution of the system (5-6) are discussed in [4,5]. We recall here the simple condition at origin…”

In-medium nucleon-nucleon potentials in configuration space

“…[23]. Alternatively, we way utilize the properties of Jost functions as elaborated in [19][20][21][22]. To do so we first derive a phase equivalent local potential to Eq.…”

“…We explicitely show that for the two-nucleon problem, to begin with, a deuteronlike in-medium state can be identified as an anti-bound state. To arrive at this result we use the technique of Jost functions elaborated for local potentials in [19][20][21][22]. The application to larger clusters will be postponed to a future work.…”