A new effective interaction for the trapped Fermi gas

We apply the configuration-interaction method to calculate the spectra of two-component Fermi systems in a harmonic trap, studying the convergence of the method at the unitary interaction limit. We find that for a fixed regularization of the two-body interaction the convergence is exponential or better in the truncation parameter of the many-body space. However, the conventional regularization is found to have poor convergence in the regularization parameter, with an error that scales as a low negative power of this parameter. We propose a new regularization of the two-body interaction that produces exponential convergence for systems of three and four particles. From the systematics, we estimate the ground-state energy of the four-particle system to be (5.05 +- 0.024)hbar omega.Comment: 4 pages, 3 figure

Number of quantal resonances

Employing the concept of time-delay, a relation is found which counts the number of quantal resonances supported by a potential. Several simple and advanced illustrations include a treatment of square-well, Dirac delta barrier, an interesting physical situation from neutron reflectometry, and the Delta resonance appearing in the scattering of \pi meson from proton.Comment: 9 pages, 5 figure