Level Density in the Complex Scaling Method

It is shown that the continuum level density (CLD) at unbound energies can becalculated with the complex scaling method (CSM), in which the energy spectraof bound states, resonances and continuum states are obtained in terms of $L^2$basis functions. In this method, the extended completeness relation is appliedto the calculation of the Green functions, and the continuum-state part isapproximately expressed in terms of discretized complex scaled continuumsolutions. The obtained result is compared with the CLD calculated exactly fromthe scattering phase shift. The discretization in the CSM is shown to give avery good description of continuum states. We discuss how the scattering phaseshifts can inversely be calculated from the discretized CLD using a basisfunction technique in the CSM.Comment: 14 pages, 9 figures, To be published in Progress of Theoretical Physic