Level Density in the Complex Scaling Method

Abstract

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

Four-body resonances of7B using the complex scaling method

“…[20,24,25]. The reliability of the continuum discretization in CSM has already been shown using continuum level density [38] and phase-shift analysis [27].…”

Virtual-state character of the two-body system in the complex scaling method

“…In the calculation we adopt a sufficiently large number of N to keep the numerical accuracy and to make the θ dependence negligible in the solutions [25].…”

Decomposition of scattering phase shifts and reaction cross sections using the complex scaling method

“…The extended completeness relation has been proven for single-and coupled-channel systems [17,18]. In the case of eigenstates within a finite number of L 2 basis states, the integration for continuum states is approximated by the summation of discretized states as [9] It has been investigated that the reliability of the approximation of the continuum states are confirmed by using a sufficiently large basis number of N in the CSM [5,12].…”

“…In the calculation we adopt a sufficiently large number of N to keep the numerical accuracy and to make the θ dependence negligible in the solutions [12]. Thus we calculate the phase shift from…”

“…It is possible to investigate the resonance contributions and to obtain a deep understanding of resonance structure by separation of a scattering quantity. Suzuki et al [12] showed that scattering phase shifts can be calculated from the continuum level density (CLD), which is expressed using the complex scaled Green's function. The CLD is also called a time delay and has a relation with the S matrix [13,14].…”