Continuum level density of a coupled-channel system in the complex scaling method

Abstract : We study the continuum level density (CLD) in the formalism of the complex scaling method (CSM) for coupled-channel systems. We apply the formalism to the $^4$He = [$^3$H + $p$] + [$^3$He + $n$] coupled-channel cluster model where there are resonances at ow energy. Numerical calculations of the CLD in the CSM with a finite number of L$^2$ basis functions are consistent with the exact result calculated from the S-matrix by solving coupled-channel equations. We also study channel densities. In this framework, the extended completeness relation (ECR) plays an important role.