Resonance positions and lifetimes for flexible complex absorbing potentials

By adding any complex absorbing potential (CAP) -i lambda V(r) to a system Hamiltonian, the corresponding complex eigenvalues are analytical functions of lambda,E-j(lambda). It is shown here that for a quite general flexible class of CAP's the real part of lim(lambda -> 0)E(j)(lambda) provides the resonance energy. The imaginary part of that limit is the resonance width (i.e., inverse lifetime) in spite of the fact that Im E-j(0)=0. The need for the Pade approximation within this approach is explained. Application to an illustrative numerical test case model Hamiltonian is given. This method could open a gate for studying systems that could not be studied until now due to the complexity of the numerical computations. In particular, one may in this way obtain resonance energies by a modification, in a straightforward simple manner, of the widely used conventional methods that were developed for the calculations of bound states.