The complex-scaling method using a complete L²-basis

A complete set of square-integrable basis functions is used to find the matrix elements of the rotated model Hamiltonian in which the reference Hamiltonian is fully taken into account while the interchannel potential is approximated by its representation in the finite subset of the complete basis. Since the spectrum of the model Hamiltonian satisfies the Aguilar-Balslev-Combes theorem, the only discrete eigenvalues of the complex-scaled Hamiltonian are the system's bound states and complex resonance energies. We propose an efficient method to locate these resonance energies and show that they converge taster than the eigenvalues of the complex-scaled Hamiltonian using a finite basis, while being less sensitive to the variation of the rotation angle.