Note on the complex stabilization method

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Abstract
A recently proposed complex stabilization method is examined from the viewpoint of the necessity for an explicit construction of the coordinate-rotated Hamiltonian. It is demonstrated and proved that the argument for using unrotated Hamiltonians in resonance-structure determinations must be taken in a restricted sense. With the use of square-integrable basis functions, it is shown that complex rotation is necessary to directly calculate complex resonance poles. We illustrate our conclusion by a numerical model calculation.