Resonance conditions for the spectral function and single-hole states in finite nuclei
Abstract
An equation for the spectroscopic amplitudes in finite nuclei is determined both in the discrete and in the continuous spectrum of the residual nucleus hamiltonian. Its structure, involving the hole mass operator, is investigated. In the continuous spectrum, the spectroscopic amplitude equation leads to a precise definition of the hole decay width (related to the average value of the antihermitian part of the hole mass operator). Besides, one deduces a formula which describes the resonant behaviour of the spectral function in terms of the hole decay widths. Finally, the resonance conditions are investigated. Close to sharp resonances (included the ones of the discrete spectrum), one interpretes the spectroscopic amplitudes as single-hole wave functions which satisfy a Schrödinger-like equation where the hermitian part of the hole mass operator plays the role of an effective potential.
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