The Imaginary Part of the Optical Potential

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Abstract
We derive the form of the imaginary part of the optical potential as an operator for the finite nucleus. This is done by reducing the Schrodinger equation approximately. It is essentially a second order calculation but this is supported by the intermediate coupling model and the assumption that the non-diagonal elements of the interaction matrix have random signs. The imaginary part thus obtained is a non-local but almost separable potential. The form allows the physical interpretation that the imaginary part corresponds to the process in which the incident nucleon jumps down to an unoccupied single particle state below the incident energy and excites the target nucleus making the total energy nearly conserved. It is suggested that the imaginary part may become abruptly stronger as the shape resonance is passed since in this case there is a single particle state just below the incident energy and the corresponding excited states of the target are near the ground state. The relation to Bloch's theory is also discussed.

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