Electron. J. Differential Equations, Vol. 2021 (2021), No. 36, pp. 1-22.

Energy-dependent Hamiltonian in a nuclear optical model

Pierre Chau Huu-Tai, Bernard Ducomet

We study the spectral properties of a 1D model of optical potential introduced by Morillon and Romain [21] in the context of nuclear reactions. We can localize the discrete spectrum and estimate the number of eigenvalues. We also study the continuous spectrum with possibly embedded spectral singularities and give an expansion formula for an arbitrary function on a set of generalized eigenfunctions. We briefly study the resonances of a related model.

Submitted December 17, 2020. Published May 4, 2021.
Math Subject Classifications: 35J10, 35P15, 47A55.
Key Words: Nonselfadjoint; complex potential; energy dependent potential; S-wave.
DOI: https://doi.org/10.58997/ejde.2021.36

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Pierre Chau Huu-Tai
CEA, DAM, DIF, F-91297 Arpajon France, and
Université Paris-Saclay, CEA
Laboratoire Matière en Conditions Extrêmes
91680 Bruyères le Chatel, France
email: huu-tai.chau@cea.fr
Bernard Ducomet
Université Paris-Est Créteil, LAMA (UMR 805)
CNRS, 61 Avenue du Général de Gaulle
F-94010 Créteil, France
email bernard.ducomet@u-pec.fr

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