Summary
A formalism for calculating the photonuclear reaction cross-sections has been developed by extending a natural boundary condition method employed so far for the accurate description of the nucleon-induced reactions from a definite nuclear model. The comparison of the present approach with some coupled-channel-type methods for the one-particle continuum treatment is also discussed.
Riassunto
È stato sviluppato un formalismo per il calcolo delle sezioni d’urto di reazione fotonucleare; partendo dal metodo della condizione al contorno naturale, fino ad ora impiegato sulla base di un prefissato modello nucleare per la descrizione accurata delle reazioni indotte da nucleoni. Il presente approccio è confrontato con alcuni metodi di canali accoppiati per il trattamento di una particella nel continuo.
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It should be remarked here that the present form appears as the result of considering the orthonormal basis states within the internal region. This in turn implies that the single-particle statesϕ i(r A)are orthogonal to the states of theA-1 particles constituting the target. This assertion holds, however, so long as all the single-particle wave functions in theA-particle system are treated on equal footing. In case, for example, the target wave function results from the Slater determinant of theA-1 single-particle wave functions in the Hartree-Fock basis andϕ i(r A)results from the Saxon-Woods or some other basis, the basis states become nonorthogonal. Consequently the closure relation used in the derivation of eq. (12) needs to be replaced by Σ |ξ i〉[N −1] ij 〈ξ j|=1 with [N] ij =〈ξ i|ξ j〉 ≠δ ij. However, since the single-particle potential of eq. (5) may be assumed to simulate the Hartree-Fock potential to a certain extent (17), we shall deal throughout with the orthonormal basis sets.
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Work supported in part by INFN under the contract No. 720: 6/10/78.
An erratum to this article is available at http://dx.doi.org/10.1007/BF02899969.
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Ahmad, S.S. On a one-particle in the continuum approach for the photoreaction cross-sections. Nuov Cim A 54, 129–142 (1979). https://doi.org/10.1007/BF02899783
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DOI: https://doi.org/10.1007/BF02899783