Abstract
Shell-model calculations include very often single-particle configurations whose energy is larger than the particle emission threshold in the corresponding channel. Nevertheless the continuum nature of the energy spectrum is not taken into account and only a discrete eigen-value problem is solved. In this paper, the schematic Brown model is extended to include configurations in the energy continuum. It is shown that, if there are potential resonances, an “equivalent” discrete problem can be found, thereby giving an overall justification of the usual procedure. At the same time, the limitations of the “equivalent” discrete problem in reproducing the features of the actual problem are exhibited.
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