Solving the Bogolyubov equations for semi-infinite nuclear matter in the case of a nonlocal gap

In the superfluidity problem treated on the basis of the Brueckner approach implemented with a separable nucleon-nucleon potential, a method is develo ped for solving the equation for the gag Delta in semi-infinite nuclear mat ter. The proposed method relies on the concept of effective interaction act ing in a model space where the equation for Delta is specified. This equati on is recast into a simpler form such that Delta is expressed in terms of t he quantity that has the meaning of an anomalous density in the model space . The gap Delta proves nonlocal, and the corresponding Bogolyubov equations are integro-differential. A method for numerically solving these equations is developed and applied to several examples by way of illustration.