Solution of a pairing problem in the continuum

13 pags., 12 figs., 10 tabs.We present a generalized Richardson solution for fermions interacting with the pairing interaction in both discrete and continuum parts of the single-particle (s.p.) spectrum. The pairing Hamiltonian is based on the rational Gaudin model which is formulated in the Berggren ensemble. We show that solutions of the generalized Richardson equations are exact in the two limiting situations: (i) in the pole approximation and (ii) in the s.p. continuum. If the s.p. spectrum contains both discrete and continuum parts, then the generalized Richardson equations provide accurate solutions for the Gamow shell model.J.D. is supported by Grant No. FIS2015-63770-P (MINECO/FEDER), and N.M. is supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics under Award No. DE-SC0013365 (Michigan State University).Peer Reviewe