Volume 253, number 1,2 PHYSICS LETTERS B 3 January 1991 Bound pair states in nuclear matter B.E. Vonderfecht, C.C. Gearhart, W.H. Dickhoff Department of Physics, Washington University, Saint Louis, MO 63130, USA A. Polls Departament d'Estructura i Constituents de la Mat~ria, Universitat de Barcelona, E-8028 Barcelona, Spain and A. Ramos TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, Canada V6T 2A3 Received 16 July 1990 The self-consistency between a Brueckner like ladder equation for the effective interaction which treats particles and holes symmetrically and the Dyson equation is discussed. A study of pairing instabilities in nuclear matter for realistic nucleon-nucleon interactions is presented. Bound pair states in nuclear matter are obtained and their contribution to the interaction is compared to the continuum contribution using dispersion relations. A survey of simple pairing properties for the Reid potential is made. It is suggested that the actual ground state of nuclear matter around the empirical saturation density corresponds to a superfluid with pairing occurring with deuteron quantum numbers. Modern nuclear physics experiments directly revealing the correlated properties of nuclei have painted a pic- ture of the nucleus quite different from the traditional shell model. Exclusive electron scattering data [ 1 ] show that mean field orbitals have an identity analogous to the quasi-particle excitations of Landau's Fermi liquid theory [2 ] and when analyzed together with charge density measurements show that these orbitals are partially occupied [ 3 ]. It is therefore appropriate to pay special attention to these non-mean field properties in theoreti- cal investigations of nuclei. Recent work has argued that self-consistent Green's function theory (SCGF) is a natural framework in which to include these correlations [4]. It is presently possible to study short-range and tensor correlations in the nuclear matter problem using the SCGF formalism. In ref. [ 4 ] it is demonstrated that a symmetric treatment of particle and hole propagation at the level of ladder diagrams in the effective interaction (scattering matrix in the medium) is essential for deple- tion effects in nuclear matter analogous to those seen in experiment. When applying the method to realistic nuclear interactions one is forced to treat long-range pairing correlations contained in the ladder approximation to the effective interaction as well. This becomes inevitable since the solution of the ladder equation leads to the appearance of pairing instabilities when such realistic interactions are employed [ 5 ]. In this letter we explore some details of the first step in a self-consistent treatment of pairing phenomena in nuclear matter. The exact form of SCGF is represented by the Dyson equation in fig. 1, which displays the connection between the effective interaction (F) and the single particle propagator made through the self-energy (_r). From Brueck- ~r This research was supported by the Condensed Matter Theory Program of the Division of Materials Research of the US National Science Foundation under Grant No. DMR-9002863 which also provided computer time at the Pittsburgh Supercomputer Center. Additional support was provided by NATO under Grant No. RG 85/0684 and by CAYCIT Grant No. PB85-0072-C02-00 (Spain). 0370-2693/91/$ 03.50 © 1991 - Elsevier Science Publishers B.V. ( North-Holland ) 1