Background: One important ingredient for many applications of nuclear physics to astrophysics, nuclear energy, and stockpile stewardship are the cross sections for reactions of neutrons with rare isotopes. Since direct measurements are often not feasible, indirect methods, e.g., (d,p) reactions, should be used. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques. Purpose: Faddeev equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. While there exist several separable representations for the nucleon-nucleon interaction, the optical potential between a neutron (proton) and a nucleus is not readily available in separable form. The purpose of this paper is to introduce a separable representation for complex phenomenological optical potentials of Woods-Saxon type. Results: Starting from a global optical potential, a separable representation thereof is introduced based on the Ernst-Shakin-Thaler (EST) scheme. This scheme is generalized to non-Hermitian potentials. Applications to n + 48 Ca, n + 132 Sn, and n + 208 Pb are investigated for energies from 0 to 50 MeV and the quality of the representation is examined. Conclusions: We find a good description of the on-shell t matrix for all systems with rank up to 5. The required rank depends inversely on the angular momentum. The resulting separable interaction exhibits a different off-shell behavior compared to the original potential, reducing the high-momentum contributions.

Recently, a new approach for solving the three-body problem for (d,p) reactions in the Coulombdistorted basis in momentum space was proposed. Important input quantities for such calculations are the scattering matrix elements for proton (neutron) nucleus scattering. We present a generalization of the the Ernst-Shakin-Thaler scheme in which a momentum space separable representation of proton-nucleus scattering matrix elements in the Coulomb basis can be calculated. The success of this method is demonstrated by comparing S-matrix elements and cross sections for proton scattering from 12 C, 48 Ca, and 208 Pb with the corresponding coordinate space calculations.

Background: Deuteron induced reactions are widely used to probe nuclear structure and astrophysical information. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques. Purpose: Faddeev equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. However, it needs to be demonstrated that their solution based on separable interactions agrees exactly with solutions based on nonseparable forces. Methods: Momentum space Faddeev equations are solved with nonseparable and separable forces as coupled integral equations. Results: The ground state of 6 Li is calculated via momentum space Faddeev equations using the CD-Bonn neutron-proton force and a Woods-Saxon type neutron(proton)-4 He force. For the latter the Pauli-forbidden S-wave bound state is projected out. This result is compared to a calculation in which the interactions in the two-body subsystems are represented by separable interactions derived in the Ernst-Shakin-Thaler (EST) framework. Conclusions: We find that calculations based on the separable representation of the interactions and the original interactions give results that agree to four significant figures for the binding energy, provided that energy and momentum support points of the EST expansion are chosen independently. The momentum distributions computed in both approaches also fully agree with each other.

Background: One important ingredient for many applications of nuclear physics to astrophysics, nuclear energy, and stockpile stewardship are cross sections for reactions of neutrons with rare isotopes. Since direct measurements are often not feasible, indirect methods, e.g. (d,p) reactions, should be used. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques.Purpose: Faddeev equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. Optical potentials representing the effective interactions in the neutron (proton) nucleus subsystem are usually non-Hermitian as well as energy-dependent. Potential matrix elements as well as transition matrix elements calculated with them must fulfill the reciprocity theorem. The purpose of this paper is to introduce a separable, energy-dependent representation of complex, energy-dependent optical potentials that fulfill reciprocity exactly.Methods:: Momentum space Lippmann-Schwinger integral equations are solved with standard techniques to obtain the form factors for the separable representation.Results: Starting from a separable, energy-independent representation of global optical potentials based on a generalization of the Ernst-Shakin-Thaler (EST) scheme, a further generalization is needed to take into account the energy dependence. Applications to n+ 48 Ca, n+ 208 Pb, and p+ 208 Pb are investigated for energies from 0 to 50 MeV with special emphasis on fulfilling reciprocity. Conclusions:We find that the energy-dependent separable representation of complex, energy-dependent phenomenological optical potentials fulfills reciprocity exactly. In addition, taking into account the explicit energy dependence slightly improves the description of the S matrix elements.