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Register a new userSeparable Representation of Phenomenological Optical Potentials of Woods-Saxon Type
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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. 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.
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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. 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.
Recently, a new approach for solving the three-body problem for (d,p) reactions in the Coulomb-distorted basis in momentum space was proposed. Important input quantities for such calculations are the scattering matrix elements for proton- and neutron-nucleus scattering. We present a generalization of the Ernst-Shakin-Thaler scheme in which a momentum space separable representation of proton-nucleus scattering matrix elements can be calculated in the Coulomb basis. The viability of this method is demonstrated by comparing S-matrix elements obtained for p$+^{48}$Ca and p$+^{208}$Pb for a phenomenological optical potential with corresponding coordinate space calculations.
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. 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. Including excitations of the nucleus in the calculation requires a multichannel optical potential. The purpose of this paper is to introduce a separable, energy-dependent multichannel representation of complex, energy-dependent optical potentials that contain excitations of the nucleus and that fulfill reciprocity exactly. Momentum space Lippmann-Schwinger integral equations are solved with standard techniques to obtain the form factors for the separable representation. Starting from energy-dependent multichannel optical potentials for neutron and proton scattering from $^{12}$C, separable representations based on a generalization of the Ernst-Shakin-Thaler (EST) scheme are constructed which fulfill reciprocity exactly. Applications to n$+^{12}$C and p$+^{12}$C scattering are investigated for energies from 0 to 50~MeV.
The motion of l=0 antibound poles of the S-matrix with varying potential strength is calculated in a cutoff Woods-Saxon (WS) potential and in the Salamon-Vertse (SV) potential, which goes to zero smoothly at a finite distance. The pole position of the antibound states as well as of the resonances depend on the cutoff radius, especially for higher node numbers. The starting points (at potential zero) of the pole trajectories correlate well with the range of the potential. The normalized antibound radial wave functions on the imaginary k-axis below and above the coalescence point have been found to be real and imaginary, respectively.
The optical potential is a powerful instrument for calculations on a wide variety of nuclear reactions, in particular, for quasi-elastic lepton-nucleus scattering. Phenomenological optical potentials are successful in the description of data but may produce uncertainties in the interpretation of the results. Two recent theoretical optical potentials are presented: a global relativistic folding optical potential, that has been employed in relativistic models for quasi-elastic lepton-nucleus scattering, and a non relativistic optical potential derived from nucleon-nucleon chiral potentials at fourth order (N4LO), that has been applied to elastic proton-nucleus scattering.
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