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Register a new userPhenomenological and Theoretical Optical Potentials
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Carlotta Giusti
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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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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.
Background: Elastic scattering is probably the main event in the interactions of nucleons with nuclei. Even if this process has been extensively studied in the last years, a consistent description, i.e. starting from microscopic two- and many-body forces connected by the same symmetries and principles, is still under development. Purpose: In this work we study the domain of applicability of microscopic two-body chiral potentials in the construction of an optical potential. Methods: We basically follow the KMT approach to build a microscopic complex optical potential and then we perform some test calculations on 16O at different energies. Results: Our conclusion is that a particular set of potentials with a Lippmann-Schwinger cutoff at relatively high energies (above 500 MeV) has the best performances reproducing the scattering observables. Conclusions: Our work shows that building an optical potential within Chiral Perturbation Theory is a promising approach to the description of elastic proton scattering, in particular, in view of the future inclusion of many-body forces that naturally arise in such framework.
A qualitative discussion on the range of the potentials as they result from the phenomenological meson-exchange picture and from lattice simulations by the HAL QCD Collaboration is presented. For the former pion- and/or $eta$-meson exchange are considered together with the scalar-isoscalar component of correlated $pipi /K bar K$ exchange. It is observed that the intuitive expectation for the behavior of the baryon-baryon potentials for large separations, associated with the exchange of one and/or two pions, does not always match with the potentials extracted from the lattice simulations. Only in cases where pion exchange provides the longest ranged contribution, like in the $Xi N$ system, a reasonable qualitative agreement between the phenomenological and the lattice QCD potentials is found for baryon-baryon separations of $r gtrsim 1$ fm. For the $Omega N$ and $OmegaOmega$ interactions where isospin conservation rules out one-pion exchange a large mismatch is observed, with the potentials by the HAL QCD Collaboration being much longer ranged and much stronger at large distances as compared to the phenomenological expectation. This casts some doubts on the applicability of using these potentials in few- or many-body systems.
An approach is outline to constructing an optical potential that includes the effects of antisymmetry and target recoil. it is based on the retarded Greens function, which could make it a better starting point for applications to direct nuclear reactions, particularly when extended to coupled channels. Its form retains a simple connection to folding potentials, even in the presence of three-body forces.
We construct nucleonic microscopic optical potentials by combining the Greens function approach with the coupled-cluster method for $rm{^{40}Ca}$ and $rm{^{48}Ca}$. For the computation of the ground-state of $rm{^{40}Ca}$ and $rm{^{48}Ca}$, we use the coupled-cluster method in the singles-and-doubles approximation, while for the A = $pm 1$ nuclei we use particle-attached/removed equation-of-motion method truncated at two-particle-one-hole and one-particle-two-hole excitations, respectively. Our calculations are based on the chiral nucleon-nucleon and three-nucleon interaction $rm{NNLO_{sat}}$, which reproduces the charge radii of $^{40}$Ca and $^{48}$Ca, and the chiral nucleon-nucleon interaction $rm{NNLO_{opt}}$. In all cases considered here, we observe that the overall form of the neutron scattering cross section is reproduced for both interactions, but the imaginary part of the potential, which reflects the loss of flux in the elastic channel, is negligible. The latter points to neglected many-body correlations that would appear beyond the coupled-cluster truncation level considered in this work. We show that, by artificially increasing the parameter $eta$ in the Greens function, practical results can be further improved.
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