This chapter presents an overview of the optical model description of nucleon-nucleus scattering and reactions based on fundamental nuclear two-body and many-body forces. The chapter begins with a historical review followed by a discussion of several commonly used theoretical techniques for deriving nucleon-nucleus optical model potentials that account for antisymmetry, Pauli blocking, and multiple scattering. This is followed by a summary of current efforts to derive microscopic nuclear forces consistent with the fundamental theory of strong interactions, quantum chromodynamics, and the use of such interactions in the construction of microscopic optical potentials. The chapter will also outline the dispersive optical potential approach, which despite being primarily phenomenological, has its origins in formal Green's function theory. Finally, the results from modern optical potentials will be benchmarked to experimental data.
Microscopic descriptions of exotic nuclei are the subject of much experimental and theoretical effort. Not only are such important in their own right but are also necessary for applications in nuclear astrophysics. Evaluations of model wave functions may be done with analyses of elastic and inelastic scattering from hydrogen. Those require a realistic model of nucleon-nucleus scattering as scattering from hydrogen translates to proton scattering in the inverse kinematics. The Melbourne g-folding model for intermediate energy is presented along with various examples. Implications for existing a…
Various modern nucleon-nucleon (NN) potentials yield a very accurate fit to the nucleon-nucleon scattering phase shifts. The differences between these interactions in describing properties of nuclear matter are investigated. Various contributions to the total energy are evaluated employing the Hellmann - Feynman theorem. Special attention is paid to the two-nucleon correlation functions derived from these interactions. Differences in the predictions of the various interactions can be traced back to the inclusion of non-local terms.
We study the symmetry energy in infinite nuclear matter employing a non-relativistic Brueckner-Hartree-Fock approach and using various new nucleon-nucleon (NN) potentials, which fit np and pp scattering data very accurately. The potential models we employ are the recent versions of the Nijmegen group, Nijm-I, Nijm-II and Reid93, the Argonne $V_{18}$ potential and the CD-Bonn potential. All these potentials yield a symmetry energy which increases with density, resolving a discrepancy that existed for older NN potentials. The origin of remaining differences is discussed.
We study ground-state properties of the doubly magic nuclei 4He, 16O, and 40Ca employing the Goldstone expansion and using as input four different high-quality nucleon-nucleon (NN) potentials. The short-range repulsion of these potentials is renormalized by constructing a smooth low-momentum potential V-low-k. This is used directly in a Hartree-Fock approach and corrections up to third order in the Goldstone expansion are evaluated. Comparison of the results shows that they are only slightly dependent on the choice of the NN potential.
We present results for the $^3P_2 - ^3F_2$ pairing gap in neutron matter with several realistic nucleon-nucleon potentials, in particular with recent, phase-shift equivalent potentials. We find that their predictions for the gap cannot be trusted at densities above $ρ\approx 1.7ρ_0$, where $ρ_0$ is the saturation density for symmetric nuclear matter. In order to make predictions above that density, potential models which fit the nucleon-nucleon phase shifts up to about 1 GeV are required.
We report on a study of neutron-rich even-mass Te isotopes in terms of the shell model employing a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential. The strong short-range repulsion of the latter is renormalized by constructing a smooth low-momentum potential, V-low-k, that is used directly as input for the calculation of the effective interaction. In this paper, after a brief review of the theoretical framework, we present our results. Comparison shows that they are in very good agreement with the available experimental data.
Coulomb displacement energies, i.e., the differences between the energies of corresponding nuclear states in mirror nuclei, are evaluated using recent models for the nucleon-nucleon (NN) interaction. These modern NN potentials account for breaking of isospin symmetry and reproduce $pp$ and $pn$ phase shifts accurately. The predictions by these new potentials for the binding of $^{16}O$ are calculated. A particular focus of our study are effects due to nuclear correlations and charge-symmetry breaking (CSB). We find that the CSB terms in the modern NN interactions substantially reduce the discr…
The properties of $T=1/2$ mirror nuclei in the $fp$ shell have been studied with a microscopic residual interaction. The isospin-nonconserving interaction is derived from a high-precision charge-dependent Bonn \textit{NN} potential using the folded-diagram renormalization method. The level structures of the nuclei are calculated, obtaining excellent agreements with experimental observations till the $0f_{7/2}$ band termination. The role played by isospin symmetry breaking on ground-state displacement energies and mirror energy differences is discussed, which may help to explain the long-standi…
The lowest order constrained variational method is applied to calculate the polarized symmetrical nuclear matter properties with the modern $AV_{18}$ potential performing microscopic calculations. Results based on the consideration of magnetic properties show no sign of phase transition to a ferromagnetic phase.
We have performed shell-model calculations starting from the CD-Bonn free nucleon-nucleon NN potential and making use of a new approach for the calculation of the effective interaction. This consists in deriving from the NN potential a low-momentum effective potential V-low-k, defined within a given cut-off momentum Lambda. Being a smooth potential it can be used directly in nuclear structure calculations. To assess the practical value of this approach, we have also performed calculations within the framework of the usual Brueckner G-matrix formalism. Comparison of the calculated results betwe…
We study momentum distributions and short-range correlation probabilities in $A$=2 and $A$=3 systems. First, we show results with phenomenological and meson-theoretic two- and three-nucleon forces to verify consistency with previous similar studies. We then apply most recent high-quality chiral nucleon-nucleon potentials up to fifth order in the chiral expansion together with the leading chiral three-nucleon force. Predictions are examined in the context of a broader discussion of short-range correlation probabilities extracted from analyses of inclusive electron scattering data, addressing th…
For 52 target nuclei with deuteron as projectile, we calculate the reaction cross sections and elastic scattering angular distributions, as well as the $χ^2$ values for 11 kinds of deuteron optical model potentials: our global deuteron optical potentials and 10 folding optical potentials calculated with 2 phenomenological global nucleon optical potentials given by Koning \textit{et al}(KD) and by Varner\textit{et al}(CH89), and 8 microscopic nucleon optical potentials with the generalized Skyrme force parameters(GS1-6) and modified Skyrme force parameters(SKa, SKb). We find that for constructi…
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 fo…
We study the $K^{+}d$ scattering at low energies using the optical potential. Our optical potential consists of the first-order and second-order terms. The total, integrated elastic and elastic differential cross sections at incident kaon momenta below 800 MeV/c are calculated using our optical potential. We found that our results are consistent with the Faddeev calculation as well as the data and especially the second-order optical potential is essential to reproduce them at low energies. We also discuss the multiple scattering effects in this process.
We formulate a microscopic optical potential from chiral two- and three-body forces. The real and imaginary central terms of the optical potential are obtained from the nucleon self-energy in infinite matter, while the real spin-orbit term is extracted from a nuclear energy density functional constructed from the density matrix expansion using the same chiral potential. The density-dependent optical potential is then folded with the nuclear density distributions for selected Calcium isotopes resulting in energy-dependent nucleon-nucleus optical potentials from which we study proton-nucleus ela…
It is shown that the neutron matter interacting through Argonne V18 pair-potential plus modern variants of Urbana or Illinois three-body forces is unstable. For the energy of $N$ neutrons $E(N)$, which interact through these forces, we prove mathematically that $E(N) = -cN^3 + \mathcal{O}(N^{8/3})$, where $c>0$ is a constant. This means that: (i) the energy per particle and neutron density diverge rapidly for large neutron numbers; (ii) bound states of $N$ neutrons exist for $N$ large enough. The neutron matter collapse is possible due to the form of the repulsive core in three-body forces, wh…
We investigate the effect of the deuteron breakup on the optical potential for the elastic scattering of 56 MeV deuterons from $^{51}$V. The breakup probabilities calculated within the post-form distorted wave Born-approximation theory of breakup reactions are fitted to derive the contribution to the optical potential from the breakup channels. The breakup potentials are found to have large real as well as imaginary parts. Thus the dynamical polarization potential due to the breakup process is expected to modify strongly the real part of the optical potential calculated by the double folding m…
A generalized optical potential for elastic scattering induced by light nuclei is calculated within the Feshbach projection operator method. The model explicitly takes into account the contribution of the projectile break-up continuum treated within a microscopic few-cluster model. In this work we formulate the model, deriving an explicit expression for the optical potential, and show ability of the model applying it to deuteron elastic scattering.
A microscopic optical potential based on a chiral model is used as a starting point for studying kaonic atoms levels. We add to this potential a phenomenological part fitted to the experimentally known shifts and widths of kaonic levels. This fitted potential is used to predict deeply bound atomic levels, as well as nuclear levels. Comparison with the predictions of other optical models found in the literature is done. Also the effects on the kaonic atoms levels of certain known non-local contributions to the optical potential are also analyzed.
Optical potential parameters in nuclear model calculations are determined by fitting elastic scattering angular distribution data. Due to the dominance of Coulomb part, elastic scattering is performed at much higher energies. A different approach using ($α$,n) reaction is suggested to determine the alpha optical potentials suitable for astrophysically relevant low energy regions. Reaction on p-nuclei in the mass region A $\approx$ 92-168 have been chosen and a modified McFadden-Satchler $α$-optical potential is obtained from fitting the ($α$,n) reaction data. The effect of level density and $γ…
We construct a microscopic optical potential including breakup effects for elastic scattering of weakly-binding projectiles within the Glauber model, in which a nucleon-nucleus potential is derived by the $g$-matrix folding model. The derived microscopic optical potential is referred to as the eikonal potential. For $d$ scattering, the calculation with the eikonal potential reasonably reproduces the result with an exact calculation estimated by the continuum-discretized coupled-channels method. As the properties of the eikonal potential, the inaccuracy of the eikonal approximation used in the …
The calculations of three-body direct nuclear reactions with nonlocal optical potentials are performed for the first time using the framework of Faddeev-type scattering equations. Important nonlocality effect is found for transfer reactions like d+16O -> p + 17O often improving the description of the experimental data.
A simple recipe for revealing classical-like contributions in optical potential cross sections is proposed. The recipe is based on the fact that the classical-like properties are not expected to depend on the actual value of $\hbar$. This allows us to identify the classical-like characteristics of an optical potential cross section by simply repeating the calculation with different values of $\hbar$, and observing which properties of the cross section are invariant. This method is applied to the cross sections of a few optical potentials used to describe the recent data of light heavy-ion elas…
The $^6$He+$^{12}$C elastic scattering data at beam energies of 3, 38.3 and 41.6 MeV/nucleon are studied utilizing the microscopic optical potentials obtained by a double-folding procedure and also by using those inherent in the high-energy approximation. The calculated optical potentials are based on the neutron and proton density distributions of colliding nuclei established in an appropriate model for $^6$He and obtained from the electron scattering form factors for $^{12}$C. The depths of the real and imaginary parts of the microscopic optical potentials are considered as fitting parameter…
We compute the isospin-asymmetry dependence of microscopic optical model potentials from realistic chiral two- and three-body interactions over a range of resolution scales $Λ\simeq 400-500$\,MeV. We show that at moderate projectile energies, $E_{\rm inv} = 110 - 200$\,MeV, the real isovector part of the optical potential changes sign, a phenomenon referred to as isospin inversion. We also extract the strength and energy dependence of the imaginary isovector optical potential and find no evidence for an analogous phenomenon over the range of energies, $E \leq 200$\,MeV, considered in the prese…
An approach is outline to constructing an optical potential that includes the effects of antisymmetry and target recoil. it is based on the retarded Green's 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.
Optical model potentials for elastic nucleon nucleus scattering are calculated for a number of target nuclides from a full-folding integral of two different realistic target density matrices together with full off-shell nucleon-nucleon t-matrices derived from two different Bonn meson exchange models. Elastic proton and neutron scattering observables calculated from these full-folding optical potentials are compared to those obtained from `optimum factorized' approximations in the energy regime between 65 and 400 MeV projectile energy. The optimum factorized form is found to provide a good appr…
We study the energy per particle of symmetric nuclear matter and pure neutron matter using realistic nucleon--nucleon potentials having non central tensor and spin--orbit components, up to three times the empirical nuclear matter saturation density, $ρ_0=0.16$ fm$^{-3}$. The calculations are carried out within the frameworks of the Brueckner--Bethe--Goldstone (BBG) and Correlated Basis Functions (CBF) formalisms, in order to ascertain the accuracy of the methods. The two hole--line approximation, with the continuous choice for the single particle auxiliary potential, is adopted for the BBG app…
Experimental evidence exists that the $Ξ$-nucleus interaction is attractive. We search for $NNΞ$ and $NNNΞ$ bound systems on the basis of the AV8 $NN$ potential combined with either a phenomenological Nijmegen $ΞN$ potential or a first principles HAL QCD $ΞN$ potential. The binding energies of the three-body and four-body systems (below the $d+Ξ$ and $^3{\rm H}$/$^3{\rm He}+Ξ$ thresholds, respectively) are calculated by a high precision variational approach, the Gaussian Expansion Method. Although the two $ΞN$ potentials have significantly different isospin ($T$) and spin ($S$) dependence, the…
The $^1S_0$ pairing in neutron matter has been investigated in presence of realistic two-- and three--nucleon interactions. We have adopted the Argonne $v_{8^\prime}$ NN and the Urbana IX 3N potentials. Quantum Monte Carlo theory, specifically the Auxiliary Field Diffusion Monte Carlo method, and Correlated Basis Function theory are employed in order to get quantitative and reliable estimates of the gap. They both fully take into account the medium modifications due to the interaction induced correlations. The two methods are in good agreement up to the maximum gap density and both point to a …
The validity of using a pion optical potential to incorporate the effects of final state interactions on HBT interferometry is investigated. We find that if the optical potential is real, the standard formalism is modified as previously described in the literature. However, if the optical potential is complex, a new term involving pion emission from eliminated states must be included. The size of such effects in previous work by Cramer and Miller is assessed.
