Nucleon-nucleus Optical Potential Research Articles

Nonlocal optical potential with core excitation in [formula omitted] and [formula omitted] reactions

We propose a new nonlocal form of the nucleon-nucleus optical potential and demonstrate its reliability. We extend the nonlocal potential to include the excitation of the nuclear core and develop energy-independent proton-Be10 potential reasonably reproducing the experimental data at low energies. We apply the new potential to the study of deuteron stripping and pickup reactions Be10(d,p)11Be and Be11(p,d)10Be using rigorous three-body Faddeev-type equations for transition operators that are solved in the momentum-space partial-wave framework. The achieved description of the experimental data is considerably more successful as compared to previous studies with local potentials. The values of spectroscopic factors consistent with the data are determined, exhibiting only weak energy dependence. The results possibly indicate an increased predicting power of the proposed calculational scheme.

Study of6,8He+p elastic scattering using the BHF formalism with three-body forces

In the present work, we have analyzed the elastic scattering data of6He+p at 25.6, 38.6, 40.9, and 71 MeV/A and8He+p at 15.6, 25.6, 32.5, 66, and 72 MeV/A, using the microscopic local optical potential calculated within the framework of the Brueckner–Hartree–Fock (BHF) formalism. The calculation requires mainly two inputs: (1) the nucleon–nucleon (NN) interaction and (2) the nucleon distributions in target nuclei. In the present work, realistic internucleon (NN) potential from Argonne v18 (AV18) and the Urbana IX (UVIX) model of three-body forces with several nucleon density distributions are used for generating the nucleon–nucleus optical potential. We have used the exact method for calculating both the direct and the exchange parts of the spin–orbit potential. We confirm the earlier results that the spin–orbit potential for these neutron-rich nuclei is diffused and extended. Our results show that the different density distributions reproduce rather well the experimental differential cross sections for both isotopes, while the phenomenological density with a two-neutron halo gives satisfactory results for6He-p analyzing power data. None of the densities used for8He can reproduce the experimentally analyzed power data. Our analysis reveals that the calculated microscopic optical potentials, with and without three-body forces using the BHF approach, provide satisfactory agreement with the elastic scattering data for6,8He+p.

Global Microscopic Description of Nucleon-Nucleus Scattering with Quantified Uncertainties.

We develop for the first time a microscopic global nucleon-nucleus optical potential with quantified uncertainties suitable for analyzing nuclear reaction experiments at next-generation rare-isotope beam facilities. Within the improved local density approximation and without any adjustable parameters, we begin by computing proton-nucleus and neutron-nucleus optical potentials from a set of five nuclear forces from chiral effective field theory for 1800 target nuclei in the mass range 12≤A≤242 for energies between 0 MeV<E≲150 MeV. We then parameterize a global optical potential for each chiral force that depends smoothly on the projectile energy as well as the target nucleus mass number and isospin asymmetry. Uncertainty bands for elastic scattering observables are generated from a full covariance analysis of the parameters entering in the description of our global optical potential and benchmarked against existing experimental data for stable target nuclei. Since our approach is purely microscopic, we anticipate a similar quality of the model for nucleon scattering on unstable isotopes.

Excitation functions for 209Bi reactions induced by threshold to 50 MeV energy alpha particles

Excitation functions for 209Bi(α,2n)211At, 209Bi(α,3n)210At and 209Bi(α,4n)209At reactions were calculated using TALYS-1.95 nuclear code from threshold to 50 MeV by invoking suitable options for level densities, nucleon-nucleus optical model potentials and alpha optical model potentials. Statistical factors were used to verify the quality of matching between theoretical model calculations and the experimental data from the EXFOR database. The TTY of 211At calculated using the excitation function of 209Bi(a,2n)211At reaction is compared with existing experimental studies from literature The results of the present study are important for the validation of nuclear model approaches with increased predictive power for 209Bi(α,xn) reactions for the production of 211At.

Coupled-Cluster Computations of Optical Potential for Medium-Mass Nuclei

Recent progress in the numerical resolution of the nuclear many-body problem and in the development of nuclear Hamiltonians rooted in Quantum Chromodynamics, have opened the door to first-principles computation of nuclear reactions. In this article, we discuss the current status of ab initio calculations of nucleon-nucleus optical potential for medium-mass systems, with a focus on results obtained with the coupled-cluster method.

Energy Dependence and Surface Contribution of the Nucleon-Nucleus Optical Potential

The M3Y folding optical potential (OP) is used to analyze $^{9}$Be (p,p) $^{9}$Be elastic scattering at energies from few to 1000 MeV/nucleon. The M3Y folding-model is used for the real part whereas the volume and surface imaginary parts of OP are taken within the high-energy approximation model that based on the Glauber theory. In addition, the Brieva–Rook approximation is used for the spin-orbit OP. The angular distributions for elastic-scattering cross sections and analyzing powers, reaction, and total cross sections, are calculated using the optical model analysis with the partial-wave expansion method. The results show that these experimental data are reproduced well at a wide range of energy. In addition, clear and interesting energy dependencies are found for the different parts of the OP. A new behavior of the surface imaginary is found at scattering at high energies where the results show that the surface contribution to the imaginary part is very important at high energies as well as at low energies. The volume integrals show systematic energy dependencies. A new energy dependence formula is assumed for M3Y-Paris NN interaction to avoid the negative values of the OP at high energies.

Proton-capture Reaction Cross Sections on the Sr Isotopes Relevant to the p-process Nucleosynthesis

Proton-capture reaction cross sections on the 86,87,88Sr isotopes have been determined at energies from 1.4 to 5 MeV by measuring γ-angular distributions at the 4 MV single-ended Dynamitron accelerator of the University of Stuttgart as well as at the 5 MV VdG Tandem accelerator of NCSR "Demokritos", Athens. In the former case an array of 4 HPGe detectors with relative efficiency εr≈100%, each shielded with BGO crystals, were used. In the case of the measurements carried out at "Demokritos" we used only one HPGe detector (εr≈80%) with no BGO shield. Cross sections ranging from 0.5 μb to 5 mb as well as the relevant S factors were obtained. The data were compared with statistical model calculations using the code MOST. In the calculations, various combinations of microscopic and phe- nomenological models of the nucleon-Nucleus Optical Model Potentials (OMP) and Nuclear Level Densities (NLD) were used and a good agreement between the data and theoretical predictions was found.

Non-Linear Derivative Interactions in Relativistic Hadrodynamics

The Lagrangian of Relativistic Hadrodynamics (RHD) is extended by introducing non-linear derivative (NLD) operators into the interactions between the nucleon with the meson elds. As the novel feature of the NLD model, the nucleon selfenergy depends on both, on energy and density. Our approach contains a single cut-o parameter, which determines the density dependence of the nuclear equation of state (EoS) and the energy dependence of the nucleon-nucleus optical potential. The NLD formalism is compatible with results from microscopic nuclear matter calculations as well as with Dirac phenomenology.

Non-Linear Derivative Interactions in Relativistic Hadrodynamics

The Lagrangian of Relativistic Hadrodynamics (RHD) is extended by introducing non- linear derivative (NLD) operators into the interactions between the nucleon with the meson fields. As the novel feature of the NLD model, the nucleon selfenergy depends on both, on energy and density. Our approach contains a single cut-off parameter, which determines the density dependence of the nuclear equation of state (EoS) and the energy dependence of the nucleon-nucleus optical potential. The NLD formalism is compatible with results from microscopic nuclear matter calculations as well as with Dirac phenomenology.

Weak sensitivity of three-body ( d,p ) reactions to np force models

Adiabatic distorted-wave approximation (ADWA) study of three-body $(d,p)$ transfer reactions [G.W. Bailey, N.K. Timofeyuk, and J.A. Tostevin, Phys. Rev. Lett. 117, 162502 (2016)] reported strong sensitivity of cross sections to the neutron-proton $(np)$ interaction model when the nucleon-nucleus optical potential is nonlocal. The verification of this unusual finding using more reliable methods is aimed for in the present work. A rigorous Faddeev-type three-body scattering theory is applied to the study of $(d,p)$ transfer reactions. The equations for transition operators are solved in the momentum-space partial-wave framework. Differential cross sections for $^{26}$Al$(d,p)^{27}$Al reactions are calculated using nonlocal nuclear optical potentials and a number of realistic $np$ potentials. Only a weak dependence on the $np$ force model is observed, typically one order of magnitude lower than in the previous ADWA study. The shape of the angular distribution of the experimental data is well reproduced. Cross sections of $(d,p)$ transfer reactions calculated using a rigorous three-body method show little sensitivity to the $np$ interaction model. This indicates a failure of the ADWA in the context of nonlocal potentials. Some evident shortcomings of the ADWA are pointed out.

Separable representation of multichannel nucleon-nucleus optical potentials

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.

Microscopic optical potential for He4 scattering based on the effective Skyrme interaction

Microscopic optical potential of $^{4}\mathrm{He}$ interaction with nuclei is constructed by means of the single-folding model using the nucleon-nucleus optical potentials, which earlier were successfully applied to describing the neutron and proton scattering and are obtained from approximate calculations of the mass operator of the one-particle Green's function with the effective Skyrme nucleon-nucleon forces. The $^{4}\mathrm{He}$ scattering processes are described in a self-consistent approach based on the standard and extended Skyrme forces, which simultaneously provide a satisfactory description of nuclear structure and nucleon-nucleus scattering. The performed calculations reasonably describe experimental data on differential cross sections of the elastic and inelastic $\ensuremath{\alpha}$-particle scattering on different target nuclei in the mass-number range from $^{28}\mathrm{Si}$ to $^{208}\mathrm{Pb}$ at different projectile energies below or about 100 MeV, as well as the energy dependences of $\ensuremath{\alpha}$-particle reaction cross sections on nuclei in a wide energy range.

Explicit inclusion of nonlocality in(d,p)transfer reactions

Background: Traditionally, nucleon-nucleus optical potentials are made local for convenience. In recent work we studied the effects of including nonlocal interactions explicitly in the final state for (d,p) reactions, within the distorted wave Born approximation. Purpose: Our goal in this work is to develop an improved formalism for nonlocal interactions that includes deuteron breakup and to use it to study the effects of including nonlocal interactions in transfer (d,p) reactions, in both the deuteron and the proton channel. Method: We extend the finite-range adiabatic distorted wave approximation to include nonlocal nucleon optical potentials. We apply our method to (d,p) reactions on 16O, 40Ca, 48Ca, 126Sn, 132Sn, and 208Pb at 10, 20 and 50 MeV. Results: We find that nonlocality in the deuteron scattering state reduces the amplitude of the wave function in the nuclear interior, and shifts the wave function outward. In many cases, this has the effect of increasing the transfer cross section at the first peak of the angular distributions. This increase was most significant for heavy targets and for reactions at high energies. Conclusions: Our systematic study shows that, if only local optical potentials are used in the analysis of experimental (d,p) transfer cross sections, the extracted spectroscopic factors may be incorrect by up to 40% due to the local approximation.

Description of elastic polarized-deuteron scattering in the optical model with Skyrme forces

Microscopic deuteron-nucleus optical potential was constructed on the basis of the nucleon-nucleus optical potentials recently obtained by the authors from approximate calculations of the mass operator of the single-particle Green function using the Skyrme forces, which in general involve additional density- and momentum-dependent terms. Both the nucleon- and deuteron-nucleus elastic scattering processes are described in a self-consistent approach using the effective nucleon-nucleon forces, which simultaneously provide a satisfactory description of nuclear structure. The calculations performed using the Watanabe-type approximation have made it possible to obtain reasonable results for describing differential cross sections and polarization observables for the elastic deuteron scattering in a wide range of target-nucleus mass numbers at different incident deuteron energies, when using several Skyrme-force variants both from literature and proposed by the authors. Contributions to elastic deuteron-nucleus scattering cross sections coming from the effects of deuteron virtual breakup have been estimated in the continuum-discretized coupled channels approach.

Low-energy nucleon-nucleus scattering within the energy density functional approach

The description of nucleons scattering off doubly closed-shell nuclei $^{16}\mathrm{O}$ and $^{208}\mathrm{Pb}$ at energies below 50 MeV is carried out in a fully self-consistent framework of the particle-vibration coupling approach. The applications are performed with commonly used Skyrme-type effective interactions. Nucleon-nucleus optical potentials are thus calculated without ad hoc adjusted parameters. These potentials are then solved with standard optical model codes (dwba98 in the present case). Empirical nucleon-nucleus elastic angular distributions are thus successfully reproduced.

Coulomb problem in momentum space without screening

Background: The repulsive Coulomb force poses severe challenges when solving the three-body problem for ($d,p$) reactions on intermediate mass and heavy nuclei. Recently, a new approach based on the Coulomb-distorted basis in momentum space was proposed.Purpose: In this work, we demonstrate the feasibility of using the Coulomb-distorted basis in momentum space for calculating matrix elements expected in a wide range of nuclear reactions.Method: We discuss the analytic forms of the Coulomb wave function in momentum space. We analyze the singularities in the Coulomb-distorted form factors and the required regularization techniques. Employing a separable interaction derived from a realistic nucleon-nucleus optical potential, we compute and study the Coulomb-distorted form factors for a wide range of cases, including charge, angular momentum, and energy dependence. We also investigate in detail the precision of our calculations.Results: The Coulomb-distorted form factors differ significantly from the nuclear form factors except for the very highest momenta. Typically, the structure of the form factor is shifted away from zero momentum due to the Coulomb interaction. Unlike the Yamaguchi forms typically used in three-body methods, our realistic form factors have a short high-momentum tail, which allows for a safe and efficient truncation of the momentum grid.Conclusions: Our results show that the Coulomb-distorted basis can be effectively implemented.

Effect of spin-spin interactions on nucleon-nucleus scattering

In this thesis we investigate the interactions between nucleons, which have spin-1/2, and nuclei, which may also have intrinsic spin. The dependence of the nucleon-nucleon interaction on the relative orientations of the spin of the two particles is well known and suggests a similar dependence may be present in the interactions of nucleons with nuclei. The effect of the spin of the nucleus on the nucleon-nucleus potential has been the subject of much theoretical and experimental interest. Previous work has found that in many cases spin-spin interactions cannot be ignored, especially for high spin exotic nuclei such as those likely to be produced in the next generation of radioactive beam facilities. In this work a model has been developed for determining spin-spin terms in the nucleon-nucleus optical potential. These terms are constructed by folding a realistic effective nucleon-nucleon interaction, which includes both direct and exchange parts, over the nuclear wavefunction. The target is assumed, for our purposes, to have a simple two valence-particle structure, with the total spins of the two valence nucleons coupling to give the total spin of the nucleus. The resulting spin-spin tensors are evaluated within Distorted Wave Born Approximation to obtain the spin-spin amplitudes. This general model has been used for the specific calculation of the elastic scattering of protons by 10B, for which relevant experimental data exist. New spin-spin interactions that have higher order couplings of the target and projectile spins are included. In addition, where previous work on spin-spin interactions has only included exchange corrections for the central parts of the nucleon-nucleon interaction, we have included the non-local exchange contribution from the tensor parts of the nucleon-nucleon interaction. The effect of these spin-spin interactions on observables sensitive to the spin polarisation of the incident beam, specifically the polarisation transfer coefficient -DNN, has been investigated. We have found that the spin-spin interactions derived from this model have a significant effect on DNN when used to examine the elastic scattering of protons from 10B. The calculation of DNN has also been shown to be particularly sensitive to the parameters of the model used to describe the nuclear structure.

A systematic analysis of microscopic nucleon–nucleus optical potential for p–Ni scattering

A microscopic proton–nucleus optical potential is calculated for all even isotopes 52–112Ni within the Brueckner–Hartee–Fock framework. The reaction matrices calculated using three (Argonne v18, Reid93 and NijmII) realistic inter-nucleon potentials with and without three-body forces (Urbana IX (UVIX) and the density dependent three-nucleon interaction (TNI) model of Lagaris, Friedman and Pandharipande), have been folded over the neutron and proton density distributions of the relevant targets obtained by using the relativistic mean field approach. It is observed that the inclusion of both models of the three-body forces somewhat reduces the strength of the central part of the optical potential in the nuclear interior and affects only marginally the spin–orbit part of the potential. Further, the calculated volume integral of the real part of the spin–orbit optical potential as well as its peak value are found to decrease systematically with the addition of neutrons. The calculated optical potentials reproduce remarkably well the existing experimental differential cross section (dσ/dθ) and the polarization (Ay) data for p–58–64Ni scattering at 39.6 and 65 MeV projectile energies. The inclusion of three-body forces (UVIX and TNI) does not lead to any change in the calculated observables (dσ/dθ and Ay) indicating that the p–Ni scattering data analyzed here are not sensitive to the nuclear interior. Identical observations are also found in the Zr, Sn and Pb isotopic chains. Therefore, these observed features of the microscopic optical potential seem general and may hold globally.

A theoretical study of halo structure using elastic proton-nucleus scattering

Elastic proton scattering from Be, C, and O isotopes has been investigated in the relativistic impulse approximation (RIA). In the calculations, the nucleon-nucleus optical potentials are obtained using ground state nuclear matter densities, which are computed using the relativistic mean field model with the FSU parameter set. The scattering observables, including differential cross section, analyzing power, and spin-rotation function, are analyzed. It is found that the scattering observables for O isotopic chains display a clear mass dependence, for instance, the minimum analyzing power shifts to a low scattering angle with increasing mass number. While for the Be isotopic chain, the emergence of a neutron halo in 14Be breaks this trend, i.e., the minimum analyzing powers for 12Be and 14Be are almost the same as each other.

Equation of state and the nucleon optical potential with three-body forces

We report microscopic calculations of the equation of state of symmetric nuclear matter and the nucleon-nucleus optical potential in the Brueckner-Hartree-Fock approach. The calculations use several internucleon ($NN$) potentials, such as the Hamada-Johnston, Urbana v14, Argonne v14, Argonne v18, Reid93, and Nijm II along with and without two types of three-body forces (TBFs): the Urbana IX model and the phenomenological density-dependent three-nucleon interaction model of Lagris and Pandharipande [Nucl. Phys. A 359, 349 (1981)] and Friedman and Pandharipande [Nucl. Phys. A 361, 502 (1981)]. The inclusion of TBFs helps to reproduce the saturation properties for symmetric nuclear matter rather well as expected. The proton-nucleus optical potential has been calculated by folding the calculated reaction matrices (with and without three-body forces) over the nucleon density distributions obtained from the relativistic mean-field theory. The results show that the inclusion of TBFs reduces the strength of the central part of the optical potential in the nuclear interior and affects the calculated spin-orbit potential only marginally. As a test of the calculated potential, we have analyzed proton differential elastic scattering, analyzing power, and spin-rotation data from ${}^{40}$Ca and ${}^{208}$Pb at 65 and 200 MeV. It is observed that the inclusion of TBFs improves the agreement with the experiment especially for the polarization data.