Microscopic Optical Potential Research Articles

Study of 11Li+p elastic scattering using BHF formalism with three body force

In the present work we have analyzed the elastic scattering data of 11Li + p at 62, 68.4 and 75 MeV/nucleon, using the microscopic optical potential calculated within the framework of Brueckner–Hartree–Fock formalism (BHF). The calculation uses Argonne v18 and Urbana v14 inter-nucleon potentials and the Urbana IX (UVIX) model of three body force. The required nucleon-density distributions for 11Li are obtained using the semi-phenomenological model for nuclear density distributions. The optical potential has been obtained by folding the g-matrices as calculated in BHF (with and without three body forces) over the nucleon density distributions. We have used the exact method for calculating both the direct and the exchange parts of the spin–orbit potential. Our results reveal that the spin–orbit potential significantly contributes to 11Li+p elastic scattering at all three incident energies. Further, the calculated spin–orbit potential in BHF is much smaller and more diffused as compared with the phenomenological spin–orbit potential. The analysis reveals that the calculated microscopic optical potentials, with and without three body force using BHF approach with phenomenological form of density distribution, provides satisfactory agreement with the elastic scattering data for 11Li+p.

The proton microscopic optical potential based on Skyrme interaction

The proton microscopic optical potential (MOP) based on Skyrme interaction has been achieved by the Green function method in the nuclear matter, and given by the local density approximation (LDA) for finite nuclei. The reaction cross-sections, elastic scattering angular distributions, analyzing powers, and spin-rotation functions are predicted by the obtained proton MOP with Skyrme interaction SkC in the mass range of target nuclei 24[Formula: see text][Formula: see text][Formula: see text]A[Formula: see text][Formula: see text][Formula: see text]209 with incident proton energy below 100[Formula: see text]MeV. These observables are further predicted for some light nuclei and actinide nuclei below 100[Formula: see text]MeV. The prediction is compared with existing experimental data. It is revealed that the obtained proton MOP based on Skyrme interaction SkC can satisfactorily describe the proton–nucleus elastic scattering.

Chiral Nucleon-Nucleus Potentials at N3LO

Elastic scattering is probably one of the most relevant tools to study nuclear interactions. In this contribution we study the domain of applicability of microscopic two-body chiral potentials in the construction of an optical potential. A microscopic complex optical potential is derived and tested performing calculations on 16O at different energies. Good agreement with empirical data is obtained if a Lippmann-Schwinger cutoff at relatively high energies (above 500 MeV) is employed.

Covariance analysis for total neutron cross sections based on a microscopic optical model potential

The deterministic simple least square (LS) approach is employed in the covariance analysis of the total neutron cross section (n,tot) calculated by a microscopic optical potential, CTOM, which is based on a fundamental theory − Dirac Brueckner Hartree Fock. The sensitivity to the CTOM parameters is firstly systematically calculated for 77 stable nuclei in the range 12C–208Pb within neutron energy 5–200 MeV. Then, an equivalent covariance of experimental data (EVexp) is constructed to describe the experimental data uncertainties and the systematic difference between experimental data and CTOM calculation. The variance and covariance of EVexp matrix are both evaluated via the Gaussian analysis to the ratios of measured (n,tot) cross sections and the CTOM calculations. In addition, a technique named “selection of effective points (SEP)” is suggested additionally to reduce the influence of the Peelle's Pertinent Puzzle problem in this work.

Analysis of 11Be + p elastic scattering using a BHF approach

The elastic scattering of the halo nucleus 11Be on the proton at various incident energies has been analysed using the microscopic optical potential (OP) calculated within the first order non-relativistic Brueckner–Hartree–Fock (BHF) approach. Argonne v-18 inter-nucleon potential is employed to calculate the microscopic OP. The nuclear density distribution has been obtained using a semi-phenomenological model. The density used shows extended neutron distribution indicating a possible halo structure. We have also compared our results with an empirical analysis using CH89 global OP. The analysis reveals that the BHF approach provides good agreement with the experimental data for all incident energies considered in this paper.

Microscopic optical potentials within the weak density dependent nucleon-nucleon effective interactions

<p class="tomtat1">The microscopic optical potentials have been investigated in the framework of the nuclear structure approach based on the energy-density functional approaches. The effective phenomenological nucleon-nucleon interaction SLy5 is consistently used to obtain the Hartree-Fock single particle states, the collective motion at small amplitudes of the target, and the coupling between the particle and phonons. The role of the weak density dependent interaction is showed. </p>

Microscopic optical potential for He6

The microscopic optical potential for $\phantom{\rule{0.16em}{0ex}}^{6}\mathrm{He}$ with no free parameters is obtained by folding the microscopic optical potentials of its constituent nucleons with the internal wave function of $\phantom{\rule{0.28em}{0ex}}^{6}\mathrm{He}$. We use the isospin-dependent nucleon microscopic optical potential, which is derived by using the Green's function method through the nuclear matter approximation and the local density approximation based on the Skyrme nucleon-nucleon effective interaction. The internal wave function of $^{6}\mathrm{He}$ is described in a harmonic-oscillator form. The $^{6}\mathrm{He}$ microscopic optical potential is used to calculate the reaction cross sections and elastic-scattering angular distributions for target nuclei in the mass range $12\ensuremath{\le}\mathrm{A}\ensuremath{\le}209$ at incident energies up to 350 MeV. The results are compared with the experimental data and those calculated by a global phenomenological optical potential; in most cases, the microscopic optical potential reproduces the experimental data less well than the global potential. The sensitivity of scattering to the potentials as a function of radius has been investigated by using the notch perturbation method. The investigation shows that the scattering is sensitive to the optical potential in the nuclear surface region. It is concluded from the discussion that the microscopic optical potential can be improved by increasing the surface absorption contribution.

Optical potential from first principles

We develop a method to construct a microscopic optical potential from chiral interactions for nucleon-nucleus scattering. The optical potential is constructed by combining the Green's function approach with the coupled-cluster method. To deal with the poles of the Green's function along the real energy axis we employ a Berggren basis in the complex energy plane combined with the Lanczos method. Using this approach, we perform a proof-of-principle calculation of the optical potential for the elastic neutron scattering on $^{16}{\rm O}$. For the computation of the ground-state of $^{16}{\rm O}$, 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. We verify the convergence of the optical potential and scattering phase shifts with respect to the model-space size and the number of discretized complex continuum states. We also investigate the absorptive component of the optical potential (which reflects the opening of inelastic channels) by computing its imaginary volume integral and find an almost negligible absorptive component at low-energies. To shed light on this result, we computed excited states of $^{16}{\rm O}$ using equation-of-motion coupled-cluster method with singles-and-doubles excitations and we found no low-lying excited states below 10~MeV. Furthermore, most excited states have a dominant two-particle-two-hole component, making higher-order particle-hole excitations necessary to achieve a precise description of these core-excited states. We conclude that the reduced absorption at low-energies can be attributed to the lack of correlations coming from the low-order cluster truncation in the employed coupled-cluster method.

Global phenomenological and microscopic optical model potentials for alpha

The global phenomenological and microscopic optical model potentials for alpha with the incident energy up to 400 MeV are obtained. The global phenomenological optical model potential is extracted by simultaneously fitting the experimental data of total reaction cross sections and elastic scattering angular distributions in the mass range of target nuclei 20 ≤ A ≤ 209. The microscopic optical model potential is obtained by the Green function method through nuclear matter approximation and local density approximation based on the effective Skyrme nucleon-nucleon interaction. Both optical model potentials are used to calculate the reaction cross sections and elastic scattering angular distributions for the target nuclei in the mass range 12 ≤ A ≤ 209 at incident alpha energies up to 400 MeV. The calculated results are compared with the experimental data, and the calculated results by phenomenological and microscopic optical model potentials are also compared with each other.

Microscopic optical model potential based on a Dirac Brueckner Hartree Fock approach and the relevant uncertainty analysis

A relativistic microscopic optical model potential, named CTOM , for nucleon-nucleus scattering is investigated in the framework of Dirac-Brueckner-Hartree-Fock approach. The microscopic feature of CTOM is guaranteed through rigorously adopting the isospin dependent DBHF calculation within the subtracted T matrix scheme. In order to verify its prediction power, a global study n , p + A scattering are carried out. The predicted scattering observables coincide with experimental data within a good accuracy over a broad range of targets and a large region of energies only with two free items, namely the free-range factor t in the applied improved local density approximation and minor adjustments of the scalar and vector potentials in the low-density region. In addition, to estimate the uncertainty of the theoretical results, the deterministic simple least square approach is preliminarily employed to derive the covariance of predicted angular distributions, which is also briefly contained in this paper.

Comparative analysis of the pion-nucleus scattering within the microscopic Folding and the local Kisslinger type potentials

Elastic scattering cross sections are calculated and compared to the data of π ± + 28 Si and 40 Ca at energies 130, 180, and 230 MeV by using the both microscopic optical potentials (OP), the high-energy folding and the local Kisslinger type potentials. In the folding OP, we use the known nuclear density distributions while parameters of the elementary π N-scattering amplitude are fitted to the data with the aim to estimate the inmedium effect on pions scattered on bound nucleons. As to the local modified Kisslinger OP its parameters are known from the earlier studies. The cross sections for both OPs are calculated by solving the Klein-Gordon wave equation, and thus the relativistic and distortion effects on the process are accounted for exactly. A fairly well agreement with experimental data was obtained and the decisive role of a surface region of potentials was established where both OPs occur in close coincidence.

The nucleon microscopic optical potential based on the Skyrme interaction

The nucleon microscopic optical potential based on the conventional and extended Skyrme interactions are achieved by the single-particle Green function method through nuclear matter approximation and local density approximation. The nucleon-nucleon scattering observables are calculated by the obtained microscopic optical potential and the results are compared with the corresponding experimental data. Good agreement is generally obtained between them.

Nuclear data evaluation of long-lived fission products: Microscopic vs. phenomenological optical potentials

Neutron-nucleus cross sections calculated by macroscopic potentials are compared with a microscopic one to study the performance for long-lived fission products. The macroscopic potentials show a good agreement with the microscopic one at higher energies, where neutron experimental data are scarce. Besides it, analyses of differential elastic cross sections at low energies also suggest that the macroscopic potentials are still effective and applicable enough for the long-lived fission products.

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.

Microscopic optical potential for exotic isotopes from chiral effective field theory

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 $\Lambda \simeq 400-500$\,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 present work. Finally, we compute for the first time the leading corrections to the Lane parametrization for the isospin-asymmetry dependence of the optical potential and observe an enhanced importance at low scattering energies.

Theoretical optical potential derived from nucleon-nucleon chiral potentials

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.

The neutron microscopic optical potential based on skyrme interaction

The neutron microscopic optical potential (MOP) based on Skyrme interaction has been achieved by the Green function method in the nuclear matter, and given by the local density approximation (LDA) for finite nuclei. The total cross-sections, nonelastic cross-sections, elastic scattering angular distributions and analyzing powers are predicted for some light nuclei and actinide nuclei below 100[Formula: see text]MeV by the obtained neutron MOP with the Skyrme interaction SkC. These data are also predicted for targets in the mass range of [Formula: see text] which are too deformed and have rich nuclear structure properties. All of the theoretical results give reasonable agreements with the corresponding experimental data.

Effects of NN potentials on p Nuclides in the A ∼100–120 region

Microscopic optical potentials for low-energy proton reactions have been obtained by folding density dependent M3Y (DDM3Y) interaction derived from nuclear matter calculation with densities from mean field approach to study astrophysically important proton rich nuclei in mass 100–120 region. We compare [Formula: see text] factors for low-energy [Formula: see text] reactions with available experimental data and further calculate astrophysical reaction rates for [Formula: see text] and [Formula: see text] reactions. Again, we choose some nonlinear R3Y (NR3Y) interactions from relativistic mean field (RMF) calculation and folded them with corresponding RMF densities to reproduce experimental [Formula: see text]-factor values in this mass region. Finally, the effect of nonlinearity on our result is discussed.

Analysis of proton scattering of stable and exotic light nuclei using an energy-dependent microscopic optical potential

The proton elastic scattering off the 9,10,11,12 Be isotopes at a wide energy range from 3 to 200 MeV/nucleon is analyzed using the optical model with the partial-wave expansion method. The microscopic optical potential (OP) is taken within the single-folding model. The density- and isospin-dependent M3YParis nucleon-nucleon (NN ) interaction is used for the real part and the NN -scattering amplitude of the highenergy approximation for the imaginary one. The cross-section data are reproduced well at energies up to 100 MeV/nucleon by use of the partial-wave expansion. For higher energies, the eikonal approximation is successfully used. The volume integrals of the OP parts have systematic energy dependencies and they can be parameterized as functions of energy. From these parametrization, an energy-dependent OP can be obtained.

Study of11Li and10,11Be nuclei through elastic scattering and breakup reactions

The hybrid model of the microscopic optical potential (OP) is applied to calculate the 11 Li+p , 10,11 Be+p , and 10,11 Be+12 C elastic scattering cross sections at energies E Li+p elastic scattering, the microscopic large-scale shell model (LSSM) density of 11 Li is used, while the density distributions of 10,11 Be nuclei obtained within the quantum Monte Carlo (QMC) model and the generator coordinate method (GCM) are utilized to calculate the microscopic OPs and cross sections of elastic scattering of these nuclei on protons and 12 C. The depths of the real and imaginary parts of OP are fitted to the elastic scattering data, being simultaneously adjusted to reproduce the true energy dependence of the corresponding volume integrals. Also, the cluster models, in which 11 Li consists of 2n -halo and the 9 Li core having its own LSSM form of density and 11 Be consists of a n -halo and the 10 Be core, are adopted. Within the latter, we give predictions for the longitudinal momentum distributions of 9 Li fragments produced in the breakup of 11 Li at 62 MeV/nucleon on a proton target. It is shown that our results for the diffraction and stripping reaction cross sections in 11 Be scattering on 9 Be, 93 Nb, 181 Ta, and 238 U targets at 63 MeV/nucleon are in a good agreement with the available experimental data.