Folding Optical Potential Research Articles

Quantitative analysis of (3He,t) charge exchange reactions at 140 MeV/u beam energy

Composite particle, [Formula: see text], charge exchange reactions on targets [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] at 140 MeV/u beam energy have been analyzed by employing distorted wave impulse approximation (DWIA). Specifically, unit cross-section and angular distribution have been calculated using normal optical model potential (NOMP) and single folding optical model potential (SFOMP) for both relativistic and non-relativistic cases. The sensitivity of present results on exchange terms has also been examined and it is pertinent to report here that the inclusion of these effects reduces the cross-section in magnitude up to 60%, which in turn brings it closer to the data except for [Formula: see text].

Analysis of the pion-nucleus scattering within the folding and the Kisslinger type potentials

Elastic cross sections are calculated and compared with the data on π± scattering on 28Si, 40Ca, 58Ni, 208Pb nuclei in the energy range from 130 to 290 MeV. To this end, both the folding optical potential (OP) and the local modified Kisslinger-type OP were calculated, and then the πA cross sections were obtained by solving the Klein-Gordon equation to account for the relativization and distortion wave effects. In the folding OPs, the parameters of the elementary πN amplitude were fitted when describing the πA scattering data, and thus the essential in-medium effect on the parameters of the πN amplitude was established since the pion is scattered not on a free but on a bound nuclear nucleon. Fairly good agreement with experimental data was obtained for both models of optical potentials and their forms turn out to be in coincidence in the region of their surfaces.

Pion-nucleus elastic scattering studies within the microscopic folding potential

The pion-nucleus elastic scattering cross sections are calculated and compared to the data of pion scattering on 28Si, 58Ni, 208Pb at energies 162 and 291 MeV by using two kinds of the microscopic optical potentials (OPs). The first one is the folding OP, where the known nuclear density distributions are used while parameters of the elementary pion-nucleon amplitude of scattering are fitted to the data with the aim to estimate the in-medium effect, when pions are scattered not on the free but on the nuclear bounded nucleons. The analysis given when calculations are made using the local Kisslinger type OP, whose parameters are fitted to the data. The cross sections for both OPs are obtained by solving the Klein-Gordon wave equation. The role of a surface region of potentials is discusses.

Analysis of 6Li+16O elastic scattering using different potentials

Available experimental angular distributions for 6Li elastically scattered from 16O nucleus in the energy range 13.0–50.0 MeV are reanalyzed within the framework of optical potential, double folding optical potential as well as cluster folding potential. Special interest was paid to the cluster folding based on the well-known cluster structure of 6Li. Elastic scattering data for 6Li+16O system plotted as a function of momentum transfer showed that the real Coulomb nuclear interference region independent of the bombarding energy. This structural behavior for the data could be used to define the interaction potential with some certainty and to extract reliable values for the renormalization factors.

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.

Astrophysical S-Factor for 7Li(P,γ)8Be by Different Sets of Optical Parameters

The available experimental data for 7Li(p,p)7Li elastic scattering have been investigated using both optical potential as well as single folding optical potential in which the real part of potential is derived on the basis of single folding model. Approximated optical potential parameters have been obtained for real part using DFPOT code. The real part was normalized and imaginary part was optimized at all range of energies. The calculated normalization factor NR was 0.8. The agreement between experimental data and theoretical calculations has been achieved at the different concerned energies using ECISS88 program. The calculation of astrophysical S-factor for 7Li(p,γ)8Be radiative capture reaction has been performed using potential model. Different sets of optical potential parameters have been used during analysis. It has been found that different potential parameters play a crucial role and has a significant effect on the calculated S-factor. It has been shown that optical parameters have the greatest effect on astrophysical S-factor through our calculation.

Elastic scattering of one-proton halo nucleus 17F on different mass targets using semi microscopic potentials

The elastic scattering of 17F have been studied for different mass targets (e.g. 12C, 14N, 58Ni, 208Pb) at different energies. We used the double folding optical model potential based on the density-dependent DDM3Y effective nucleon-nucleon interaction. Both version of the density distribution of the one-proton halo 17F nucleus has been taken into account in the above mentioned potential. The data for angular distributions of the elastic scattering differential cross section and reaction cross sections has been successfully reproduced at different energies using the above potentials. The energy dependence and the target mass number dependence of scattering in the imaginary volume integrals and the total reaction cross sections has also been studied.

Irreducible nonlocality of optical model potentials based on realistic NN interactions

We investigate the nonlocal structure of optical model potentials for nucleon-nucleus scattering based on microscopic approaches. To this purpose, \emph{in-medium} folding optical potentials are calculated in momentum space and their corresponding coordinate-space counterpart are examined, paying special attention to their nonlocal shape. The nucleon-nucleon effective interaction consists of the actual full off-shell $g$ matrix in Brueckner-Hartree-Fock approximation. The nonlocality of effective interactions is preserved throughout all stages in the the calculation. Argonne $v_{18}$ bare potential and chiral next-to-next-to-next-to-leading order bare interaction are used as starting point. The study is focused on proton elastic scattering off $^{40}$Ca at beam energies between 30 and 800 MeV. We find that the gradual suppression of high-momentum contributions of the optical potential results in quite different-looking coordinate-space counterparts. Despite this non-uniqueness in their nonlocal structure, the implied scattering observables remain unchanged for momentum cutoff above a critical one, which depends on incident energy of the projectile. We find that coordinate-space potentials with momentum cutoffs at the critical value yield the least structured nonlocal behavior. Implications of these findings are discussed.

Single Folding Optical Potential for Elastic Scattering of Protons from 14N and 16O in a Wide Range of Energies

Available experimental data for protons elastically scattered from 14N and 16O target nuclei are reanalyzed within the framework of single folding optical potential (SFOP) model. In this model, the real part of the potential is derived on the basis of single folding potential. The renormalization factor N r is extracted for the two aforementioned nuclear systems. Theoretical calculations fairly reproduce the experimental data in the whole angular range. Energy dependence of real and imaginary volume integrals as well as reaction cross sections are discussed.

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.

Global relativistic folding optical potential and the relativistic Green's function model

Optical potentials provide critical input for calculations on a wide variety of nuclear reactions, in particular, for neutrino-nucleus reactions, which are of great interest in the light of the new neutrino oscillation experiments. We present the global relativistic folding optical potential (GRFOP) fits to elastic proton scattering data from C-12 nucleus at energies between 20 and 1040 MeV. We estimate observables, such as the differential cross section, the analyzing power, and the spin rotation parameter, in elastic proton scattering within the relativistic impulse approximation. The new GRFOP potential is employed within the relativistic Green's function model for inclusive quasielastic electron scattering and for (anti) neutrino-nucleus scattering at MiniBooNE kinematics.

Detailed study for 16O → 12C + α and 12C → 11B + p spectroscopic factors

We have measured the angular distributions for 16 O elastically scattered on 12 C nuclei at energy 28 MeV and also for 12 C ion beam elastically scattered on 11 B target nuclei at energy 18 MeV. These measurements were performed in the cyclotron DC-60 INP NNC RK. Calculations were performed using both empirical Woods–Saxon and double folding optical model potentials. Both elastic scattering and transfer reaction were taken into consideration. We have extracted the spectroscopic factors for the configurations 16 O → 12 C + α and 12 C → 11 B + p and compared them with other calculated or extracted values at different energies from literature. The extracted spectroscopic factor for the configuration 12 C → 11 B + p from the current work is in the range 2.7–3.1, which is very close to Cohen–Kurath prediction. While for the configuration 16 O → 12 C + α, spectroscopic factors show fluctuation with energy which could be due to the well-known resonant-like behavior observed in 16 O + 12 C excitation function.

An investigation of p+8He elastic scattering

The vector analyzing power and differential cross-section for the elastic scattering of 8 He nucleus from polarized protons at 71 MeV/nucleon have been analyzed in the framework of the optical model potentials. Microscopic single folding (SF) optical potentials (OP) have been constructed based upon two different effective nucleon–nucleon (NN) interactions, namely Jeukenne–Lejeune–Mahaux (JLM) and BDM3Y1 effective interactions. The effect of 8 He nuclear structure has been tested through two different choices of the nuclear density distribution. It is concluded that the nucleus 8 He may be considered as a thick skin exotic nucleus. In order to investigate the vector analyzing power data, besides the Thomas phenomenological representation, three different forms of the spin–orbit (SO) part of the OP have been considered. These forms are based directly or indirectly upon the density distribution of 8 He nucleus. It is found that SO potentials of larger root mean square radii are able to successfully describe the vector analyzing power data more than those of shorter radii.

Elastic interaction of protons with stable and exotic light nuclei

The proton elastic-scattering data on ${}^{4,6,8}$He and ${}^{6,7,9,11}$Li nuclei are analyzed over a wide range of incident energies below 160 MeV/nucleon using the single-folding optical model. The real part of the folding optical potential (OP) is calculated using the M3Y nucleon-nucleon interaction and microscopic densities. The Green's function Monte Carlo density is used for the stable nuclei, whereas the large-scale shell model density is used for the exotic nuclei. The high-energy approximation calculation is used for the volume imaginary OP. The spin-orbit and surface imaginary parts of the OP are constructed from the derivatives of the real and volume imaginary parts of the folded potentials, respectively. The volume integrals of the OPs are studied, and it is found that they show clear dependencies on energy and root-mean-square radii. Hence, it can be considered an important constraint for the choice of the optical potential. A new empirical formula is assumed and successfully applied for the real volume integrals. The obtained results of the differential and the reaction cross sections are in good agreement with the available experimental data. In general, this OP with few and limited fitting parameters, which have systematic behavior with incident energy, successfully describes the proton elastic-scattering data with stable and exotic light nuclei at energies below 160 MeV/nucleon.

Open shell effects in a microscopic optical potential for elastic scattering of6(8)He

Elastic scattering observables (differential cross section and analyzing power) are calculated for the reaction ${}^{6}$He($p,p$)${}^{6}$He at projectile energies starting at 71 MeV/nucleon. The optical potential needed to describe the reaction is based on a microscopic Watson first-order folding potential, which explicitly takes into account that the two neutrons outside the ${}^{4}$He core occupy an open $p$ shell. The folding of the single-particle harmonic oscillator density matrix with the nucleon-nucleon $t$ matrix leads for this case to new terms not present in traditional folding optical potentials for closed shell nuclei. The effect of those new terms on the elastic scattering observables is investigated. Furthermore, we study the influence of an exponential tail of the $p$-shell wave functions on the scattering observables, as well as the sensitivity of the observables to variations of matter and charge radius. Finally, elastic scattering observables for the reaction ${}^{8}$He($p,p$)${}^{8}$He are presented at selected projectile energies.

Microscopic Optical Potentials for Helium-6 Scattering off Protons

The differential cross section and the analyzing power are calculated for elastic scattering of $^6$He from a proton target using a microscopic folding optical potential, in which the $^6$He nucleus is described in terms of a $^4$He-core with two additional neutrons in the valence p-shell. In contrast to previous work of that nature, all contributions from the interaction of the valence neutrons with the target protons are taken into account.

On the unabridged 7D-folding structure of the optical model potential for nucleon-nucleus scattering

Microscopic optical model potentials for nucleon-nucleus collisions, based on density-dependent effective interactions, involve multi-dimensional integrals to ac- count for the Fermi motion of the bound nucleons of the target. If a spherical matter distribution is assumed, each matrix element of the optical potential in momentum space requires the evaluation of seven-dimensional integrals. Here we describe the structure of these potentials and report results from their actual evaluation. Results for the scatter- ing observables are compared with those based on alternative approximations, observing moderate sensitivity. These findings validate the use of simpler expressions to evaluate folding optical potentials, from which higher-order or unconventional effects in the effec- tive interaction can safely be investigated.

The folding deuteron optical model potentials

For 52 target nuclei with deuteron as projectile, we calculate the reaction cross sections and elastic scattering angular distributions, as well as the $\chi^2$ 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 constructing the folding deuteron optical potential, both SKa and SKb are the best Skyrme force parameters of the microscopic nucleon optical potential proposed by Q. Shen \textit{et al}.

Analysis of heavy ions elastic scattering using the double folding cluster model

The nucleus–nucleus double folding optical potentials were constructed using the α-cluster structure of nuclei. We derived these potentials by folding an α– α interaction with density distributions of α-clusters inside projectile and target nuclei. Twenty sets of elastic scattering data in the energy range 2–22 MeV /u were analyzed using the resulted potentials. Successful descriptions of the angular distribution cross sections were obtained, particularly at energies less than 15 MeV /u. Double folded optical potentials were also calculated based upon the α-cluster structure of the projectile nucleus and an α-nucleon effective interaction. The behavior of the required renormalization factors to obtain the potential depths at the strong absorption radii for 14 reactions is quite consistent with that found for the M3Y double folded optical potentials.

Density-independent folding analysis of the [formula omitted] Li elastic scattering at intermediate energies

The differential cross sections of 6,7 Li elastic scattering from 12 C, 28 S, 40 Ca, 58 Ni, 90 Zr and 208 Pb targets at E/A P =12.5 –53 MeV / u have been analyzed using density-independent double folding optical potentials. The calculations are built upon a very simple phenomenological nucleon–nucleon effective interaction, which is represented by a single Yukawa term with a complex strength. The complex microscopic potentials have successfully reproduced the elastic scattering data for most of the analyzed sets. However, more success has been obtained when the single Yukawa term was considered for the real part only while the imaginary part was formulated in a phenomenological Woods–Saxon form. The predictions of the calculated potentials are compared with those obtained by the phenomenological and the M3Y double folded optical potentials. The effects of the knock-on exchange contribution, the variation of the range of the interaction and the target density uncertainty have been investigated. Also, the target mass number dependence in the real volume integrals and the total reaction cross sections has been studied.