Optical Model Potential Research Articles

Angular zone of influence for fusion and direct reactions on elastic scattering of 6Li with 58Ni, 59Co, 64Ni, and 64Zn

Recently, a systematic study of fusion and elastic scattering data was performed for the 6Li + (58Ni, 59Co, 64Ni, 64Zn) systems. Appropriate polarization potentials satisfying the dispersion relation were extracted, which can be associated to fusion and direct reaction couplings, respectively. By examining the relative strengths of the corresponding absorptive parts, a semiclassical analysis can be carried out which gives an indication about the angular range where direct (fusion) reactions are more important in determining the elastic scattering angular distributions. The results of such an analysis are presented for all four systems. The developed method is useful to explore the sensitivity of the elastic scattering angular distributions to the radial details of the phenomenological optical model potential. An example is presented where large sensitivity to distances smaller than the Coulomb barrier radius is evident.

Measurement and analysis of nuclear γ -ray production cross sections in proton interactions with Mg, Si, and Fe nuclei abundant in astrophysical sites over the incident energy range E=30–66 MeV

Gamma-ray production cross section excitation functions have been measured for $30$, $42$, $54$ and $66$ MeV proton beams accelerated onto targets of astrophysical interest, $^{nat}$C, C + O (Mylar), $^{nat}$Mg, $^{nat}$Si and $^{56}$Fe, at the Sector Separated Cyclotron (SSC) of iThemba LABS (near Cape Town, South Africa). The AFRODITE array equipped with 8 Compton suppressed HPGe clover detectors was used to record $\gamma$-ray data. For known, intense $\gamma$-ray lines the previously reported experimental data measured up to $E_{p}\simeq$ $25$ MeV at the Washington and Orsay tandem accelerators were extended to higher proton energies. Our experimental data for the last 3 targets are reported here and discussed with respect to previous data and the Murphy \textit{et al.} compilation [ApJS 183, 142 (2009)], as well as to predictions of the nuclear reaction code TALYS. The overall agreement between theory and experiment obtained in first-approach calculations using default input parameters of TALYS has been appreciably improved by using modified optical model potential (OMP), deformation, and level density parameters. The OMP parameters have been extracted from theoretical fits to available experimental elastic/inelastic nucleon scattering angular distribution data by means of the coupled-channels reaction code OPTMAN. Experimental data for several new $\gamma$-ray lines are also reported and discussed. The astrophysical implications of our results are emphasised.

Comparison between optical-model potentials in G -matrix folding method and improved local-density approximation method

Microscopic optical-model potentials evaluated by two methods in a nuclear matter approach, namely a $G$-matrix folding method and an improved local-density approximation (LDA) method, are compared. The real parts agree well and show good correspondence to a phenomenological Woods-Saxon potential when second-order contributions are taken into account. On the other hand, the resemblance is not so good in an imaginary part. The reason for the similarity in the real part of the two methods is examined. The improved LDA, which requires less numerical effort, is useful to apply in other cases such as hyperon potentials.

Semimicroscopic analysis of Li6 elastic scattering at 40 MeV/nucleon

Analysis of the differential cross sections for $^{6}\mathrm{Li}$ elastic scattering from $^{24}\mathrm{Mg}$, $^{28}\mathrm{Si}$, $^{40}\mathrm{Ca}$, $^{48}\mathrm{Ca}$, $^{58}\mathrm{Ni}$, $^{90}\mathrm{Zr}$, and $^{116}\mathrm{Sn}$ at 40 MeV/nucleon is performed within the framework of the optical double folding model. Simple phenomenological effective nucleon-nucleon interaction represented by a density-independent single Yukawa term is utilized to generate the real optical potential part. The derived potentials in conjunction with imaginary parts expressed in phenomenological volume Woods-Saxon forms have been successfully used to reproduce the seven sets of data. For the sake of comparison, the same measurements are reanalyzed using folded potentials based upon the density-independent M3Y effective interaction. Furthermore, reasonably successful reproduction of the data is obtained by Woods-Saxon-type optical model potentials. The radial sensitivity of the derived real potentials to the calculating elastic-scattering angular distributions has been investigated using the notch perturbation technique. The target mass dependence in real and imaginary volume integrals as well as total reaction cross sections are also investigated.

Dispersive optical model description of nucleon scattering on Pb and Bi isotopes

A recently derived dispersive optical model potential (DOMP) for $^{208}$Pb is extended to consider the non-locality in the real potential and the shell-gap in the definition of the nuclear imaginary potentials near the Fermi energy. The modified DOMP improves the simultaneous description of nucleon scattering on $^{208}$Pb and of the $^{208}$Pb particle-hole bound states. The new potential is shown to give a very good description of nucleon scattering data on near-magic targets $^{206,207}$Pb and $^{209}$Bi.

Bayesian analysis on interactions of exotic nuclear systems

Even though the Bayesian method has been proved to be powerful in the field of nuclear physics, it has not yet been implemented to study the properties of the reaction systems with exotic nuclei, for instance, the gross feature of the phenomenological interaction potential. So far, the optical model potential was typically evaluated by the traditional frequentist approach. However, contradictive conclusions were drawn, especially on the near-threshold behavior of the imaginary potential: threshold anomaly and abnormal threshold anomaly were derived for 6Li+209Bi and 6He+208Pb even with the same elastic scattering data. In this study, we first applied the Bayesian framework to analyze the elastic scattering data of 6Li+209Bi. It was found that the results of Bayesian statistics strongly depend on the imposed prior distributions. Therefore, the Bayesian method has to be used with extreme caution, since the improper prior knowledge could lead to completely wrong conclusions. Since the elastic scattering data is not informative enough to constrain the prior and posterior distributions, our analysis further indicates that the results from the non-constraint frequentist approach or the flat prior distribution with a reasonable physical-boundary can be employed as convincing prior knowledge of the Bayesian framework. Based on this result, we further applied the Bayesian approach to the transfer reaction 208Pb(7Li,6He)209Bi, to investigate the optical potentials of the neutron halo system 6He+209Bi in the outgoing channel. With the proper prior distributions, the Bayesian analysis on both the 6Li+209Bi and 6He+208Pb confirm the presence of the abnormal threshold anomaly. Therefore the applicability of the dispersion relation remains in doubt.

Nuclear effects in proton transport and dose calculations

Interactions of protons with nuclei are modeled in a form that is suitable for Monte Carlo simulation of proton transport. The differential cross section (DCS) for elastic collisions of protons with neutral atoms is expressed as the product of the Rutherford DCS, which describes scattering by a bare point nucleus, and two correction factors that account for the screening of the nuclear charge by the atomic electrons and for the effect of the structure of the nucleus. The screening correction is obtained by considering the scattering of the projectile by an atom with a point nucleus and the atomic electron cloud described by a parameterization of the Dirac-Hartree-Fock-Slater self-consistent electron density. The DCS for scattering by this point nucleus atom is calculated by means of the eikonal approximation. The nuclear correction to the DCS for elastic collisions is calculated by conventional partial-wave analysis with a global optical-model potential that describes the interaction with the bare nucleus. Inelastic interactions of the projectile with target nuclei are described by using information from data files in ENDF-6 format, which provide cross sections, multiplicities, and angle-energy distributions of all reaction products: light ejectiles (neutrons, protons, …), gammas, as well as recoiling heavy residuals. These interaction models and data have been used in the Monte Carlo transport code penh, an extension of the electron-gamma code penelope, which originally accounted for electromagnetic interactions only. The combined code system penh/penelope performs simulations of coupled electron-photon-proton transport. A few examples of simulation results are presented to reveal the influence of nuclear interactions on proton transport processes and on the calculation of dose distributions from proton beams.

Insight into the radial sensitivity of phenomenological nucleus-nucleus interaction potentials

The optical model potential, which reflects an overall feature of the nuclear property and reaction dynamics, has been widely adopted to describe the nucleus-nucleus interaction phenomenologically. Experimentally, knowledge of the optical potential can only be learned in the vicinity of a sensitive radius. In this study, the notch technique was applied to extract the radial sensitive regions of the tightly bound system $^{16}\mathrm{O}+^{208}\mathrm{Pb}$ and weakly bound systems $^{9}\mathrm{Be}+^{208}\mathrm{Pb}$ and $^{6}\mathrm{He}+^{209}\mathrm{Bi}$ at energies around the Coulomb barrier. It is the first time that we observed two distinct sensitive regions, corresponding to the inner volume absorption and the outer surface absorption processes. Strong energy dependence of the sensitive regions was found as well. Based on this result, we further investigated the interaction property of $^{9}\mathrm{Be}+^{208}\mathrm{Pb}$ and found that the threshold anomaly was observed in the volume interaction, whereas the abnormal near-threshold behavior was presented in the surface part.

Analysis of the reaction cross sections of $$^{15,16}C+^{12}C$$ and $$^{15,16}C+^{27}Al$$ at intermediate energies using microscopic optical potential and Glauber model

Analysis of the reaction cross sections of $$^{15,16}C+^{12}C$$ and $$^{15,16}C+^{27}Al$$ at intermediate energies using microscopic optical potential and Glauber model

Analysis of scattering and breakup reactions of 12,14Be within the microscopic model of optical potential

Analysis of the differential cross sections of scattering of neutron-rich nuclei 12,14Be on 12C at 56 MeV/nucleon and on protons at energy near 700 MeV/nucleon is carried out within the microscopic model of optical potential (OP). The real part of the 12,14Be+12C OP is calculated by using the double-folding procedure accounting for the anti-symmetrization effects, while the imaginary part of OP is obtained in the framework of the high-energy approximation (HEA). As to the 12,14Be+p scattering at relativistic energies, calculations of the both real and imaginary OPs were made within the HEA approach. In this framework, the only free parameters of OP are the depths of its real and imaginary parts obtained by fittingto experimental data. The role of the 12,14Be density models is considered when reproducing the experimental data. A contribution of the inelastic channels with excitations of 2+ and 3− states in 12C when calculating the quasielastic cross sections is analysed. Also, the 14Be cluster model, in which this nucleus consists of a 2n-halo and the 12Be core, is applied to calculate the cross sections of diffraction breakup and stripping reactions in the 14Be+12C collisions at the energy of 56 MeV/nucleon. A good agreement of the theoretical results with the available experimental data of both scattering and breakup processes is obtained.

A comprehensive description of elastic scattering angular distributions for eight different density distribution of 32S nucleus

The elastic scattering angular distributions of 32S projectile by 12C, 27Al, 40Ca, 48Ca, 48Ti, 58Ni, 63Cu, 64Ni, 76Ge, 96Mo and 100Mo targets over the energy range 83.3 - 180 MeV are analyzed in the framework of the double folding model based on the optical model. The real part of the optical model potential is obtained by using double folding model for eight different density distributions of 32S which consist of Ngo, SP, 2pF, G1, G2, S, 3pF, and HFB. The imaginary part of the optical model potential is accepted as the Woods-Saxon (WS) potential. The theoretical results successfully reproduce the experimental data over both a wide energy and a wide target nucleus. Finally, simple and useful formulas which predict imaginary potential depths of each density are derived based on the elastic scattering results.

Scattering of e± from the neon isonuclear series over the energy range 1 eV–0.5 GeV

This work calculates the differential, integral and momentum transfer cross sections for the scattering of e± by the neutral neon over the energy range 1 eV–0.5 GeV and those of e− by the ions (Ne+–Ne10+) over the range 1 eV–1 keV. It also includes the estimation of the viscosity, inelastic, total and total ionization cross sections and Sherman function for the e±-atom systems over the same energy range. Our calculations involve two approaches, the optical potential model (OPM) and the nuclear structure approach (NSA), depending upon the collision energy. Both the approaches employ Dirac partial wave analysis but differ in the potentials. In OPM, a complex projectile-target optical potential, comprising static, exchange, polarization and imaginary components, is employed. In the NSA, only the nuclear potential is used, neglecting the screening of the electrons. Moreover, we have determined positions of critical minima, in energy and angle, from the analysis of elastic differential cross sections and Sherman function at different energies. Our results agree reasonably well with the available experimental data and other theoretical calculations.

Relativistic mean-field approach in nuclear systems

A new scheme to study the properties of finite nuclei is proposed based on the Dirac-Brueckner-Hartree-Fock (DBHF) approach starting from a bare nucleon-nucleon interaction. The relativistic structure of the nucleon self-energies in nuclear matter depending on density, momentum and isospin asymmetry are determined through a subtracted T-matrix technique and parameterized, which makes them easily accessible for general use. The scalar and vector potentials of a single particle in nuclei are generated via a local density approximation (LDA). The surface effect of finite nuclei can be taken into account by an improved LDA (ILDA), which has successfully been applied in microscopic derivations of the optical model potential for nucleon-nucleus scattering. The bulk properties of nuclei can be determined in a self-consistent scheme for nuclei all over the nuclear mass table. Calculated binding energies agree very well with the empirical data, while the predicted values for radii and spin-orbit splitting of single-particle energies are about 10 \% smaller than the experimental data. Basic features of more sophisticated DBHF calculations for finite nuclei are reproduced.

Theoretical Cross-Section Calculations for the ($$\mathbf{\alpha}$$, $$\boldsymbol{n}$$) and ($$\mathbf{\alpha}$$, $$\boldsymbol{2n}$$) Reactions on $${}^{\mathbf{46}}$$Ti, $${}^{\mathbf{50}}$$Cr, $${}^{\mathbf{54}}$$Fe, and $${}^{93}$$Nb Isotopes

The employment of the fusion mechanism for the energy production is a promising solution to the continuously growing global energy demand. The correct material selection for this cutting edge technology is just as important as the efforts to understand the related nuclear reaction mechanisms. A value which is relevant to nuclear reactions and is of considerable importance is the cross-section of the reaction. Among many parameters, which affect the theoretical calculations of this quantity, level density models and alpha optical model potentials have played an important role, due to their direct effects on the calculations. By considering the importance of the materials used in the fusion technology and the aforementioned parameters, the aim of this work is to study the effects of level density models, alpha optical model potentials and their combinational usage in the cross-section theoretical calculations on the alpha particle induced reactions for $${}^{46}$$ Ti, $${}^{50}$$ Cr, $${}^{54}$$ Fe and $${}^{93}$$ Nb isotopes. The examined reaction routes are limited to the alpha particle induced single and double neutron emitting reactions. All calculations were performed by using the 1.9 version of the TALYS code, in which six level density models and eight alpha optical model potentials are available. The results of the present work are compared with the existing literature data, taken from the Experimental Nuclear Reaction Database (EXFOR) library, by performing a mean weighted deviation analysis calculation. The more consistent results in comparison with the experimental data were obtained with the combinational use of the models.

Analysis of α+11B elastic and inelastic scattering using microscopic and semi-microscopic representations

In the present study angular distributions of the differential cross section for elastic and inelastic scattering of alpha (α)-particles of 11В nuclei at different bombarding energies have been analyzed in the framework of the optical model (OM) potential. Two OM folding approaches were adopted in order to construct the real part of the α-nucleus potential. First, we generated the semi-microscopic single folding (SF) potential by folding an effective α-nucleon (α-N) interaction over the nuclear matter density of the target (11B) nucleus. In addition, the double folding (DF) approach was employed in order to deduce a microscopic representation of the optical potential by folding an effective density-dependent (DDM3Y) nucleon–nucleon interaction over the matter densities of the colliding nuclei. Successful theoretical predictions of six sets of experimental elastic scattering data have been obtained over the whole measured angular range. However, it was found that introducing real renormalization coefficients (∼0.9–1.6) is essential in order to obtain best fits with data. On the other side, sixteen sets of the inelastic scattering data at several excited states of 11B nucleus were analyzed using the constructed SF and DF deformed potentials. In general, reasonable description of the data is obtained. However underestimated predictions of data were obtained at backward measured angles. The deduced reaction (absorption) cross sections and nuclear deformation lengths were also investigated.

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.

(p,γ) Reaction Cross Sections Relevant to the p process: First Results for the Se Isotopes

Proton-capture reaction cross sections of Se isotopes were determined in the 1-6 MeV energy range by means of γ-angular distribution measurements as well as via the activation technique. In this report we compare our first cross-section results with statistical model calculations performed using various microscopic and phenomenological approaches of Optical Model Potentials and Nuclear Level Densities.

Microscopic Calculation of the Optical Model Potential from One Boson Exchange Poten­tials

A new method for calculating the optical model potential from One Boson Exchange Potentials (OBEPs) is developed. The G-matrix is calculated by solving the Bethe-Goldstone equation in momentum space. Using vector brackets these G-matrix elements can be transformed from the center of mass representation into the laboratory system. This allows the evaluation of the (r-matrix interaction between nucleons in bound states and those in a plane-wave state. The lowest order contribution to the real part of the potential comes from the Hartree-Fock term, while the lowest order contribution to the imaginary part comes from the two-particle-one-hole (2p1h) diagram. Calculations for 16O and 40Ca have been carried out. Local approximations are obtained by describing the results for the central part in terms of a Woods-Saxon potential and those for the spin-orbit part in terms of the corresponding derivatives. The dependence of these potentials on energy and angular momentum is discussed. The parameters for these local approximations are in good agreement with empirical fits.

Nucleon inelastic scattering cross sections on O16 and Si28

This paper reports cross-section measurements of the ($n,{n}^{\ensuremath{'}}$) and ($p,{p}^{\ensuremath{'}}$) reactions on $^{16}\mathrm{O}$ and $^{28}\mathrm{Si}$ at Geel Electron Linear Accelerator and at the 9-MV Tandem Accelerator of Horia Hulubei National Institute for Physics and Nuclear Engineering, respectively. The main purpose was to measure the neutron- and proton-induced inelastic $\ensuremath{\gamma}$-production cross sections for all observed transitions in $^{16}\mathrm{O}$ and $^{28}\mathrm{Si}$, followed by the calculation of the corresponding total inelastic cross section. The results are compared with theoretical calculations performed using the talys 1.9 code, evaluated nuclear data, and previously reported experimental data. The broader goal of this work is to study whether and to what extent the neutron-induced inelastic cross sections of these nuclei can be inferred from those obtained using suitable charged particle reactions. We show that, by making use of the formal similarities between the neutron- and the proton-target optical model potentials and isospin symmetry in mirror nuclei, one can develop a procedure that combines experimental proton-induced inelastic cross sections with theoretical calculations to infer neutron inelastic cross sections. For $^{16}\mathrm{O}$ and $^{28}\mathrm{Si}$, the precision associated with this procedure is around 10--20% for most of the incident energy range.

Rearrangement term in the folding model of the nucleon optical potential

Based on the mean-field determination of the single-particle energy in nuclear matter that contains naturally a rearrangement term (RT) implied by the Hugenholtz–van Hove theorem, the folding model of the nucleon optical potential (OP) is extended to take into account the RT using the effective, density dependent CDM3Yn interaction. With the exchange part of the nucleon folded OP treated exactly in the Hartree–Fock manner, a compact nonlocal version of the folding model is suggested in the present work to determine explicitly the isospin-dependent, nonlocal central term of the nucleon OP. To solve the optical model (OM) equation with a complex nonlocal OP, the calculable R-matrix method is used to analyse the elastic neutron and proton scattering on 40,48Ca, 90Zr, and 208Pb targets at low energies. The inclusion of the RT into the folding model calculation of the nonlocal nucleon OP was shown to be essential for the overall good OM description of elastic nucleon scattering. To validate the nonlocal version of the folding model, the OM results given by the nonlocal folded nucleon OP are also compared with those given by the global parametrization of the nonlocal OP using the analytical nonlocal form factor suggested by Perey and Buck.