Optical Model Potential Research Articles

α -induced reactions on In115 : Cross section measurements and statistical model analysis

[Background] Alpha-nucleus optical potentials are basic ingredients of statistical model calculations used in nucleosynthesis simulations. While the nucleon+nucleus optical potential is fairly well known, for the alpha+nucleus optical potential several different parameter sets exist and large deviations, reaching sometimes even an order of magnitude, are found between the cross section predictions calculated using different parameter sets. [Purpose] A measurement of the radiative alpha-capture and the alpha-induced reaction cross sections on the nucleus 115In at low energies allows a stringent test of statistical model predictions. Since experimental data is scarce in this mass region, this measurement can be an important input to test the global applicability of alpha+nucleus optical model potentials and further ingredients of the statistical model. [Methods] The reaction cross sections were measured by means of the activation method. The produced activities were determined by off-line detection of the gamma-rays and characteristic x-rays emitted during the electron capture decay of the produced Sb isotopes. The 115In(alpha,gamma)119Sb and 115In(alpha,n)118Sbm reaction cross sections were measured between Ec.m. = 8.83 MeV - 15.58 MeV, and the 115In(alpha,n)118Sbg reaction was studied between Ec.m. = 11.10 MeV - 15.58 MeV. The theoretical analysis was performed within the statistical model.

Calculation of total reaction cross sections of 6He, 8,9Li on nuclei within the microscopic optical potential model

Experimental data on total reaction cross sections of exotic nuclei 6He, 8,9Li interaction with the 181Ta, 59Co, 28Si and 9Be targets in a wide energy range are analyzed in the framework of a hybrid model of microscopic optical potential (OP). The real part of OP is obtained on the basis of the double folding model, while the imaginary part of OP is calculated within the high energy approximation. This theoretical approach demonstrates the fairly well agreement with experimental data at the wide energy regions.

The neutron transmission of natFe, 197Au and natW

Neutron total cross sections of natFe, 197Au and natW have been measured at the n ELBE neutron time-of-flight facility in the energy range 0.15-8MeV with an uncertainty due to counting statistics of up to 2% and a total uncertainty due to systematic effects of 1%. The neutrons are produced with the superconducting electron accelerator ELBE using a liquid lead circuit as photo-neutron target. By periodical sample-in-sample-out measurements the transmission of the sample materials has been determined using a low-threshold plastic scintillation detector. The resulting effective total cross sections show good agreement with previously measured data that cover only part of the energy range available at n ELBE. The results have also been compared to evaluated library files and recent calculations based on a dispersive coupled channel optical model potential.

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.

Global phenomenological optical model potential for the Li7 projectile nucleus

A new global phenomenological optical model potential for the $^{7}\mathrm{Li}$ projectile is derived from the available experimental data of elastic-scattering angular distributions and reaction cross sections from $^{27}\mathrm{Al}$ to $^{208}\mathrm{Pb}$ with incident energies below 200 MeV. It is based on a smooth, unique functional form for the energy dependence of the potential depths, and physically constrained geometry parameters. The elastic-scattering angular distributions and reaction cross sections for other targets are also predicted by the obtained $^{7}\mathrm{Li}$ global phenomenological optical model potential at different incident energies. These results are further compared with the corresponding experimental data. The performance shows that the $^{7}\mathrm{Li}$ global phenomenological optical model potential can give a satisfactory description for $^{7}\mathrm{Li}$ elastic scattering.

Reaction channel coupling effects for nucleons on O16 : Induced undularity and proton-neutron potential differences

Background: Precise fitting of scattering observables suggests that the nucleon-nucleus interaction is $l$ dependent. Such $l$ dependence has been shown to be $S$-matrix equivalent to an undulatory $l$-independent potential. The undulations include radial regions where the imaginary term is emissive.Purpose: To study the dynamical polarization potential (DPP) generated in proton-$^{16}\mathrm{O}$ and neutron-$^{16}\mathrm{O}$ interaction potentials by coupling to pickup channels. Undulatory features occurring in these DPPs can be compared with corresponding features of empirical optical model potentials (OMPs). Furthermore, the additional inclusion of coupling to vibrational states of the target will provide evidence for dynamically generated nonlocality.Methods: The fresco code provides the elastic channel $S$-matrix ${S}_{lj}$ for chosen channel couplings. Inversion, ${S}_{lj}\ensuremath{\rightarrow}V(r)+\mathbf{l}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{s}\phantom{\rule{0.16em}{0ex}}{V}_{\mathrm{SO}}(r)$, followed by subtraction of the bare potential, yields an $l$-independent and local representation of the DPP due to the chosen couplings.Results: The DPPs have strongly undulatory features, including radial regions of emissivity. Certain features of empirical DPPs appear, e.g., the full inverted potential has emissive regions. The DPPs for different collective states are additive except near the nuclear center, whereas the collective and reaction channel DPPs are distinctly nonadditive over a considerable radial range, indicating dynamical nonlocality. Substantial differences between the DPPs due to pickup coupling for protons and neutrons occur; these imply a greater difference between proton and neutron OMPs than the standard phenomenological prescription.Conclusions: The onus is on those who object to undularity in the local and $l$-independent representation of nucleon elastic scattering to show why such undulations do not occur. This work suggests that it is not legitimate to halt model-independent fits to high-quality data at the appearance of undularity.

Calculation of neutron cross-sections on copper-63 and -65

ABSTRACT Toward the development of the next version of Japanese Evaluated Nuclear Data Library (JENDL) general-purpose file, we calculate neutron cross-sections on 63, 65Cu from 50 keV to 20 MeV, which is the incident energy range above the resolved resonance region in JENDL-4.0. A dispersive optical model potential is adopted with a coupled-channel method for interaction between neutron and 63, 65Cu. Direct, pre-equilibrium, and compound processes are taken into account in the calculation. All cross-sections, differential and double-differential cross-sections are consistently calculated with a single set of model parameters. The calculation results reproduce the measured data very well. In addition, disagreement between the calculated and experimental values seen in an integral test for the 63Cu(n, α)60Co reaction is improved by using the cross-section data obtained from the present work.

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.

γ-process reaction studies via in-beam γ-ray spectroscopy at HORUS

The predictions for reaction rates from the Hauser-Feshbach statistical model as they are needed for γ-process reaction-network calculations crucially depend on the accuracy of the nuclear physics input-parameters like nuclear-level densities, γ-ray strength functions, and particle+nucleus optical-model potentials. At the Institute for Nuclear Physics of the University of Cologne, several charged-particle induced reactions were investigated via the in-beam method with HPGe detectors at the high-efficiency γ-ray spectrometer HORUS. One outstanding feature of this experimental method is the access to partial cross-sections, thus, cross-sections for the population of excited states in the reaction product via a radiative capture of an charged particle. Here, recent results for the reactions 89Y(p,γ)90Zr and 112Sn(α,γ)116Te will be presented.

Doubly differential and integral cross sections for electron elastic scattering by hydrogen chloride and hydrogen fluoride

We report theoretical doubly differential and integrated cross sections for electron elastic scattering by hydrogen chloride as well as by hydrogen fluoride over wide impact energies ranging from 10 eV up to 20 keV, where the non-relativistic theory is available. The calculations are performed by considering a target molecular state described by means of single-center molecular wave functions within the partial-wave formalism by means of a spherical optical potential model taking into account a static contribution deduced from a single-center Hartree-Fock target description as well as fine effects, like correlation-polarization and exchange contributions. The theoretical results obtained in this model pointed out clearly the role played by the exchange and correlation-polarization potentials, particularly at lower incident energies. The numerical results, obtained in this parameter free model for both doubly differential and integral cross sections for electron scattering by HCl and HF molecular targets, are compared with the available experimental data and satisfactory agreements are observed in the whole energy range.

Elastic scattering of e∓ by Na atoms

ABSTRACTThe differential, integrated elastic, momentum transfer, viscosity and total cross-sections along with Sherman function for the elastic scattering of electrons and positrons by sodium atoms have been calculated within the framework of complex projectile–atom optical potential model at the impact energies 0.1 ≤ Ei ≤ 104 eV for both the projectiles. The relativistic Dirac partial wave techniques, with accurate analytical charge densities, are used to obtain the scattering amplitudes. The present results produce satisfactory agreement with the experimental measurements and other theoretical calculations available in the literature.

Abnormal behavior of the optical potential for the halo nuclear system He6+Bi209

In a recent transfer reaction measurement of $^{208}\mathrm{Pb}$($^{7}\mathrm{Li},^{6}\mathrm{He}$)$^{209}\mathrm{Bi}$ at energies around and below the Coulomb barrier, the optical model potentials of the halo nuclear system $^{6}\mathrm{He}+^{209}\mathrm{Bi}$ were extracted by fitting the experimental data with the theoretical frameworks of the distorted-wave Born approximation and coupled reaction channels, respectively. With the high-precision result, a complete picture of the behavior of the optical potential for this halo system is clearly derived for the first time. The real potential presents a bell-like shape around the barrier as a normal threshold anomaly. However, for the imaginary part, it first increases with the energy decreasing below the barrier and then falls quickly to 0, hence the threshold energy can be determined by fitting the variation trend. Moreover, the result also provides some evidence that the dispersion relation does not hold for this halo nuclear system, which calls for further investigation of the underlying physics.

Consistent optical potential for incident and emitted low-energy α particles. II. α emission in fast-neutron-induced reactions on Zr isotopes

Background: Challenging questions of the $\alpha$-particle optical-model potential (OMP) are still pointed out by recent high-precision measurements of $\alpha$-induced reaction data below the Coulomb barrier. Moreover, the reliability of a previous OMP for $\alpha$-particles on nuclei within the mass number range 45$\leq$$A$$\leq$209 has been recently proved for emitted $\alpha$ particles as well, but only in the case of proton-induced reactions on Zn isotopes [Phys. Rev. C {\bf 91}, 064611 (2015), Paper I]. Purpose: Analysis of most recent $(\alpha,\gamma)$ reaction data for Ge and Zr isotopes, which provides an additional validation of the above-mentioned potential, is related to a further account of $\alpha$-particle emission in neutron-induced reactions on Zr isotopes, at the same time with a suitable description of all competitive processes. Methods: A consistent parameter set, established or validated by independent analysis of recent various data, particularly $\gamma$-ray strength functions, have been involved within model calculation of the $(\alpha,\gamma)$ as well as $(n,\alpha)$ reaction cross sections. The latter are part of the whole analysis of the neutron activation of Zr isotopes, in order to avoid any error compensation or latent ambiguity. Results: The aforesaid potential provides a consistent description of recent $\alpha$-induced reaction data with no empirical rescaling factors of the $\gamma$ and/or nucleon widths. On the other hand, its use leads to underestimated predictions of the pre-equilibrium emission and statistical models for the $(n,\alpha)$ reaction cross sections. Conclusions: An optical potential with a volume imaginary component seems to be needed to describe the low-energy $\alpha$-particle evaporation, while only surface absorption occurs in $\alpha$-induced reactions at similar energies.

Evaluation of cross sections for neutron interactions with 238U in the energy region between 5 keV and 150 keV

.Cross sections for neutron interactions with 238U in the energy region from 5keV to 150keV have been evaluated. Average total and capture cross sections have been derived from a least squares analysis using experimental data reported in the literature. The resulting cross sections have been parameterised in terms of average resonance parameters maintaining full consistency with results of optical model calculations by using a dispersive coupled channel optical model potential. The average compound partial cross sections have been expressed in terms of transmission coefficients by applying the Hauser-Feshbach statistical reaction theory including width-fluctuations. A generalized single-level representation compatible with the energy-dependent options of the ENDF-6 format has been applied using standard boundary conditions. The results have been transferred into a full ENDF-6 compatible data file.

Nuclear-matter radius studies fromNi58(α,α)experiments at the GSI Experimental Storage Ring with the EXL facility

A novel method for measuring nuclear reactions in inverse kinematics with stored ion beams was successfully used to extract the nuclear-matter radius of Ni58. The experiment was performed at the experimental heavy-ion storage ring at the GSI facility using a stored Ni58 beam at energies of 100 and 150 MeV/u and an internal helium gas-jet target. Elastically scattered α-recoils at low momentum transfers were measured with an in-ring detector system compatible with ultrahigh vacuum. Experimental angular distributions were fitted using density-dependent optical model potentials within the eikonal approximation. This permitted the extraction of the point-matter root-mean-square radius of Ni58 with an average value of 3.70(7) fm. Results from this work are in good agreement with several experiments performed in the past in normal kinematics. This pioneering experiment demonstrates a major breakthrough towards future investigations with far-from-stability stored beams using the present technique.Received 22 June 2017DOI:https://doi.org/10.1103/PhysRevC.96.034617©2017 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAccelerator/storage ring control systemsH & He induced nuclear reactionsNuclear charge distributionNuclear matterProperties39 ≤ A ≤ 58Nuclear PhysicsAccelerators & Beams

The cross section calculation of 112Sn(α,γ)116Te reaction with different nuclear models at the astrophysical energy range

The theoretical cross section calculations for the astrophysical p process are needed because most of the related reactions are technically very difficult to be measured in the laboratory. Even if the reaction was measured, most of the measured reactions have been carried out at the higher energy range from the astrophysical energies. Therefore, almost all cross sections needed for p process simulation have to be theoretically calculated or extrapolated to the astrophysical energies. \(^{112}\hbox {Sn}(\alpha ,\gamma )^{116}\hbox {Te}\) is an important reaction for the p process nucleosynthesis. The theoretical cross section of \(^{112}\hbox {Sn}(\alpha ,\gamma )^{116}\hbox {Te}\) reaction was investigated for different global optical model potentials, level density, and strength function models at the astrophysically interested energies. Astrophysical S factors were calculated and compared with experimental data available in the EXFOR database. The calculation with the optical model potential of the dispersive model by Demetriou et al., and the back-shifted Fermi gas level density model and Brink-Axel Lorentzian strength function model best served to reproduce experimental results at an astrophysically relevant energy region. The reaction rates were calculated with these model parameters at the p process temperature and compared with the current version of the reaction rate library Reaclib and Starlib.

Measurements of angular distributions for7Li elastically scattered from58Ni at energies around the Coulomb barrier

Recently, experimental measurements of elastic scattering angular distributions for the system7Li+58Ni at ten different energies around the Coulomb barrier were made by the Heavy-Ion Group. The measurements were made at the Tandem Van de Graaff Particle Accelerator Laboratory in the National Institute for Nuclear Research (ININ) in Mexico. In this work, preliminary elastic scattering angular distributions for five energies (Elab, = 12.0, 12.5, 13.0, 13.5 and 14.22 MeV) are presented. The preliminary experimental data were analyzed using the São Paulo Optical Model Potential (SPP) which is based on a double-folding potential, reproducing very well these data. A comparison is made with old data reported back in 1973 and in 2012. Further analysis is in progress in order to fully understand this particular system, specially because7Li is known to be a weakly bound nucleus.

Unitary version of the single-particle dispersive optical model and single-hole excitations in medium-heavy spherical nuclei

A unitary version of the single-particle dispersive optical model was proposed with the aim of applying it to describing high-energy single-hole excitations in medium-heavy mass nuclei. By considering the example of experimentally studied single-hole excitations in the 90Zr and 208Pb parent nuclei, the contribution of the fragmentation effect to the real part of the optical-model potential was estimated quantitatively in the framework of this version. The results obtained in this way were used to predict the properties of such excitations in the 132Sn parent nucleus.

Study of the nuclear medium by 12C + 12C elastic scattering analysis at low energy region

The nuclear medium is investigated by studying the 12C + 12C elastic scattering at the low energies in the framework of optical model (OM) potential. Both frozen and adiabatic density approximations are used for the description of the nuclear medium during the colliding process. In the OM calculation, the double folding procedure using the realistic CDM3Y3 effective nucleon-nucleon (NN) interactions and the wave functions of colliding nuclei is employed to describe the nucleus-nucleus potential at low energy region below 10 MeV per nucleon. The obtained results from the elastic scattering analyses show that the adiabatic density approximation is more reasonable than the frozen density approximation to describe the overlapping density (the so-called nuclear medium) for the 12C + 12C system at low energy region.

Translation invariance and antisymmetry in the theory of the nucleon optical model

The first step in any formalism that aims to connect a many-nucleon theory of nucleon-nucleus scattering and the concept of an optical model potential in the sense pioneered by Feshbach is to explain what is meant by the optical model wavefunction. By definition this is a function of a single space coordinate plus a set of single nucleon internal variables. This article gives a critique of the definitio as it is frequently expressed in 2nd Quantisation language and suggest a new definition which is more consistent with the requirements of antisymmetry and translational invariance. A modification of the time-dependent Green's function formalism is suggested.