Nuclear Optical Model Potential Research Articles

Peripheral reactions and elastic scattering induced by strongly bound, weakly bound and exotic nuclei

A phenomenological study of peripheral reactions induced by strongly bound, weakly bound and exotic projectiles on different targets is presented. A large number of experimental elastic scattering differential cross sections at energies close to the Coulomb barrier is studied on the basis of a simple nuclear optical model potential that depends on a small number of parameters. The derived wave functions, together with the imaginary component of the optical potential, allow the analysis of the radial peripheral absorption density distributions for the different kind of projectiles. These distributions, when appropriately normalized, show a clear correlation with the type of projectile regardless of the involved target and indicate that projectiles more prone to break up show a more peripheral absorption density distribution. This manifests in their magnitude, location and width. The relationship of these variables in the strongly bound group and the weakly bound group are described with a simple exponential function, while the exotic projectiles show two distinct groups, namely the neutron-halo and the proton-halo. For the neutron-halo projectiles such as He6, Li11 and Be11 there is a notable increment of the radial peripheral absorption density peak and the total reaction cross section as the breakup separation energy decreases. The same relationship is established for the proton-halo projectiles B8 and F17 but their reduced effective dipole charge leads to a lower probability of dipole Coulomb breakup that results in a substantial reduction in the extent of their peripheral absorption.

Systematic analysis of elastic α scattering on [formula omitted] nuclei around the Coulomb barrier

Alpha elastic scattering angular distributions on target nuclei 118, 124Sn and 120-130Te at energies near the Coulomb barrier are analyzed. We used three versions of the nuclear optical model potentials (OMP) to analyze twenty-nine data sets. JLM and the density and energy-dependent DDM3Y1 with finite range exchange term effective interactions were used to generate these potentials. Two real folded potentials based on JLM and DDM3Y1 effective interactions supplied with the conventional Wood–Saxon (WS) imaginary potential are used in the cross sections calculations. These potentials are denoted as JLM-R and DDM3Y1-FR, respectively. In addition, we used the full complex folded OMP, denoted as JLM-RI, to analyze the same data. These potentials successfully predict the cross section of the systems under study. We found that the JLM-R and DDM3Y1-FR could reproduce the measured cross sections over the full angular range very well compared to microscopic JLM-RI potential. Our calculated potentials have a clear energy dependence and in addition a weak target mass dependence. The total reaction cross section and volume integral are investigated in comparison to previous studies. The derived potentials are very promising for the construction of a new global α-nucleus potential and provide new parameters of α–induced reactions and scattering at the energy range 17–27 MeV.

Recommended Cross Sections and Optical Potential of Dy Isotopes for Neutron Induced Reactions at 14.0 MeV

The evaluation is based mainly on the calculations of the nuclear optical model potential and the relevant parameters which are collected and selected from References Input Parameter Library (RIPL-3) which is being developed under the international project coordinated by the International Atomic Energy Agency (IAEA). The analyzing of a complete energy range has been done starting from threshold energy for each reaction. The cross sections are reproduced in fine steps of incident neutron energy with 0.01MeV intervals with their corresponding errors. The recommended cross sections for available experimental data taken from EXFOR library have been calculated for all the considered neutron induced reactions for Dy (Z=66; A=162-164) isotopes. The calculated results are analyzed and compared with the experimental data. The optimized optical potential model parameters give a very good agreement with the experimental data over the energy range 13.4-14.87MeV for neutron induced cross section reactions (n,p) for spherical Dy-162 target element, (n,2H), (n,d), (n,n+p),and (n,p) for spherical Dy-163 target element, and (n,2H) and (n,p) for spherical Dy-164 target element.

Recommended Cross Sections and Optical Potential of Dy Isotopes for Neutron Induced Reactions at 14.0 MeV

The evaluation is based mainly on the calculations of the nuclear optical model potential and the relevant parameters which are collected and selected from References Input Parameter Library (RIPL-3) which is being developed under the international project coordinated by the International Atomic Energy Agency (IAEA). The analyzing of a complete energy range has been done starting from threshold energy for each reaction. The cross sections are reproduced in fine steps of incident neutron energy with 0.01MeV intervals with their corresponding errors. The recommended cross sections for available experimental data taken from EXFOR library have been calculated for all the considered neutron induced reactions for Dy (Z=66; A=162-164) isotopes. The calculated results are analyzed and compared with the experimental data. The optimized optical potential model parameters give a very good agreement with the experimental data over the energy range 13.4-14.87MeV for neutron induced cross section reactions (n,p) for spherical Dy-162 target element, (n,2H), (n,d), (n,n+p),and (n,p) for spherical Dy-163 target element, and (n,2H) and (n,p) for spherical Dy-164 target element.

Optical Model Potential Using CINDA Library for Neutron Induced Cross Section Reactions for Spherical Uranium-235,238 Isotopes

The calculation are based mainly on the nuclear optical model potential and relevant parameters are collected and selected from References Input Parameter Library (RIPL) which is being developed under the international project coordinated by the International Atomic Energy Agency (IAEA). The analyzing of a complete energy range has done starting from threshold energy for each reaction. The cross sections are reproduced in fine steps of incident neutron energy with 0.01MeV intervals with their corresponding errors. The recommended cross sections for available experimental data taken from CINDA library have been calculated for all the considered neutron induced reactions for spherical U-235 and U-238 isotopes. The calculated results are analyzed and compared with the experimental data. The optimized optical potential model parameters give a very good agreement with the experimental data over the energy range 0.001-20MeV for neutron induced cross section reactions (n,f), (n,tot), (n,el), (n,inl), (n,2n), (n,3n), and (n,γ) for spherical U-235 and U-238 target elements.

Evaluation of Optical Model Potential Using Neutron Induced Cross Section Reaction for Spherical Uranium-238 Isotope up to 20MeV

The evaluation are based on mainly on the calculations of the nuclear optical model potential and relevant parameters are collected and selected from References Input Parameter Library (RIPL) which is being developed under the international project coordinated by the International Atomic Energy Agency (IAEA). The analyzing of a complete energy range has done starting from threshold energy for each reaction. The cross sections are reproduced in fine steps of incident neutron energy with 0.01MeV intervals with their corresponding errors. The recommended cross sections for available experimental data taken from EXFOR library have been calculated for all the considered neutron induced reactions for U-238 isotopes. The calculated results are analyzed and compared with the experimental data. The optimized optical potential model parameters give a very good agreement with the experimental data over the energy range 0.001-20MeV for neutron induced cross section reactions (n,f), (n,tot), (n,el), (n,inl), (n,2n), (n,3n), and (n,γ) for spherical U-238 target elements.

Optical Model Potential Using CINDA Library for Neutron Induced Cross Section Reactions for Spherical Uranium-235,238 Isotopes

The calculation are based mainly on the nuclear optical model potential and relevant parameters are collected and selected from References Input Parameter Library (RIPL) which is being developed under the international project coordinated by the International Atomic Energy Agency (IAEA). The analyzing of a complete energy range has done starting from threshold energy for each reaction. The cross sections are reproduced in fine steps of incident neutron energy with 0.01MeV intervals with their corresponding errors. The recommended cross sections for available experimental data taken from CINDA library have been calculated for all the considered neutron induced reactions for spherical U-235 and U-238 isotopes. The calculated results are analyzed and compared with the experimental data. The optimized optical potential model parameters give a very good agreement with the experimental data over the energy range 0.001-20MeV for neutron induced cross section reactions (n,f), (n,tot), (n,el), (n,inl), (n,2n), (n,3n), and (n,γ) for spherical U-235 and U-238 target elements.

Evaluation of Optical Model Potential Using Neutron Induced Cross Section Reaction for Spherical Uranium-238 Isotope up to 20MeV

The evaluation are based on mainly on the calculations of the nuclear optical model potential and relevant parameters are collected and selected from References Input Parameter Library (RIPL) which is being developed under the international project coordinated by the International Atomic Energy Agency (IAEA). The analyzing of a complete energy range has done starting from threshold energy for each reaction. The cross sections are reproduced in fine steps of incident neutron energy with 0.01MeV intervals with their corresponding errors. The recommended cross sections for available experimental data taken from EXFOR library have been calculated for all the considered neutron induced reactions for U-238 isotopes. The calculated results are analyzed and compared with the experimental data. The optimized optical potential model parameters give a very good agreement with the experimental data over the energy range 0.001-20MeV for neutron induced cross section reactions (n,f), (n,tot), (n,el), (n,inl), (n,2n), (n,3n), and (n,γ) for spherical U-238 target elements.

An Investigation of 4He+12C and 4He+16O Reactions Using the Cluster Model

The α-target semimicroscopic single folding potentials have been derived by folding a composite (repulsive and attractive) effective α-α interaction with the α-cluster distribution density in the target nuclei. The obtained potentials are considered as the real part of the nuclear optical model potentials, while the imaginary parts are phenomenologicaly expressed using the Woods—Saxon form. Nine sets of measured experimental data of the 4He+12C and 4He+16O elastic rainbow scattering over the energy range 80–240 MeV are analyzed using the obtained potentials. The data are successfully reproduced using the extracted potentials. The resulted reaction cross sections are also investigated and compared with the available corresponding data.

Dispersion relations in the nuclear optical model

We have developed a code to calculate integrals arising from the dispersion relation between the real and the imaginary parts of the nuclear optical model potential (OMP). Both, analytical solution for the most common dispersive OMP, and the general numerical solution, are included. In the numerical integration, fast convergence is achieved by means of the Gauss–Legendre integration method, which offers accuracy, easiness of implementation and generality for dispersive optical model calculations. The numerical method is validated versus analytical solution. The use of this package in the OMP parameter search codes allows for an efficient and accurate dispersive analysis.

Microscopic nucleon optical model potential at low energies

Nuclear optical model potentials at low energies have been computed utilizing the two (Micro I and Micro II) versions of the microscopic optical model of Jeukenne et al. A comparison has been made of the experimental nucleon-nucleus interaction data for $E<10$ MeV with the theoretical predictions obtained using the microscopic optical model.NUCLEAR REACTIONS Microscopic nucleon optical model potential at low energies; comparison of neutron and proton data with the theoretical predictions.

General properties of energy independent nuclear optical model potentials

An energy independent optical potential for nucleon-nucleus scattering is formally derived. A simple relation between energy dependent and energy independent potentials is established showing that the latter has the same thresholds as the former. A generalized dispersion relation for energy independent potentials is found and compared to the conventional dispersion relation of the generalized energy dependent optical potentials.

Fusion Cross Section in Terms of the Nuclear Optical Model Potential

A definition for the fusion cross section is proposed in terms of the optical model potential by assuming that fusion is ascribed to its short-ranged imaginary component with a sharp edge. Two examples are given to show that the definition proposed here is useful in reproducing the observed fusion cross sections.

Theory of Energy-Independent Nuclear Optical-Model Potentials

With use of an equation-of-motion approach, a new microscopic theory of the nuclear optical-model potential which is explicitly energy independent has been derived. This theory suggests the possibility of replacing a wide range of conventional energy-dependent optical-model potentials by a single, energy-independent but nonlocal, optical-model potential.

Nuclear optical model potential in the Λ10 approximation

The complex mass operator is calculated in the framework of the Λ 10 theory using a nonlocal separable central potential. The imaginary part of the on-shell and of the off-shell mass operators is found to be sensitive to off-shell effects and to differ from those derived from the Λ 00 approximation.

Symmetry energies of nuclear matter and the spin and isospin dependence of the nuclear single-particle potential in the Landau theory

The spin and spin-isospin symmetry energies of nuclear matter and the spin and isospin dependent terms of the nuclear single-particle potential at the Fermi surface are calculated within the frame of the Landau theory of the normal Fermi liquid from the existing sets of the Landau parameters. The possibility of the relation of these parameters to the experimental energies of certain collective nuclear excited states is pointed out. The results are also applied to the calculation of the symmetry and the spin-spin terms in the low energy nuclear optical model potential.

The spin and isospin dependence of the imaginary part of the nuclear optical model potential

The spin and isospin dependent terms of the imaginary part of the medium and high energy nuclear optical model potential for infinite nuclear matter are calculated using the approximation which includes some of the exclusion principle and dispersion effects of the medium. Numerical results are obtained with the Livermore phase parameters and applied to finite nuclei using the local density approximation.

Evidence for energy dependence in the isospin dependent part of the nuclear optical model potential

Angular distributions and the excitation function of the total cross section for the 208Pb(p, n) charge exchange reaction are fitted with DWBA calculations. Isospin potentials which have the relative real volume and surface imaginary strengths found in the optical model studies of Becchetti and Greenlees provide adequate fits to the angular distributions. The excitation function indicates a strong energy dependence in the strength of the isospin potential.

Average nuclear properties

A generalized treatment of average nuclear properties is presented. The theory is developed on two levels: First a refinement of the Liquid Drop Model, called the Droplet Model, is described. The degrees of freedom in this model, in addition to the usual shape variables, are variables specifying deviations from uniformity of the neutron and proton densities. The form of the Hamiltonian defining the Droplet Model, of which only the potential energy part is considered in this paper, is derived by expanding the volume, surface, and Coulomb energies in Taylor series around the standard Liquid Drop Model values. Such an expansion, designed to retain all terms in the total energy up to order A 1 3 , I 2A 2 3 , and I 4 A, where I = (N − Z) A , turns out to contain eleven parameters, two of which may be eliminated. Four of the resulting nine parameters are the standard adjustable parameters of the Liquid Drop Model and five are new coefficients specifying various properties of nuclear systems. (Nuclear compressibility and the curvature correction to the surface tension are two examples.) Minimizing the Droplet Model potential energy with respect to density variations leads to equations, in closed form, specifying the separate neutron and proton radii and the density nonuniformities. The minimized energy expression leads to a refined Droplet Model Mass Formula with nine parameters. The second level at which average nuclear properties are treated is based on assuming a concrete model of a two-component saturating system, consisting of neutrons and protons interacting by velocity-dependent Yukawa forces (and Coulomb forces). When this model is treated in the Thomas-Fermi approximation a pair of coupled integral equations results, which can be used as the basis of a self-contained model of all average static nuclear properties. The solutions of these equations are discussed in the idealized situations of nuclear matter and semi-infinite nuclear matter, and for finite nuclei both with and without Coulomb energy. One result of these studies is the determination of the values of the five new Droplet Model parameters. Other results have to do with the nuclear density distributions, and the binding energies. The applications of the Droplet Model and Thomas-Fermi Model discussed in this paper include predictions concerning neutron and proton radii (in particular the presence of a neutron skin), the isotope effect in proton radii, the compression of the nucleus by the surface tension and the dilatation by the Coulomb energy, and the central depression in the densities caused by the Coulomb repulsion. Calculations are made for the surface curvature correction, for the surface symmetry energy, and for a modification to the volume symmetry energy at a large neutron excess. A revised estimate is made for the value of the symmetry energy of nuclear matter. Also treated is the question of whether or not neutron matter is bound, and some discussion is given of the spatial distribution, the energy dependence, and the composition dependence to be expected for nuclear optical model potentials on the basis of the statistical methods used in this paper.

A semi-phenomenological nuclear optical-model potential

A new semi-phenomenological form of the nuclear optical-model potential for the description of the average elastic scattering of nucleons is proposed. It consists of an energy-independent, nonlocal “single-particle” term and a sum of energy-dependent, factorable terms exhibiting “intermediate structure”.