Paris Potential Research Articles

APPLICATION OF THE NEW B3Y-FETAL POTENTIAL IN THE SEMI-MICROSCOPIC ANALYSIS OF THE SCATTERING OF ACCELERATED 6LI - LITHIUM AND 16O - OXYGEN NUCLEI FROM THE 12C - CARBON NUCLEUS

The phenomenological and semi-microscopic values of the potentials found in the angular distribution of scattering of ions 6Li -lithium, 16О -oxygen from the target nucleus 12C-carbon accelerated at low energies are determined.The experimental data of elastic scattering were analyzed based on the optical model and the doublefolding model.Based on the folding model, the density-dependent new Fetal potential of Yukawa 3 terms of effective nucleon-nucleon interactions was first used. The density-dependent Fetal, Paris, Reid microfolding potentials were constructed in the doublefolding model as a real part of the optical potential. The efficacy of the new Fetal micropotential at laboratory energies of 28 MeV and 30 Mev for the 16О+12С nuclear system was studied in comparison with the Reid, Paris variants. The efficacy of the new Fetal potential at laboratory energies of 12.3 MeV and 20 MeV for the 6Li+12Csystem has been studied in comparison with Reid and Paris potentials. The relative errors of phenomenological theoretical analysis and experimental cross-sections were determined in the range of 1.1 -3.0. As a result of semimicroscopic analysis, the coefficients of renormalization of folding potentials in the range Nr=0.8-1.0 were determined. The data obtained will be used in various fundamental research, in particular in future thermonuclear installations and nuclear astrophysics

Attractive Spin-Orbit Potential from the Skyrme Model.

We derive the nucleon-nucleon isoscalar spin-orbit potential from the Skyrme model and find good agreement with the Paris potential. This solves a problem that has been open for more than 30years and gives a new geometric understanding of the spin-orbit force. Our calculation is based on the dipole approximation to skyrmion dynamics and higher order perturbation theory.

Approximation of scattering phases for Argonne v18 potential

Purpose. This article is dedicated to the study of phase shifts for single-channel neutron-proton scattering. The phase shifts, which are obtained in the variable phase approach, are studied. For the approximation of phase shifts, a function — 2019 is used in the form of a known formula for a parabolic-type quadratic function y(x)=a+bx+cx2 , which was proposed by M.A. Dolgopolov, L.A. Minin and V.A. Rabotkin in the study of phase shifts for the Paris potential. It is necessary to find the coefficients a, b, c for y(x) when approximating the np- scattering phases for the Argonne v18 potential. Methods. Approximation is used to find the coefficients of the function y(x). Find the optimal values of the coefficients a, b, c at a minimum value χ 2 . Results. An approximation of the neutron-proton scattering phases obtained by various methods for the phenomenological nucleon-nucleon potential Argonne v18 was made. The calculated coefficients of this function obtained for phase shifts by means of the variable phase approach are compared with the results of the approximation of the scattering phases from the original paper. For illustration graphs are given for phase shifts for four spin states for the np- system ( 1S0, 3P1, 1D2, 3D2). Conclusions. The obtained coefficients for the function y(x) can be used to calculate the values of the scalar scattering amplitude, the full cross-section and the partial scattering amplitude for any phase value within the energy interval for the approximation carried out. In next studies one can obtain and compare the coefficients and parameters of approximation for scattering phases for other modern phenomenological nucleon-nucleon potentials. Keywords: variable phase approach, nucleon-nucleon scattering, approximation, phase shifts, Arg

Spin observables of (d,p) reactions off $^{12}$C within the Paris potential

Deuteron elastic scattering off $^{12}$C is described in the framework of three-body Faddeev-type equations. Analyzing powers are calculated using the PEST16 potential which is a separable rank-one representation of the Paris potential. Satisfactory agreement with the experimental data is found.

Prediction of Alpha Decay Half-Lives of Z = 118–121 Superheavy Nuclei with A ≤ 300 by Using the Double-Folding Potential

Abstract The alpha decay half-lives of Z = 118–121 superheavy nuclei with A ≤ 300 are calculated by using the density-dependent nuclear potential in the framework of the WKB method. The Paris and Ried M3Y nucleon-nucleon potentials are used in the calculation of the double-folding potential, which the Paris potential predicts to be the larger value of the half-lives. The obtained half-lives with Paris parameterisation are compared with those using three semi-empirical formulas, namely the improved Sahu formula, the universal decay law for alpha decay, and the formula for both alpha decay and cluster decay. The predicted half-lives with double-folding lie in between the improved Sahu and universal decay law formulas for both alpha and cluster decay. However, it is closer to the universal decay law formula and obeys its trend in all the studied superheavy nuclei.

Approximation properties of the Paris potential of nucleon–nucleon interaction

The phenomenological Paris potential of nucleon–nucleon interaction is analyzed in terms of the independence of the coefficients of various components. Analysis of the determinant of the Gram matrix reveals the extremely high dependences of the coefficients, demanding a revision of the system of basic functions.

Two-photon exchange in electron-trinucleon elastic scattering

We discuss two-photon exchange (TPE) in elastic electron scattering off the trinucleon systems, 3He and 3H. The calculations are done in the semirelativistic approximation with the trinucleon wave functions obtained with the Paris and CD-Bonn nucleon-nucleon potentials. An applicability area of the model is wide enough and includes the main part of kinematical domain where experimental data exist. All three TPE amplitudes (generalized form factors) for electron 3He elastic scattering are calculated. We find that the TPE amplitudes are few times more significant in the scattring of electrons off 3He then in the electron proton scattering.

In search of baryonium

Recent experimental hints of the existence of nucleon-antinucleon quasi-bound states are presented and discussed. One, very broad and weakly bound S wave state is indicated in two decay modes of the J/Ψ meson. It finds additional support in the level widths measured in light antiprotonic atoms. Another, a narrow P-wave state, is found instrumental in the understanding of several results obtained in heavy antiprotonic atoms. Both states have a natural explanation in a fairly traditional Paris potential model of the NN̄ interactions.

Three-BodypdScattering with a Possible Long-Range Force

The nucleon-nucleon (NN) phase shifts are represented by using a hybrid potential which is composed a short range potential of mesonic origin and a possible long range potential where the short range σ-meson potential is replaced by a Van der Waals (VW)-type potential. Therefore, “the on-shell equivalent but off-shell different” hybrid NN potentials are characterized by only two or four parameters instead of the original σ-meson potential. These potentials are used to calculate pd elastic scattering and to compare with that of the Paris (PEST) potential. Since the hybrid potential needs a longer numerical calculation time due to slower Padé convergence, we utilized only ten single channel hybrid potentials together with four coupled-channel short-range PEST potentials for the pd calculation. The pd results seem to be unreasonable in fitting the short range case, although it is not a complete calculation. In spite of using such hybrid off-shell different potentials only for 1S0 and 3P0 -states plus the short range NN for the other states, the pd differential cross section could well represent the short range potential results except in the minimam cross section region.

The microscopic pairing gap in a slab of nuclear matter for the Argonne v 18NN-potential

Ab initio gap equation for 1S 0 pairing in a nuclear slab is solved for the Argonne v 18 NN-potential. The gap function is compared in detail with the one found previously for the separable form of the Paris potential. The difference between the two gaps turned out to be about 10%. Dependence of the gap on the chemical potential μ is analyzed.

Constructing effective nucleon-nucleon interaction on the basis of the Idaho potential

An effective nucleon-nucleon interaction at an energy of 200 MeV is constructed for the Idaho nucleon-nucleon potential obtained on the basis of the theory of spontaneous chiral-symmetry breaking. This interaction approximates the nonlocal t matrix obtained for free nucleon-nucleon scattering from a solution to the Lippmann-Schwinger equation for the Idaho potential. The exact and approximated t matrices for the Paris potential, Idaho potential, and the von Geramb Hamburg potential are compared. The effective potential obtained in the way outlined above is used to calculate the inelastic scattering of 200-MeV polarized protons that is accompanied by the excitation of the 2+ level at 4.44 MeV and the 1+ level at 15.11 MeV in the 12C nucleus and the 6− level at 14.1 MeV in the 28Si nucleus. The results are compared with the results of the calculations on the basis of the Paris potential.

Effective pairing interaction for the Argonne nucleon-nucleon potential v18

The effective pairing interaction corresponding to the Argonne nucleon-nucleon potential v18 is found within the local potential approximation for several values of the boundary energy E 0 that specifies the model subspace S 0. A detailed comparison with the analogous effective interaction calculated previously for the Paris nucleon-nucleon potential is performed. It is shown that the effective interactions obtained for the two different nucleon-nucleon potentials at the same value of E 0 are very close to each other. In the case of the Paris potential, a very wide subspace S′ complementary to S 0 was required in calculating the effective interaction (the corresponding cutoff momentum being k max = 160−180 fm−1), whereas a much narrower subspace S′ corresponding to k max = 10−12 fm−1 could be used in the case of the Argonne potential.

Binding of charmonium with two- and three-body nuclei

The energies of the η c – d and η c – 3He bound states are calculated by using genuine three- and four-body scattering equations. For the NN interaction the separable version of the Paris potential is used. For the η c N interaction we adopted a local Yukawa-type potential which is expanded into a series of separable potentials by means of the unitary pole approximation method. The results are compared with earlier calculations.

Solution of the microscopic gap equation for a slab of nuclear matter with the Paris NN-potential

The gap equation in the S 0 1 -channel is solved for a nuclear slab with the separable form of the Paris potential. The gap equation is considered in the model space in terms of the effective pairing interaction which is found in the complementary subspace. The absolute value of the gap Δ turned out to be very sensitive to the cutoff K max in the momentum space in the equation for the effective interaction. It is necessary to take K max = 160 – 180 fm −1 to guarantee 1% accuracy for Δ. The gap equation itself is solved directly, without any additional approximations. The solution reveals the surface enhancement of the gap Δ which was earlier found with an approximate consideration. A strong surface-volume interplay was found also implying a kind of the proximity effect. The diagonal matrix elements of Δ turned out to be rather close to the empirical values for heavy atomic nuclei.

Analysis of light nuclei with the AMD method

The AMD simulation for light nuclei with realistic potentials, e.g. the Paris potential, is investigated. The results are in qualitatively good agreement with nuclear ground state energies. The framework provides a powerful tool for studying the structure of nuclei.

NN interaction derived from the Nambu–Jona-Lasinio model

The nucleon–nucleon potential is calculated within the Nambu–Jona-Lasinio (NJL) model. The effect of the quark–meson coupling constant, g, on the energy per baryon in quark matter, medium quark mass, medium pion and sigma meson masses and finally on the nucleon–nucleon potential is investigated. It is found that the potential obtained is attractive and the attraction raises with increasing coupling constant g, due to the increases in the scalar interaction. The medium and long range parts of the potential are well reproduced with g=4.6, where a better agreement with the phenomenological Paris potential is obtained. When the short range part is added to the NJL potential, through the one gluon exchange potential, the potential obtained exhibits all the qualitative features of the distance-dependence of the nucleon–nucleon interaction viz., a repulsive soft core followed by an attractive part at the right positions.

Variational Method for Infinite Nuclear Matter with the Paris Potential

The energy per nucleon for infinite nuclear matter with the parametrized Paris potential is calculated using the variational method recently proposed by Takano and Yamada. Approximate energy expressions playing an important role in this variational method are refined for the Paris potential, and in particular for the quadratic momentum parts in it. Since this variational method without any constraints gives extreme overbinding, an effective theory also proposed in conjunction with the above-mentioned variational method is applied, in a modified manner, to the calculations for symmetric nuclear matter and neutron matter with the Paris potential, as well as the Hamada-Johnston and AV14 potentials. The obtained equation of state (EOS)for the Paris potential is, unlike the unrealistically soft EOS for the AV14 potential, capable of describing neutron stars with a reasonable maximum mass of 1.65 M� .

Dynamical Study of $^1\hbox {H}(\vec {d},{\gamma})^3\hbox {He}$ Tensor Observables in the Energy Range of 80 keV to 95 MeV: Tests of Effective Two-Body Models

Realistic interactions are used to study \(\) tensor observables in the energy range of 80 keV to 95 MeV deuteron laboratory energy, as well as the differential cross section for the two-body photodisintegration of \(\). The Siegert form of the E1 multipole operator in the long-wavelength limit is taken as the sole component of the electromagnetic interaction. The three-body Faddeev equations for the bound-state and continuum wave functions are solved using the Paris, Argonne V14, Bonn-A, and Bonn-B potentials. The corresponding nucleon-nucleon t-matrices are represented in a separable form using the Ernst-Shakin-Thaler representation. The Coulomb force between protons is neglected and no three-nucleon force is included. The contribution of nucleon-nucleon P-wave components to the observables is carefully studied, not only in the angular distribution of the observables, but also as a function of the deuteron laboratory energy for fixed centre-of-mass angle. Comparison with data is shown wherever it exists.

Duration and nonlocality of a nucleon-nucleon collision

For a set of realistic nucleon-nucleon potentials we evaluate microscopic parameters of binary collisions: a time duration of the scattering state, a mean distance and a rotation of nucleons during a collision. These parameters enter the kinetic equation as non-instantaneous and non-local corrections of the scattering integral, i.e., they can be experimentally tested. Being proportional to off-shell derivatives of the scattering T-matrix, non-instantaneous and non-local corrections make it possible to compare the off-shell behavior of different potentials in a vicinity of the energy shell. The Bonn one-Boson-exchange (A-C) and Paris potentials are found to yield very close results, while the separable Paris potential differs.

Calculation of Proton-Deuteron Elastic Scattering at 10 MeV with a Realistic Potential

We present the first results of a calculation of the differential cross section and of polarization observables for proton-deuteron elastic scattering at 10 MeV proton laboratory energy, for the Paris potential. The method used is the ``screening and renormalization approach'' which allows one to correctly take into account the Coulomb repulsion between the two protons. Comparison is made with the precise experimental data of Sagara et al. [Phys. Rev. C 50, 576 (1994)] and of Sperison et al. [Nucl. Phys. A422, 81 (1984)].