Paris Nucleon-nucleon Potential Research Articles

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.

Momentum distribution of nucleons in the deuteron on the basis of the Moscow potential

Themomentum distribution of nucleons in the deuteron is calculated for the Moscow and Paris nucleon-nucleon potentials. It is shown that the Moscow potential provides a better description of the distribution deduced from data on the reaction d(e, e′p)n in the region close to the kinematical region of quasielastic proton knockout.

Testing effective nucleon-nucleon forces to describe diagonal spin-transfer coefficients for the scattering of polarized protons with the excitation of the 1+ levels in 12C

The diagonal coefficients of spin-transfer Dii in the small-angle inelastic scattering of polarized protons with the excitation of the two lowest 1+ levels in 12C are analyzed. The isoscalar (T = 0, E* = 12.71MeV) and isovector (T = 1, E* = 15.11 MeV) transitions are considered. The coefficients Dii are calculated within DWBA using different effective nucleon-nucleon (NN) interactions between an incident proton and the nucleons of the nucleus. We consider the Franey-Love interaction and the Geramb effective interactions based on the Paris NN potential, and also the effective NN potential based on the chiral perturbation theory, etc. The impact of the wave function antisymmetrization is studied from the coefficients Dii in a system that includes a projectile and nucleons of the nucleus, along with the impact of other effects.

7D-folding integral in a density-dependent microscopic optical model potential for nucleon-nucleus scattering

Microscopic optical model potentials, based on density-dependent effective interactions, involve multidimensional integrals to account for the full Fermi motion of the target struck nucleon throughout the nucleus. If a spherical matter distribution is assumed, then each matrix element of the optical potential requires the evaluation of seven-dimensional integrals. In this work we provide a full account of these integrals, retaining the genuine off-shell structure of the nucleon-nucleon effective interaction. The evaluation is based on the asymptotic separation of the optical model potential for nucleon-nucleus scattering in momentum space, where the potential is split into a free $t$-matrix contribution and another which depends exclusively on the gradient of the density-dependent $g$ matrix. The calculated potentials, based on the Paris nucleon-nucleon ($NN$) potential, are applied to proton elastic scattering from ${}^{16}$O and ${}^{90}$Zr at beam energies between 30 and 65 MeV. The results were compared with two approximations to the unabridged expression, revealing moderate differences among their scattering observables. When comparing with results based on the Argonne ${v}_{18}$ $NN$potential, these differences appear smaller than those attainable by the choice of the internucleon potential.

ParisNN¯potential constrained by recent antiprotonic-atom data andn¯ptotal cross sections

We report on an updated optical Paris nucleon-antinucleon potential. The long- and intermediate-range parts are obtained by G-parity transformation of the Paris nucleon-nucleon potential based on a theoretical dispersion-relation treatment of the correlated and uncorrelated two-pion exchange. The parametrized real and imaginary short range parts are determined by fitting not only the existing experimental data included in the 1999 version of the Paris nucleon-antinucleon potential, but also the recent antiprotonic-hydrogen data and antineutron-proton total cross sections. The description of the experimental observables is improved. Only this readjusted potential generates an isospin zero 1S0, 52 MeV broad quasi-bound state at 4.8 MeV below the threshold. Recent BES data on J/psi decays could support the existence of such a state.

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.

Chemical-potential dependence of the pairing gap in a nuclear-matter slab

The equation for the pairing gap {delta} in a slab of nuclear matter governed by the Paris nucleon-nucleon potential is solved for various values of the chemical potential {mu} in the range from -8 MeV, which corresponds to stable nuclei, to -0.1 MeV, which corresponds to nuclei in the vicinity of the nucleon drip line. The slab is placed in a one-dimensional Woods-Saxon potential whose parameters are set to values typical of nuclei. Two models are considered. In the first, the potential-well depth is fixed at U{sub 0} = -50 MeV, the density within the slab growing as vertical bar {mu} vertical bar is reduced. In the second model, the density is fixed at the center of the slab, vertical bar U{sub 0} vertical bar decreasing as vertical bar {mu} vertical bar is reduced. The behavior of the gap {delta} as a function of {mu} is model-dependent. In the first model, {delta} decreases with decreasing vertical bar {mu} vertical bar , while, in the second, it increases. At the same time, the effect of the surface enhancement of {delta} becomes more pronounced with decreasing vertical bar {mu} vertical bar in both models.

Approximation of the microscopic effective pairing interaction by the off-shell T matrix for free nucleon-nucleon scattering

The effective pairing interaction in the 1S0 channel as calculated microscopically within the Brueckner method for a planar slab of nuclear matter by using the separable version of the Paris nucleon-nucleon potential is investigated. The effective interaction is determined for the model space including all negative-energy single-particle states. An analysis is performed for two values of the chemical potential, μ=−8 and −4 MeV. It is shown that, to a high precision, the effective interaction can be approximated by the off-shell T matrix for free nucleon-nucleon interaction, the T matrix in question being taken at a negative value of the total energy of two nucleons E=2μ.

Generalized folding model for elastic and inelastic nucleus–nucleus scattering using realistic density dependent nucleon–nucleon interaction

A generalized double-folding model for elastic and inelastic nucleus–nucleus scattering is presented. It is designed to accommodate effective nucleon–nucleon (NN) interactions that depend upon the density of nuclear matter in which the two nucleons are immersed. A recently parametrized density dependent M3Y interaction, based on the G-matrix elements of the Paris NN potential, has been used in the present folding calculation. The effects of knock-on exchange of the interacting nucleon pair are included in an accurate local approximation. Examples of the application of this model to study the refractive elastic and inelastic scattering data of 12 C+ 12 C and α+ 58,60Ni systems are presented. A detailed comparison of the use of deformed optical potential (DP) and microscopic folded potential in the analysis of inelastic scattering has shown that the use of DP fails to reproduce the inelastic 12 C+ 12 C scattering data measured over a wide angular range, which covers both the diffractive and refractive regions. The use of the DP model also significantly underestimates the nuclear deformation lengths of the quadrupole and octupole excitations under study.

Microscopic calculation of a pairing gap in semi-infinite nuclear matter

The pairing gap in semi-infinite nuclear matter has been calculated microscopically by solving the gap equation for a nonlocal interaction with the aid of the method proposed by V.A. Khodel, A.V. Khodel, and J.W. Clark [Nucl. Phys. A 598, 390 (1996)] for the case of infinite nuclear matter. The calculation employs the effective pairing interaction obtained previously for semi-infinite geometry on the basis of the separable 3×3 representation of the Paris nucleon-nucleon potential. The gap found in this way changes sharply in the surface region, where it has a pronounced maximum. The dependence of the surface effect on the chemical potential of nuclear matter has been investigated.

Level structure of120Sn:High resolution(p,t)reaction and shell model description

The $(p,t)$ reaction on ${}^{122}\mathrm{Sn}$ has been studied in a high resolution experiment at an incident proton energy of 26 MeV. The cross section angular distributions for transitions to 38 levels of ${}^{120}\mathrm{Sn}$ with an excitation energy up to $\ensuremath{\sim}3500\mathrm{keV}$ have been measured. Distorted wave Born approximation analysis of experimental angular distributions using double-folded potential for the exit channel has been done. This has made it possible to confirm previous spin and parity values and to propose new assignments for a large number of states. A shell-model study of ${}^{120}\mathrm{Sn}$ has been performed using a realistic effective interaction derived from the Paris nucleon-nucleon potential. The calculations have been carried out within the framework of the seniority scheme including states with seniority up to 4. Comparison of the calculated and experimental spectra shows a one-to-one correspondence between levels up to about 2.7 MeV excitation energy and lends support to some of the spin-parity assignments given in this work.

Final state interaction effects inμ-capture induced two-body decay of3He

The $\ensuremath{\mu}$-capture process on ${}^{3}\mathrm{He}$ leading to a neutron, a deuteron, and a $\ensuremath{\mu}$-neutrino in the final state is studied. Three-nucleon Faddeev wave functions for the initial ${}^{3}\mathrm{He}$ bound and the final neutron-deuteron scattering states are calculated using the Bonn B and Paris nucleon-nucleon potentials. The nuclear weak current operator is restricted to the impulse approximation. Large effects on the decay rates of the final state interaction are found. The comparison to recent experimental data shows that the inclusion of final state interactions drastically improves the description of the data.

3He(d,p) 4He reaction calculation with three-body Faddeev equations

In order to investigate the 3He-n-p system as a three-body problem, we have formulated 3He-n and 3H-p effective potentials using both a microscopic treatment and a phenomenological approach. In the microscopic treatment, potentials are generated by means of the resonating group method (RGM) based on the Minnesota nucleon-nucleon potential. These potentials are converted into separable form by means of the Microscopic Pauli Correct (MPC) method. The MPC potentials are properly formulated to avoid Pauli forbidden states. The phenomenological potentials are obtained by modifying parameters of the EST approximation to the Paris nucleon-nucleon potential, such that they fit the low-energy 3He-n, 3H-p, and 3He-p phase shifts. Therefore, they describe the 3He-n differential cross section, the polarization observables, and the energy levels of 4He. The 3He-n-p Faddeev equations are solved numerically. We reproduce correctly the ground state and the first excited state of 5Li. Furthermore, the Paris-type potential is used to investigate the 3He(d,p) 4He reaction at a deuteron bombarding energy of 270 MeV, where the system is treated as a three-body problem. Results for the polarized and unpolarized differential cross sections demonstrate convergence of the Born series.

Parametrization of the scattering wave functions of the Paris potential

The neutron-proton scattering wave functions of the Paris nucleon-nucleon potential are parametrized for partial waves of total angular momenta less than 5 at laboratory kinetic energies between 0 MeV and 400 MeV. The inner parts of the wave functions are approximated by polynomials with a continuous transition to the outer parts, which are given by the asymptotic regime and determined by the respective phase shifts. The smooth variation in energy of the phase shifts and of the coefficients of the polynomials permits a further parametrization of these quantities in terms of polynomials of low degree. The scattering wave functions can then be calculated at any given energy below 400 MeV. Special attention is devoted to the zero-energy limit of the low partial waves. An easy-to-use FORTRAN program, which allows the user to calculate these parametrized wave functions, is available via electronic mail.

Nuclear structure calculations with realistic effective interactions

In this paper, we present some results of realistic shell-model calculations for the Sn isotopes and the N=82 isotones. As regards the former nuclei, we focus attention on the light even isotopes, 102,104,106Sn. The calculations are performed by making use of two realistic effective interactions derived from the Bonn A and Paris nucleon-nucleon potentials, respectively. From the comparison of the calculated spectra with the experimental ones it turns out that the best agreement is obtained with the weaker tensor force potential (Bonn A). For the N=82 isotones, we study the behavior of the energy of some low-lying states in the nuclei with A ranging from 134 to 148. In this case, only the results obtained by using the Bonn potential are reported. The agreement between theory and experiment is quite satisfactory for all of the considered nuclei. This evidences the merit of modern realistic interactions in nuclear structure calculations.

Realistic shell-model calculations for neutron deficient Sn isotopes.

We have performed shell-model calculations for $^{102,103,104,105}\mathrm{Sn}$ using two realistic effective interactions derived from the Bonn A and Paris nucleon-nucleon potentials, respectively. From the comparison of the calculated spectra of $^{104}\mathrm{Sn}$ and $^{105}\mathrm{Sn}$ with the experimental ones it turns out that the best agreement is obtained with the weaker tensor force potential (Bonn A). This agreement appears to be significantly better than for other nuclear regions, such as the sd shell, and thus encourages use of modern realistic potentials in shell-model calculations for medium- and heavy-mass nuclei. In addition, it supports confidence in our predictions of the spectra of the hitherto unknown isotopes $^{102}\mathrm{Sn}$ and $^{103}\mathrm{Sn}$. \textcopyright{} 1996 The American Physical Society.

Complete 0ℏgw shell model Monte Carlo calculations of 94Ru, 96Pd, 96,98Cd and 100Sn

We perform shell model Monte Carlo calculations for nuclei in the 100Sn region within the complete 0 g-1 d-2 s oscillator shell using an effective interaction derived from the Paris nucleon-nucleon potential. We find good agreement with empirically calculated masses, and reproduce the observed quenching of the total Gamow-Teller strengths in this mass region. The Gamow-Teller strength in 100Sn is predicted to be nearly a factor of 3 smaller than the single particle estimate.

Equation of state for cold nuclear matter from refractive 16O+16O elastic scattering.

The nuclear density overlap, which occurs during refractive heavy-ion scattering, opens an alternative approach to study the equation of state (EOS) for cold nuclear matter. For this purpose elastic [sup 16]O+[sup 16]O scattering at incident enegies of 145, 250, 350, and 480 MeV has been measured very accurately, up to large angles. A systematic folding analysis of these data has been performed using an effective density dependent interaction based on the [ital G]-matrix elements of the Paris nucleon-nucleon potential. We find, with the observed refractive scattering patterns, that a soft EOS (with the nuclear incompressibility [ital K] around 200 MeV) is the most realistic one.

Energy Dependence of the πN Amplitude and the Three-Nucleon Interaction

By calculating the contribution of the $\pi-\pi$ three-body force to the three-nucleon binding energy in terms of the $\pi N$ amplitude using perturbation theory, we are able to determine the importance of the energy dependence and the contribution of the different partial waves of the $\pi N$ amplitude to the three-nucleon force. A separable representation of the non-pole $\pi N$ amplitude allows us to write the three-nucleon force in terms of the amplitude for $NN\rightarrow NN^*$, propagation of the $NNN^*$ system, and the amplitude for $NN^*\rightarrow NN$, with $N^*$ being the $\pi N$ quasi-particle amplitude in a given state. The division of the $\pi N$ amplitude into a pole and non-pole gives a procedure for the determination of the $\pi NN$ form factor within the model. The total contribution of the three-body force to the binding energy of the triton for the separable approximation to the Paris nucleon-nucleon potential (PEST) is found to be very small mainly as a result of the energy dependence of the $\pi N$ amplitude, the cancellation between the $S$- and $P$-wave $\pi N$ amplitudes, and the soft $\pi NN$ form factor.

Binding effects in proton-nucleus elastic scattering.

The effects of the struck nucleon-core binding potential on the first-order term of the Kerman, McManus, and Thaler (KMT) expansion of the nucleon-nucleus optical potential are calculated for the elastic scattering of protons from $^{16}\mathrm{O}$ at 200 MeV. The binding effects are expressed as a momentum-transfer-dependent energy shift in the off-shell nucleon-nucleon t matrix. Numerical results are based on the Paris nucleon-nucleon potential together with both harmonic oscillator or Woods-Saxon single-particle wave functions for the target. The calculations show that these binding effects introduce only small corrections to the optical potential and calculated observables in the intermediate energy region when compared with the impulse approximation.