Realistic Two-nucleon Potentials Research Articles

Non-monotonic potential description of alpha-40Carefractive elastic scattering

Experimental differential cross sections of elastic scattering by 40Ca, over a wide range of incident energies, have been analyzed in terms of non-monotonic (NM) potentials, generated from the energy density functional (EDF) theory using a realistic two-nucleon potential coupled with an appropriate consideration of the Pauli principle. The Airy structure of the nuclear rainbow scattering data in the energy range of 36.1–42.6 MeV is well accounted for the first time by the shallow NM potential.

Radiative pion capture in 2H, 3He and 3H

We investigate the π– + 2H → γ + n + n, π– + 3He → γ + 3H, π– + 3He → γ + n + d, π– + 3He → γ + n + n + p and π– + 3H → γ + n + n + n capture reactions using realistic two-nucleon and three-nucleon potentials and the single nucleon Kroll-Ruderman-type transition operator. We obtain predictions for the total capture rates for all these processes, calculating rigorously the initial and final nuclear states.

Four-body calculation of H2(d,p)H3 and H2(d,n)He3 reactions above breakup threshold

Nucleon transfer reactions in deuteron-deuteron collisions at energies above the three- and four-body breakup threshold are described using exact four-body equations for transition operators that are solved in the momentum-space framework. Differential cross sections, analyzing powers, polarizations, and spin transfer coefficients are obtained using realistic two-nucleon potentials and including the Coulomb repulsion between protons. Overall good agreement between predictions and experimental data is found. Most remarkable discrepancies are seen around the minima of the differential cross section at higher energies and in the outgoing nucleon polarization at lower energies.

Large-scale shell-model study of the Sn isotopes

We summarize the results of an extensive study of the structure of the Sn isotopes using a large shell-model space and effective interactions evaluated from realistic two-nucleon potentials. For a fuller account, see ref. [1].

Large-scale shell-model study of the Sn isotopes

We summarize the results of an extensive study of the structure of the Sn isotopes using a large shell-model space and effective interactions evaluated from realistic two-nucleon potentials. For a fuller account, see ref. [1].

Non-monotonic potential description of alpha–Zr refractive elastic scattering

Experimental differential cross sections of α elastic scattering by 90Zr in the 15.0–141.7 MeV range of the bombarding energies have been analysed within the framework of an optical model using non-monotonic (NM) potentials. These potentials are generated from the energy-density functional theory using a realistic two-nucleon potential coupled with an appropriate consideration of the Pauli principle. The NM nature of the real part of the potential seems to be gradually diminishing at energies beyond 118.0 MeV. The Airy structure of the nuclear rainbow scattering data in the energy range of 79.5–141.7 MeV is for the first time well accounted for by the shallow NM potential. Two potential families, which are located in the real part, bear a linear variation of a volume integral in the energy range 25.0–141.7 MeV with a threshold anomaly at the lower energies. The potential contains an interior repulsive part that, with energy, shifts towards the surface and gradually weakens until it is almost lost in the nuclear surface. The requirement of a deep attractive real part of the nuclear potential seems to be generally non-stringent for describing the nuclear rainbow oscillations. Some discrete ambiguities in the potentials seem to persist even when the ‘exponential falloff’ in the angular distribution following the ‘rainbow angle’ is well reproduced in this investigation using the NM real part of the optical potentials.

Non-monotonic potentials for 6Li elastic scattering at 88 MeV

This work compares the performance of the traditional phenomenological Woods–Saxon (WS) and squared WS (SWS) potentials with that of a non-monotonic (NM) potential, for 6Li elastic scattering by targets of a wide range, namely 24,25,26Mg, 27Al, 40,44Ca, 59Co, 60Ni, 197Au and 206,208Pb at an incident energy of 88 MeV. The real part of this NM potential is derived microscopically using the energy-density functional (EDF) formalism, from a realistic two-nucleon potential, that includes the Pauli principle. The experimental differential cross sections (DCSs) for the 6Li elastic scattering are well accounted for using this raw EDF-generated real part along with an empirical imaginary part, referred to as the NM-1 potential, which needs no renormalization. To make this potential more consistent in terms of the variations of the volume integrals per nucleon pair of its real part with the target mass numbers, a completely empirical NM potential, referred to as the NM-2 potential, is derived that fits the data more satisfactorily. The DCS data are also well described by the SWS and WS potentials. However, the SWS potential is found to be inconsistent in terms of the above-mentioned criterion and the NM-2 potential has an edge over all the potentials.

Potential description of 6Li elastic scattering by 28Si

This work compares the performance of traditional phenomelogical Woods-Saxon (WS) and squared WS (SWS) potentials with that of a non-monotonic (NM) potential, microscopically derived using the energy-density functional (EDF) formalism from a realistic two-nucleon potential that includes the Pauli priciple. The experimental differential cross-sections (DCS) for the 6Li elastic scattering by 28Si over the incident energies E$Li$ = 7.5-99.0 MeV are well accounted for using the NM potential without the need of renormalization. At higher energies, in the range of 135.0-318.0MeV, the EDF-generated NM potential parameters need a revision for the satisfactory description of the DCS data. The DCS data in the entire energy range of 7.5-318.0 are also well described by the WS and SWS potentials. The inclusion of a static spin-orbit potential to the NM, WS and SWS central potentials is found to reproduce the features of the vector analyzing power iT11 data at 22.8MeV reasonably well in each of the cases. However, the WS and SWS potential parameters needed to describe the DCS and iT11 data are found inconsistent in terms of the variations of the real volume integrals per nucleon pair (VJR) with the incident energy. On the other hand, the EDF-generated NM potential is found to be consistent in terms of VJR and satisfactorily accounts for the DCS data in the entire range of energies considered herein and the features of the iT11 data at 22.8MeV.

NON-MONOTONIC ALPHA- AND6Li-POTENTIALS FROM ENERGY DENSITY FUNCTIONAL FORMALISM

The present status of the α-nucleus potential, generated from the energy density functional (EDF) formalism using a realistic two-nucleon potential, which incorporates the Pauli principle, is discussed. The EDF potentials, calculated using a density distribution of α-particle that yields a binding energy of 20 MeV with a reasonable root-mean-squared radius and observed density distributions of6Li and various target nuclei, are found to be shallow and non-monotonic in character. This non-monotonic EDF potential reproduces satisfactorily the experimental elastic scattering data, particularly at energies above the Coulomb barrier. Since the elastic scattering data and the binding energies of all nuclei considered herein are well reproduced using the mean field generated from a realistic two-nucleon potential for nuclear and nucleonic matter, one may conclude to have reasonable information on the equation of states of nuclear and nucleonic matter from a very low to the saturation density from the present investigation.

Realistic two-nucleon potentials for the relativistic two-nucleon Schrödinger equation

The potentials V (v) in the nonrelativistic (relativistic) nucleon–nucleon (NN) Schrödinger equation are related by a quadratic equation. That equation is numerically solved, thus providing phase equivalent v-potentials related for instance to the high precision NN potentials, which are adjusted to NN phase shift and mixing parameters in a nonrelativistic Schrödinger equation. The relativistic NN potentials embedded in a three-nucleon (3N) system for total NN momenta different from zero are also constructed in a numerically precise manner. They enter into the relativistic interacting 3N mass operator, which is needed for relativistic 3N calculations for bound and scattering states.

ALPHA-ALPHA AND ALPHA-NUCLEUS POTENTIALS: AN ENERGY-DENSITY FUNCTIONAL APPROACH

The real parts of the alpha-alpha and alpha-nucleus potential, particularly for40,44,48Ca and58Ni targets are determined from a realistic two-nucleon potential using an energy-density functional approach and are found to be non-monotonic with a short range repulsion in their functional forms that are similar to those needed in accounting for elastic scattering data. The deduced alpha-alpha potential has no bound states and the calculated decay width of8Be of about 6.4 eV at about 200 keV energy is in agreement with the measurement.

Four-Body Calculation of Proton-He3Scattering

The four-body equations of Alt, Grassberger, and Sandhas are solved, for the first time, for proton-3He scattering including the Coulomb interaction between the three protons using the method of screening and renormalization as was done recently for proton-deuteron scattering. Various realistic two-nucleon potentials are used. Large Coulomb effects are seen on all observables. Comparison with data at different energies shows large deviations in the proton analyzing power but quite reasonable agreement in other observables. The effect of the nucleon-nucleon magnetic moment interaction and correlations between p-d and p-3He analyzing powers are studied.

Erratum: Structure of andE2transition inC16in aC14+n+nmodel [Phys. Rev. C 73, 037304 (2006)

A three-body model of $^{14}$C+n+n is applied to study the energy spectrum and the hindered $E$2 transition in $^{16}$C. A realistic two-nucleon potential is used for the valence neutrons. Both spin singlet and triplet components for the neutrons are taken into account. The three-body problem with a Pauli constraint is solved in a stochastic variational method. For the n-$^{14}$C potential chosen to reproduce the properties of $^{15}$C, the low-lying energy spectrum agrees reasonably well with experiment, but the ground state is predicted to be about 1 MeV high. The calculated $B(E2$; $2_1^+ \to 0^+_1)$ value is about twice the measured value if the polarization charge of the valence neutrons is taken to be the same as that required to fit the $^{15}$C data. The correlated motion of the valence neutrons is displayed through the two-neutron density distribution.

Structure of andE2transition inC16in aC14+n+nmodel

A three-body model of $^{14}\mathrm{C}$ $+n+n$ is applied to study the energy spectrum and the hindered E2 transition in $^{16}\mathrm{C}$. A realistic two-nucleon potential is used for the valence neutrons. Both spin-singlet and spin-triplet components for the neutrons are taken into account. The three-body problem with a Pauli constraint is solved in a stochastic variational method. For the $n\text{\ensuremath{-}}$$^{14}\mathrm{C}$ potential chosen to reproduce the properties of $^{15}\mathrm{C}$, the low-lying energy spectrum agrees reasonably well with experiment, but the ground state is predicted to be about 1 MeV high. The calculated $B(E2$; ${2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$ value is about twice the measured value if the polarization charge of the valence neutrons is taken to be the same as that required to fit the $^{15}\mathrm{C}$ data. The correlated motion of the valence neutrons is displayed through the two-neutron density distribution.

Quantum Monte Carlo Calculations of Light Nuclei

Variational Monte Carlo and Green's function Monte Carlo are powerful tools for calculations of properties of light nuclei using realistic two-nucleon and three-nucleon potentials. Recently the GFMC method has been extended to multiple states with the same quantum numbers. The combination of the Argonne v_18 two-nucleon and Illinois-2 three-nucleon potentials gives a good prediction of many energies of nuclei up to 12C. A number of other recent results are presented: comparison of binding energies with those obtained by the no-core shell model; the incompatibility of modern nuclear Hamiltonians with a bound tetra-neutron; difficulties in computing RMS radii of very weakly bound nuclei, such as 6He; center-of-mass effects on spectroscopic factors; and the possible use of an artificial external well in calculations of neutron-rich isotopes.

Analyzing Powers in the n-d Scattering and 2-N Interaction

theory. The analyzing powers in the n·d scattering is calculated for the Argonne VIS (AVIS) potential, and the result is compared with the results for several 2·N charge independence (CI) potentials. The triton binding energy for the A VIS potential is shown. In a previous paper 1 ) we showed that, in the three-body Faddeev calculation with the use of the Paris 2 ) potential, the maximum value of the angular distribution of the analyzing power Ay in the low energy neutron-deuteron (n-d) scattering is significantly smaller than the experimental data at energies less than 18 MeV. In order to reproduce the experimental data of the nod scattering, we have modified the short range part of the Paris potential. Of course, there are many realistic two-nucleon (2-N) potentials in addition to the Paris potential, for example, the Argonne VI4 3 )(AV14), the Bonn A and B,4) the Funabashi S ) and so on. All of these potentials are constructed under the assumption of charge-independence (CI) and charge-symmetry (CS) properties. These potentials give consistent results for the 2-N on-shell data; the 2-N phase shifts, the binding

Triton calculations with pi and rho exchange three-nucleon forces.

The Faddeev equations are solved in momentum space for the trinucleon bound state with the new Tucson-Melbourne {pi} and {rho} exchange three-nucleon potentials. The three-nucleon potentials are combined with a variety of realistic two-nucleon potentials. The dependence of the triton binding energy on the {pi}{ital NN} cut-off parameter in the three-nucleon potentials is studied and found to be reduced compared to the case with pure {pi} exchange. The {rho} exchange parts of the three-nucleon potential yield an overall repulsive effect. When the recommended parameters are employed, the calculated triton binding energy turns out to be very close to its experimental value. Expectation values of various components of the three-nucleon potential are given to illustrate their significance for binding.

Nuclear charge asymmetry and charge dependence and the 3H-3He binding-energy difference.

We solve a set of Faddeev equations for some realistic two-nucleon potentials, taking into account the two-pion-exchange three-nucleon interaction, the Coulomb interaction, and the charge-independence- and charge-symmetry-breaking (CIB and CSB) interactions. After 32 case studies, we find a very good linear relationship between $^{3}\mathrm{H}$ and $^{3}\mathrm{He}$ binding energies, from which we deduce a model-independent value for the Coulomb energy difference (648\ifmmode\pm\else\textpm\fi{}4 keV for the finite-size protons) and the CIB and CSB nuclear effects. With other small effects, these effects reasonably account for the $^{3}\mathrm{\ensuremath{-}}^{3}$he binding-energy difference.

Effects of final-state interaction in inelastic electron scattering from the three-nucleon system

Inclusive electron scattering from 3He is microscopically described. The calculation assumes nucleonic degrees of freedom only for the three-nucleon states. The nucleons interact among each other through realistic two-nucleon potentials. They interact with the electron through one-nucleon electromagnetic currents. Compared to the standard plane-wave impulse approximation the theoretical description of the final three-nucleon scattering states is improved. A perturbative approach is used. Final-state interaction is approximately accounted for by one additional rescattering in terms of the two-nucleon transition matrix. The final three-nucleon scattering states are fully antisymmetrized.

Effective interactions and superfluid energy gaps for low density neutron matter

We use a polarization potential approach to calculate properties of neutron matter at sub-nuclear densities with particular attention to the superfluid pairing interaction. Our model divides the quasi-particle scattering amplitude at the Fermi surface into two distinct parts: a direct particle-hole irreducible piece and an induced particle-hole reducible contribution. The direct part is constructed from realistic two-nucleon potentials. Short-range correlations are taken into account phenomenologically by modifying the potentials at short distances. The induced contribution is generated as a self-consistent summation of particle-hole reducible diagrams. The resulting quasi-particle scattering amplitude is fully antisymmetric for all moment 0⩽ q⩽2 k F. Realistic bounds on the s-wave pairing gap are given and consequences for the dynamics of rotating neutron stars are briefly discussed.