Nucleon-nucleon Force Research Articles

Energy dependence of nucleon-deuteron elastic scattering observables and its bearing on the3 P J nucleon-nucleon interactions

The energy dependence of neutron-deuteron elastic scattering observables has been calculated from 5 to 45 MeV via rigorous three-nucleon calculations using the Bonn B nucleon-nucleon interaction. The goal of these calculations was to identify energy and angular regions that may be investigated experimentally to study the question of charge-symmetry breaking in the3PJ nucleon-nucleon forces and/or Coulomb interactions. It was found that the measurement of the neutron-deuteron elastic analyzing power at 16 and 22.7 MeV and its comparison to proton-deuteron data obtained at the same incident energy is the most promising case for studying the issue of charge-symmetry breaking in the3PJ nucleon-nucleon forces and/or Coulomb interactions.

Integro-differential equation approach. III. Triton and alpha -particle bound states. Realistic forces and two-body correlations.

Four-nucleon binding energies and Faddeev amplitudes are calculated in the integro-differential equation approach, which neglects all {ital N}-body correlations with {ital N}{ge}3, for realistic forces in the three-channel approximation. Good agreement is obtained with corresponding results recently obtained by means of the Faddeev-Yakubovsky equations. Thereby, the dominance of two-body correlations, even for realistic forces, is established. The effect of the inclusion of the hypercentral potential in the definition of the (modified) Faddeev amplitudes for realistic forces is investigated and found to be of less importance for realistic forces than for central spin-dependent forces. The three- and four-nucleon modified Faddeev amplitudes are also compared. We found that the {ital D}-state Faddeev amplitudes are less sensitive to the number of nucleons, to the inclusion of the hypercentral potential, and to the nucleon-nucleon force than the mixed symmetry {ital S}{prime}-state amplitudes.

Neutron-deuteron elastic scattering and breakup reactions below 20 MeV

In this paper we review the results of a series of high-accuracy measurements on the neutron-deuteron (n-d) scattering system at incident neutron energies below 20 MeV. These measurements were designed to: 1) provide data of sufficient accuracy to be used to refine the parametrization of the nucleon-nucleon force, 2) to test the reaction dynamics in the “rigorous” calculations of three-nucleon (3N) breakup reactions, and 3) identify 3N scattering observables that are specifically sensitive to three-nucleon forces and/or off-shell effects. At TUNL we have measured vector analyzing powers A y ( θ) for n-d elastic scattering and the breakup reaction to an accuracy better than ± 0.005 and ± 0.020, respectively. Recent results on items 1) and 2) will be presented. Also, results of cross-section measurements for n-d and p-d breakup will be compared to a “rigorous” 3N calculation.

Uncertainties in proton-proton scattering at low energies

Low-energy proton-proton scattering (LEPPS) provides information on the nucleon-nucleon forces relevant to all nuclei, including2He. Sources of uncertainties to current state of the art of experiments and data analyses are pointed out with estimates of effects.

Microscopic calculations of low-energy reaction cross sections.

Microscopic calculations of nuclear reaction cross sections and total reaction probabilities are compared with measurements for the d+Si, $^{3,4}\mathrm{He}$+Si, and d+Ge systems at energies ranging from 2 to 53 MeV/nucleon. Good agreement is obtained, except for $^{3}\mathrm{He}$+Si at the very lowest energies, when zero-range nucleon-nucleon forces are assumed and realistic nuclear density distributions are used in the tail regions, where the models are most sensitive. The agreement is less good for finite-range forces. A strong absorption model gives much poorer agreement with the recent $^{4}\mathrm{He}$+Si measurements than do the microscopic models.

On the composition of the lightest nucleus

The composition of the lightest nucleus, the nucleon, is discussed here in terms of relativistic quark-gluon models which are based on the non-abelian gauge theory of the strong interactions, Quantum Chromodynamics. This composition of the nucleon is manifest in momentum-dependent meson-nucleon vertex functions which are necessary for a detailed understanding of the nucleon-nucleon force. The precise knowledge of the nucleon-nucleon interaction is a prerequisite for any progress in the field-theoretic description of the nuclear force. I emphasize the role of the neutron in the investigation of the internal spin and charge distribution of the nucleon.

Skyrmions for two-baryon systems

We survey the application of skyrmions to nucleon-nucleon forces, starting from general background material on the search for appropriate degrees of freedom (nucleonic, mesic, quark,…) for few-nucleon systems. We stress that skyrmions may offer a link in the chain from quantum chromodynamics (QCD) as a theory of strong interactions on the one hand to nuclear structure on the other. We briefly consider possible extensions of the skyrmion approach to the strange sector, where one may treat, among other systems, NΛ, NΣ and ΛΛ forces.

Explanation of the apparent charge dependence of the pion-nucleon coupling.

A recent, careful analysis of the world data on pp scattering concluded that the pp${\ensuremath{\pi}}^{0}$ coupling constant was 3%--4% less than expected from charge independence and the known pn${\ensuremath{\pi}}^{+}$ coupling constant. We propose a much simpler interpretation of the analysis of the pp data which involves no unreasonable level of charge dependence. Instead one must recognize that the pion-nucleon form factor needed in a boson-exchange model of the nucleon-nucleon force differs significantly from that relevant to a free nucleon.

Spin-spin and tensor observables in the isovector nucleon-nucleon force.

We justify the inclusion of the rho meson in the Bonn potential in terms of the NN\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi} helicity amplitude analysis. The tensor observables are well reproduced with the resulting interaction. Consequences for the momentum dependence of the spin-longitudinal and spin-transverse effective interactions are discussed.

Investigation of the nucleus-nucleus interaction at small distances in elastic scattering of 6li and the reaction ( 6Li, 6He) on carbon isotopes

The cross sections of elastic scattering of 6Li and of the charge-exchange reaction ( 6Li, 6He) on the nuclei 13C and 14C were measured at the projectile energy 93 MeV. A theoretical analysis of the reaction was carried out using microscopic DWBA with central and tensor components of the nucleon-nucleon forces and the decomposition of the reaction amplitude to near side and far side components. The far components were seen to dominate both the elastic scattering and the reaction for the angles above 30°, and a small shoulder in the differential cross section curves around 90° in elastic scattering and in 14C( 6Li, 6He) 14N(3.95) may be interpreted as a rudimentary nuclear rainbow. The analysis of the scattering data lead to a new family of potentials for the systems 6Li + 12,13,14C. The reproduction of the differential cross sections for population of the 1 + states in the charge-exchange reaction at large angles called for a change of the form factors, compared to the theoretical ones, for radii which were considerably smaller than the strong absorption radius. It is possible that to reproduce the ( 6Li, 6He) reaction data, a 20% difference between the imaginary potentials of 6He and 6Li is needed.

Pions and Nuclei

The pion has emerges as the main feature of nuclear structure beyond the traditional description in terms of neutrons and protons. It manifests itself in a number of areas which are normally only loosely interlinked, but intimately related to the pion-nucleon and pion-nuclear interactions: the nucleon-nucleon force; the nuclear many-body problem; nuclear electromagnetic and weak interactions; nuclear spinisospin interactions; pion-nucleus scattering and reactions; etc. This book is a systematic introduction to and survey of nuclear pion physics, a major sub-field of nuclear pion physics. The theoretical foundations are padagogically developed and the physical picture is illustrated with supporting experimental examples.

The intermediate-range attraction of the nucleon-nucleon force in a skyrme model with explicit σ-mesons

Abstract Explicit inclusion of scalar mesons into the Skyrme model produces in a natural and transparent way the intermediate-range attraction in the central part of the baryon-baryon interaction.

A New Method for Calculating the Double Beta Decay Probability

A new method of calculating decay probability is derived. It is shown that with the present knowledge of nucleon-nucleon force and reasonable nuclear wave functions for the parent and daughter nuclei this method can provide a reliable result without using closure approximation.

The use of skyrmions for two-nucleon systems

We first define our goals for studying the nucleon-nucleon force with skyrmions by discussing briefly the general issue of the formulation of nuclear physics using degrees of freedom based on quarks and gluons. A short review is then given of the use of the skyrmion description for single-hadrons in order to prepare the way for the application of this method to two-nucleon systems. In the context of the B = 1 sector, we discuss cursorily how the skyrmion arises as an approximation to quantum chromodynamics (QCD) for the artificial situation where the number of colors N is very large, and the use of the original Skyrme lagrangian, and various modifications of it, in that situation. We consider the hedgehog solution for that lagrangian, noting how integer baryon number emerges in the course of fulfilling the necessary boundary conditions. First-quantization, which allows for the treatment of spin and isospin, is introduced. A detailed discussion of the use of the London-Heitler method—which applies the B = 1 hedgehog solution, in one form or another, to the B = 2 case—is presented. This includes such issues as the use of higher-order terms in the lagrangian, the incorporation of higher-order dynamic terms, and the mutual distortion of hedgehog solutions in the B = 2 system. In order to emphasize one area of potential usefulness of skyrmions in nuclear physics, we consider their application to the calculation of exchange currents as well as the more common usage for studying the nucleon-nucleon potential. More recently, studies of skyrmions for B = 2 systems have gone well beyond the simplest form of London-Heitler form with hedgehog skyrmions. We review briefly the treatment of B = 2 systems with skyrmions using a full three-dimensional computation without recourse to these assumptions. Last, we discuss three mechanisms that yield some degree of attraction in the central potential: (i) the admixture of states involving nucleon-Δ and Δ-Δ components along with the asymptotic nucleon-nucleon ones; (ii) the use of a form of the London-Heitler method that takes into account the proper symmetries of the two-skyrmion state; and (iii) the treatment of internal excitations of the single-baryon and their effects on the nucleon-nucleon force.

Approximations in the quasiparticle random phase evaluation of double beta decay rates.

Within the quasiparticle random phase approximation, we compare two-neutrino double beta decay amplitudes calculated with zero-range and finite-range nucleon-nucleon interactions. We find that if, as is customary, interaction constants are fit to energies of giant Gamow-Teller states and to β+ strengths, the two interactions lead to very similar two-neutrino double beta amplitudes. We discuss additional approximations related to the inclusion (or neglect) of the Hartree-Fock part of the pairing interaction, and to the treatment of differences between the initial and final nuclear ground states. The numerical values of the amplitudes depend more on the way these approximations are made than on the form of the nucleon-nucleon force.

On some recent developments in microscopic nuclear models

An overview of the status of development of some microscopic nuclear models is presented. Special attention is paid to the calculations starting from the effective nucleon-nucleon force, to the angular momentum projection method before variation, to the multiphonon method and to the selfconsistent coordinate method. The success and the limitations of the three last mentioned models are illustrated in the example of 168Er.

"Optimal" approximation and the realistic nucleon-nucleon interactions.

The principal aim of introducing the so-called “optimal” approximation [1,2] for the projectile-nucleus elastic scattering is to take into account the binding and the recoil effects at the relatively large momentum transfers where the impulse or Glauber approximations break down. The accuracy of this approximation has been studied [3] for the proton-deuteron elastic scattering at intermediate energies using the local nucleon-nucleon interactions independent of the target nucleon spin. The deuterium target has been chosen because the deuteron wave function and the off energy shell two body scattering T matrix elements are sufficiently well known far the large relative proton-neutron momenta. The direct studies of the three-nucleon scattering at the incoming nucleon energies of several hundred MeV are in progress for the modern nucleon-nucleon forces although they have been done at the lower energies of 10 and 20 MeV [4].

Model dependence of charge-symmetry breaking in the neutron-proton interaction.

The effects of charge-symmetry breaking of nuclear forces can be observed in neutron-proton elastic scattering as a difference between neutron and proton analyzing powers. A formalism has previously been developed and applied to compute these effects in terms of electromagnetic interactions, one-boson exchange potentials, the two-pion exchange potential, and possible quark effects. The results were found to be in agreement with the one existing measurement. Here we extend this work and study in detail how these charge-symmetry breaking predictions vary with the particular choice for the nucleon-nucleon force. We compare predictions for Reid soft-core, Paris, coordinate-space Bonn, and hybrid quark-meson potentials. We show in particular that charge-symmetry breaking measurements can place strong restrictions on models of the nucleon-nucleon interaction.

The nucleon-nucleon force and the quark degrees of freedom

This review gives a detailed overview of the current status of our understanding of the nucleon-nucleon forces. The authors review the known long-range meson exchange forces and explain how these forces originate from an underlying quark model constrained by chiral symmetry, a symmetry that is very well satisfied in low-energy nuclear phenomena. These effective meson exchange forces describe the large-impact-parameter nucleon-nucleon scattering. The authors show how the small-impact-parameter nucleon-nucleon scattering can be explained by the quark structure of the nucleons and why this quark model is successful in reproducing the energy dependence of the "measured" $S$- and $P$- wave nucleon-nucleon phase shifts.

Trinucleon magnetic moments: 34-channel results.

Impulse approximation and isovector pion-exchange current contributions to the trinucleon magnetic moments are calculated using wave functions generated from solutions of the configuration-space form of the Faddeev equations for the Reid soft core, Argonne ${\mathrm{V}}_{14}$, and super-soft-core C nucleon-nucleon force models and the Tucson-Melbourne or Brazilian three-nucleon force models. Numerical results for solutions with two-body partial waves having j\ensuremath{\le}4 (up to 34 channels) are reported. Agreement between theory and experiment appears reasonable for these nonrelativistic Hamiltonians which are restricted to one-pion exchange currents.