Two-nucleon Data Research Articles

Correlations among neutron-proton and neutron-deuteron elastic scattering observables

We employ two models of the nucleon-nucleon force: the OPE-Gaussian as well as the chiral N4LO and N4LO+ interactions with semilocal regularization in momentum space to study correlations among two-nucleon and three-nucleon elastic scattering observables. These models contain a number of free parameters whose values and covariance matrices are evaluated from a fit to the two-nucleon data. Such detailed knowledge of parameters allows us to create, using various sets of statistically generated parameters, numerous versions of these potentials and next apply them to two- and three-nucleon scattering to make predictions of various observables at the reaction energies up to 200 MeV. This permits a systematic analysis of correlations among two-nucleon and three-nucleon observables, basing on a relatively big sample of predictions. We found that most observables in neutron-proton and neutron-deuteron systems are uncorrelated, but there are exceptions revealing strong correlations, which depend on the reaction energy and scattering angle. This information may be useful for precise fixing free parameters of two-nucleon and three-nucleon forces and for understanding dependencies and correlations between potential parameters and observables.

Relativistic corrections of two-nucleon data

It is shown that two-nucleon data applied for nucleon-nucleon potentials fitting needs relativistic corrections. The potentials, fitted to kinematically corrected data appear as more attractive and allow the improvement of the deuteron and more complex nuclei description.

Realistic Nucleon-nucleon Potential Expansion in Terms of Orthogonal Projectors

It is shown that applying the nucleon-nucleon potential projection into operators’ (central, spinorbit, square spin-orbit, square orbital angular momentum, and tensor interactions) format, only the limited amount of scattering phase shifts can be described in uncorrelated way. More operators should be considered for the complete description of two-nucleon data. This paper proposes the extension of the operator system in order to solve the problem.

Calculation of doublet capture rate for muon capture in deuterium within chiral effective field theory

The doublet capture rate Λ1/2 of the negative muon capture in deuterium is calculated employing the nuclear wave functions generated from accurate nucleon–nucleon (NN) potentials constructed at next-to-next-to-next-to-leading order of heavy-baryon chiral perturbation theory and the weak meson exchange current operator derived within the same formalism. All but one of the low-energy constants that enter the calculation were fixed from pion–nucleon and nucleon–nucleon scattering data. The low-energy constant dˆR (cD), which cannot be determined from the purely two-nucleon data, was extracted recently from the triton β-decay and the binding energies of the three-nucleon systems. The calculated values of Λ1/2 show a rather large spread for the used values of the dˆR. Precise measurement of Λ1/2 in the future will not only help to constrain the value of dˆR, but also provide a highly nontrivial test of the nuclear chiral EFT framework. Besides, the precise knowledge of the constant dˆR will allow for consistent calculations of other two-nucleon weak processes, such as proton–proton fusion and solar neutrino scattering on deuterons, which are important for astrophysics.

Ab InitioMany-Body Calculations of theH3(d,n)He4andHe3(d,p)He4Fusion Reactions

We apply the ab initio no-core shell model combined with the resonating-group method approach to calculate the cross sections of the $^{3}\mathrm{H}(d,n)^{4}\mathrm{He}$ and $^{3}\mathrm{He}(d,p)^{4}\mathrm{He}$ fusion reactions. These are important reactions for the big bang nucleosynthesis and the future of energy generation on Earth. Starting from a selected similarity-transformed chiral nucleon-nucleon interaction that accurately describes two-nucleon data, we performed many-body calculations that predict the $S$ factor of both reactions. Virtual three-body breakup effects are obtained by including excited pseudostates of the deuteron in the calculation. Our results are in satisfactory agreement with experimental data and pave the way for microscopic investigations of polarization and electron-screening effects, of the $^{3}\mathrm{H}(d,\ensuremath{\gamma}n)^{4}\mathrm{He}$ bremsstrahlung and other reactions relevant to fusion research.

Ab initio many-body calculation of the [formula omitted] radiative capture

We apply the ab initio no-core shell model/resonating group method (NCSM/RGM) approach to calculate the cross section of the Be7(p,γ)B8 radiative capture. This reaction is important for understanding the solar neutrino flux. Starting from a selected similarity-transformed chiral nucleon–nucleon interaction that accurately describes two-nucleon data, we performed many-body calculations that simultaneously predict both the normalization and the shape of the S-factor. We study the dependence on the number of 7Be eigenstates included in the coupled-channel equations and on the size of the harmonic oscillator basis used for the expansion of the eigenstates and of the localized parts of the integration kernels. Our S-factor result at zero energy is on the lower side of, but consistent with, the latest evaluation.

NN Interaction JISP16: Current Status and Prospect

We discuss realistic nonlocal NN interactions of a new type - J-matrix Inverse Scattering Potential (JISP). In an ab exitu approach, these interactions are fitted to not only two-nucleon data (NN scattering data and deuteron properties) but also to the properties of light nuclei without referring to three-nucleon forces. We discuss recent progress with the ab initio No-core Shell Model (NCSM) approach and respective progress in developing ab exitu JISP-type NN-interactions together with plans of their forthcoming improvements.

Spectroscopy of light nuclei with realistic NN interaction JISP

Recent results of our systematic ab initio studies of the spectroscopy of s- and p-shell nuclei in fully microscopic large-scale (up to a few hundred million basis functions) no-core shell-model calculations are presented. A new high-quality realistic nonlocal NN interaction JISP is used. This interaction is obtained in the J-matrix inverse-scattering approach (JISP stands for the J-matrix inverse-scattering potential) and is of the form of a small-rank matrix in the oscillator basis in each of the NN partial waves, providing a very fast convergence in shell-model studies. The current purely two-body JISP model of the nucleon-nucleon interaction JISP16 provides not only an excellent description of two-nucleon data (deuteron properties and np scattering) with χ2/datum = 1.05 but also a better description of a wide range of observables (binding energies, spectra, rms radii, quadrupole moments, electromagnetic-transition probabilities, etc.) in all s-and p-shell nuclei than the best modern interaction models combining realistic nucleon-nucleon and three-nucleon interactions.

Realistic nuclear Hamiltonian: Ab exitu approach

Fully-microscopic No-core Shell Model (NCSM) calculations of all stable $s$ and $p$ shell nuclei are used to determine realistic $NN$ interaction JISP16 describing not only the two-nucleon data but the binding energies and spectra of nuclei with $A\leq 16$ as well. The JISP16 interaction, providing rapid convergence of the NCSM calculations, is obtained in an {\em ab exitu} approach by phase-equivalent transformations of the JISP6 $NN$ interaction.

Test ofJ-matrix inverse scattering potentials on electromagnetic reactions of few-nucleon systems

The J-matrix inverse scattering nucleon-nucleon potentials (JISP), describing both two-nucleon data and bound and resonant states of light nuclei to high accuracy, are tested on the total photoabsorption cross sections of Deuteron, Triton, 3He and 4He. The calculations in the three- and four-body systems are carried out via the Lorentz integral transform method and the hyperspherical harmonics (HH) technique. To this end the HH formalism has been adapted to accommodate non-local potentials. The cross sections calculated with the JISP are compared to those obtained with more traditional realistic interactions, which include two- and three-nucleon forces. While the results of the two kinds of potential models do not differ significantly at lower energies, beyond the resonance peak they show fairly large discrepancies, which increase with the nuclear mass. We argue that these discrepancies may be due to a probably incorrect long range behavior of the JISP, since the one pion exchange is not manifestly implemented there.

Comparison of instant form and front form one-particle exchange models.

We study the use of the Okubo method for constructing effective two-particle, instant form and front form, one-particle exchange models, starting from quantum field theory vertices. The truncation of the field theory that is made in applying the Okubo method leads to mass operators that are not exactly Poincar{acute e} invariant. It is found that when the spurious terms that destroy the exact Poincar{acute e} invariance are eliminated the instant and front form potentials come out essentially the same, however they wind up in slightly different two-particle Lippmann-Schwinger equations. In order to study the practical consequences of this difference, a numerical comparison is made between instant and front form one-meson-exchange models of the two-nucleon system that have been fit to the same partial-wave analysis of the two-nucleon data. These models assume the exchange of {pi}, {eta}, {rho}, {omega}, {delta}, and {sigma} mesons. No dramatic differences are found between the instant form and front form vertex parameters obtained from the fits. {copyright} {ital 1996 The American Physical Society.}

Momentum dependence of the rho - omega mixing amplitude in a hadronic model.

We calculate the momentum dependence of the \ensuremath{\rho}-\ensuremath{\omega} mixing amplitude in a purely hadronic model. The basic assumption of the model is that the mixing amplitude is generated by NN\ifmmode\bar\else\textasciimacron\fi{} loops and thus driven entirely by the neutron-proton mass difference. The value of the amplitude at the \ensuremath{\omega}-meson point is expressed in terms of only the NN\ensuremath{\omega} and NN\ensuremath{\rho} coupling constants. Using values for these couplings constrained by empirical two-nucleon data we obtain a value for the mixing amplitude in agreement with experiment. Extending these results to the spacelike region, we find a \ensuremath{\rho}-\ensuremath{\omega} contribution to the NN interaction that is strongly suppressed and opposite in sign relative to the conventional contribution obtained from using the constant on-shell value for the mixing amplitude.

28Si + 28Si elastic scattering at energies above the Coulomb barrier

A relatively simple procedure has been used to calculate the differential cross sections for 28Si + 28Si elastic scattering at Elab = 67, 74, 77, and 120 MeV. The nuclear interactions have been calculated microscopically using the equivalence relation between the matrix elements of the generator coordinate and the resonating group methods from the two-nucleon potential, which explains the two-nucleon data fairly well. The absorption effects due to the opening of the nonelastic channels are taken into account approximately by the classical sharp cutoff of partial waves. The calculated results are in quite good agreement with the available experimental data at most of these energies.

Approximations in obe potentials and their effect on two-nucleon data

The quality of various approximations, necessary to obtain an analytic expression of one-boson-exchange potentials in r-space, is studied by calculating their effect on NN scattering phase shifts and the deuteron, starting from two OBE versions of the Bonn potential. It turns out that it is essential to keep p and P 2and Ω σL terms in order to have a good approximation to the original expression. Even then, however, the tensor force is modified appreciably in the medium-range part.

Sequential calculations for heavy-ion induced two-nucleon transfer on 14N, 15N and 16O

Abstract 11B and 13C induced two-nucleon transfer data on 14N, 15N and 16O are compared with exact finite-range sequential transfer calculations. The data appear to be consistent with this reaction model and the assumed shell-model structure of the states populated. Single-nucleon transfer data on these targets is also analyzed using the DWBA. Modifications to the exit channel optical potential are required to obtain agreement with shell-model spectroscopic factors.

Ring diagrams in nuclear matter

Ring diagrams in nuclear matter are calculated to all orders using a Bruckner G-matrix derived from a one-boson-exchange NN potential which describes the two-nucleon data accurately. When the conventional choice for the particle and hole potentials in nuclear matter is used, the convergence of the series of ring diagrams is found to be excellent. In these calculations the third order ring diagram turns out to give a positive (i.e. repulsive) contribution to the energy per particle with a strong density dependence of k f 7. This surprising fact, which is in contrast to earlier calculations using simple and too unrealistic forces, is traced back to the large coupling of the ρ-exchange of the NN potential applied in this work. Ring diagrams with intermediate Δ -isobars using π- and ρ-exchange for the relevant forces are aslo calculated. In this case, too, the contribution, which can be interpretated as a contribution from many-body forces, is positive and has the even stronger density dependence of k f 9.

The Relativistic Effects on the Two-Nucleon and Nuclear Matter Systems

Several momentum-space OBEP's together with the three-dimensional equations are constructed to reproduce the nuclear phase shifts up to 350 MeV, the two-nucleon low energy data and the deuteron properties. The influence of different OBEP's and equations is discussed. The relativistic effects incorporated with meson retardation and relativistic kinematical correction of the nucleon motion on the two-nucleon and nuclear matter systems are investigated quantitatively. Such effects are absorbed by changing the OBEP parameters in the two-nucleon system, but found to decrease the nuclear matter binding by approximately 4 MeV per particle with 0.13 fm1 decrease in the density under the value (B · E/ A= 14.1 MeV; kF= 1.59 fm1) obtained for the nonrelativistic framework.

Numerical comparison of three theories of nuclear matter

Three independent evaluations of the ground-state energy of a simple model of nuclear matter are compared. The potential chosen is central, consisting of a state-independent hard core surrounded by a spin-dependent Serber square well with parameters adjusted to produce a fit of the low-energy two-nucleon data. A careful evaluation of the energy expectation value with respect to a Jastrow wave function is performed within the Fermi-hypernetted-chain scheme of Fantoni and Rosati. At the test point k F = 1.56 fm −1, the variational result lies about 2 MeV abovē the best available Fadé approximants to the R-matrix expansion for the energy. This may be regarded as excellent agreement, considering the state-independence of the assumed Jastrow correlations. An estimate of the correction to the variational result due to the state dependence of the realistic correlations is made within the framework of the method of correlated basis functions (CBF). Both theories, R- matrix-Pad e ́ and Jastrow-CBF, yield substantially more binding than lowest-order Brueckner theory based on the choice of a self-consistent hole potential and zero particle potential in intermediate states.

Nuclear shell-model calculations and strong two-body correlations

Two-body Hamiltonians, like the Reid interaction, are derived by fitting the two-nucleon data. It is an assumption that the many-body eigenstates of this Hamiltonian form a representation of the observed nuclear states. At best this has been demonstrated for the ground states of a few nuclei, e.g., the triton, and there the binding energy is off by 15–20%, this being attributed to uncertainties in the off-shell behavior of the interaction and to many-body forces. Since 15% of the total nuclear binding energy is much greater than the typical energy spacings observed in nuclear spectra, it is not at all clear that the calculable approximations to the many-body eigenstates of the N- N interaction can give useful information for nuclear spectroscopy. Using the method of correlated basis states coupled with an extremely large “no core” shell model basis as a set of trial variational functions, it is demonstrated that almost 100 levels in light nuclei can be identified with eigenstates of the Reid interaction. In so doing, a prescription is presented for defining effective operators in large shell-model calculations and the question of nuclear center of mass motion is reexamined.

OBEP and eikonal form factor: (I). Results for two-nucleon data

A new niomentum-space one-boson-exchange potential is presented in which the phenomenological cut-off of dipole type used so far has been replaced by a form factor obtained from an eikonal approximation to multiple vector meson exchange processes. A good description of the NN scattering phase parameters ( χ 2 = 2.77) and deuteron data ( E b = 2.2246 MeV, Q = 0.2864 fm 2, P D = 4.32%) is obtained using vector meson coupling constants which are much smaller compared to former OBE models and thus are closer to determinations from other sources. This nice feature is traced back to the special structure of the eikonal form factor.