Many-body terms in the folded diagram expansion

The folded diagram expansion for the effective hamiltonian to be used in shell-model calculations for a system with A valence nucleons yields folded diagrams connecting up to A nucleons. The importance of such effective many-nucleon forces is investigated for the example of 4 valence nucleons in the 1s0d shell (²⁰Ne). The folded diagram terms turn out to reduce the binding energy for the low-lying states. The effects of the folded diagrams involving three nucleons are of the same importance as those of the two-body terms. The four-nucleon forces originating from folded diagrams are considerably weaker. This suggests that three-body operators have to be considered in a microscopic calculation of an effective energy-independent shell-model hamiltonian, whereas terms involving four nucleons may be ignored.     

Effective three-nucleon forces from the folded diagram expansion

The folded diagram expansion for the effective hamiltonian of a system of three valence nucleons in the 1s0d shell is investigated. Beside the one-body and two-body operators, which already occur in the folded diagram expansion for systems with one and two valence nucleons, also folded diagrams involving three nucleons are obtained. These terms, which can be interpreted as a contribution to an effective three-nucleon force, yield a non-negligible contribution which is repulsive for the low-lying states. Two different techniques are studied for the summation of the folded diagrams. A very good convergence is obtained using the Lee-Suzuki iteration scheme.     

Many-body correlations in shell model effective interactions derived by ab initio methods and the V_(low-k) approach

We investigate many-body correlations caused by two-and three-body(2-, 3bd) forces. Shell-model effective interactions derived from ab initio methods(coupled-cluster method, no-core shell model) are adopted.Vlow-k potentials, based on many-body perturbation theory, are also tested, especially for their cut-off dependence.We compare the central, tensor and spin-orbit interactions from microscopic theory to the fitted interactions. After the inclusion of the three-body force, the matrix elements become fairly close to those fitted directly to experimental data. Calculations of neutron-rich oxygen isotopes are performed, to clarify the effects of 3bd forces, tensor, and spin-orbit interactions on the nuclear binding and excitation energies. We find that the 3bd force can influence the binding energies greatly, which also determines the drip line position, while its effect on excitation energies is not very pronounced. The spin-orbit force, which is part of the 2bd force, can affect the shell structure explicitly, at least for neutron-rich systems.     

Δ(3, 3) excitations and effective three-nucleon forces in finite nuclei

Contributions from three-body terms with intermediate Δ(3,3) isobar excitations to the ground state energies of nuclei are investigated. These terms can either be understood as three-body clusters in a many-body theory including isobar excitations explicitly or as contributions to an effective three-nucleon force. For the example ¹⁶O the resulting contribution is attractive and its value is typically about ?0.5 MeV per nucleon. This is smaller than the typical values of 1 MeV per nucleon repulsion obtained from the modifications of the effective two-body nucleon-nucleon interaction in nuclei due to intermediate Δ(3, 3) configurations. The gain in energy from the three-body terms including Δ(3,3) configurations, however, is of the same importance as the contribution from three-body terms including nucleons only.     

Three-body structure of 6He=4He+n+n using realistic n-n potentials

With the use of realistic nucleon-nucleon forces (Paris, Bonn and Argonne potenfials) between the valence neutrons, the three-body structure of ⁶He=⁴He+n+n is investigated with emphasis on the short-range correlations between the halo neutrons and on dependence on the realistic forces. To solve the three-body problem regorously, use is made of the coupled-rearrangement-channel variational method with the Gaussian basis functions. The basis are represented by newly developed Gaussian lobe functions with infinitesimal shift parameters. Accuracy and usefulness of this basis functions are examined in the calculation of three-nucleon bound state with those realistic forces.     

Three-nucleon interaction in a quark cluster model

Taking into account the quark structure of the nucleons, a new three-nucleon potential is derived. It contains two parts: the pairwise interactions and a three-nucleon force. The pairwise interactions are described by the NN potentials of the quark-compound-bag model in the off-shell generalized form. The three-body force has the form of a separable potential which has a pole singularity on the energy axis. The residue at the pole is determined by the three-nucleon vertex given explicitly through all possible intermediate states formed by the 6q and 9q bags. The solution of the three-nucleon problem is obtained in an analytical form by means of the known solution of the problem with ordinary pairwise interaction. It is shown that: (i) the 9q bag is an additional source of an attractive interaction between three nucleons; (ii) the pole singularity of the three-nucleon force exhibits a resonance structure of the three-nucleon scattering amplitude; (iii) the total and partial widths of the quasi-discrete level are defined by the three-nucleon vertex. Some consequences of the new potential are discussed.     

Three-body forces and the structure of the sd-shell

The structures of sd-shell nuclei with open shells are studied by a method which enables us to investigate properties of excited states and bulk properties of the nucleus at the same time. An effective interaction including three-body force with 15 strength parameters is used. The bulk properties of sd-shell nuclei with mass number 18–22 and 34–38 are studied. The calculated results for bulk properties reproduce experimental values fairly well, but the results for excitation energies are poor. Some of the electromagnetic properties, moments and transition probabilities have close resemblance to those obtained by usual shell model calculations using a realisitc interaction or an effective interaction. The defects of this method and a way to improve our method are discussed.     

Effective interactions and charges in58Ni

The structure of the low-lying states of⁵⁸Ni has been calculated in shell model by assuming an inert⁵⁶Ni core plus two valence nucleons in the p_3/2, f_5/2 and p_1/2 orbitals. The two-body matrix elements are first expressed in terms of seven radial matrix elements and these are then parametrized to give best fit between the computed and the observed energies of the levels below 4 MeV. The wave-functions obtained using these two-body matrix elements are used to study the concept of effective charges. It is found that a single effective charge is not sufficient to predict theB(E2) rates equally well for the thirteen known transitions for which experimental values are available. Assumption of state-dependent effective charges gives a far better agreement. An analysis using wavefunctions obtained with Kuo’s two-body matrix elements also gives a similar result.     

Few-Baryon Interactions from Lattice QCD

We report the recent progress on the determination of three-nucleon forces (3NF) in lattice Quantum Chromodynamics (QCD). We utilize the Nambu–Bethe–Salpeter wave function to define the potential in quantum field theory, and extract two-nucleon forces and 3NF on equal footing. The enormous computational cost for calculating multi-baryon correlators on the lattice is drastically reduced by developing a novel contraction algorithm (the unified contraction algorithm). Quantum numbers of the three-nucleon system are chosen to be (I, J ^P ) = (1/2, 1/2⁺) (the triton channel), and we extract 3NF in which three nucleons are aligned linearly with an equal spacing. Lattice QCD simulations are performed using N _f = 2 dynamical clover fermion configurations at the lattice spacing of a = 0.156fm on a 16³ × 32 lattice with a large quark mass corresponding to m _π = 1.13 GeV. Repulsive 3NF is found at short distance.     

Hadronic Parity Violation in Few-Nucleon Systems

The weak interaction between quarks induces a parity-violating component in the interactions between nucleons, which is typically suppressed by a factor of \({\approx 10^{-7}}\) compared to the dominant parity-conserving part. Because of the short range of the weak interactions, it provides a unique probe of the strong dynamics that confine quarks into nucleons. An experimental program to map out this weak component of the nuclear force is underway at a number of facilities, including the Spallation Neutron Source at Oak Ridge National Laboratory. The corresponding observables are related to few-nucleon processes at very low energies, at which pionless effective field theory provides a reliable and model-independent theoretical approach to hadronic parity violation. Results in two- and three-nucleon systems, the role of parity-violating three-nucleon forces, and possible extensions to other few-nucleon systems are discussed.     

Dependence of the Three-Nucleon Binding Energy on Some Different Effects

The bound state of three-nucleon system is studied as a three-body problem which is solved following the different approaches of the Faddeev formalism as well as the unitary pole approximation. The three-body problem is reduced to a set of coupled integral equations by using separable approximations. Numerical calculations are carried out for the resulting integral equations and the separable expansion. In the present work, we calculate the ground-state binding energy of the bound three-nucleon system ³H. The main interest of the present work is to investigate the sensitivity of the three-nucleon binding energy to different effects. For this reason, we study the dependence of this energy on different forms of local and separable nucleon-nucleon potentials, the effective range of the nucleon-nucleon interaction, and on the percent of the D state in the deuteron wave function. Also we test the sensitivity of the three-nucleon binding energy to the considered number of terms from the separable expansion.     

Beta decay rates of sd-shell nuclei in stellar interiors

Gamow-Teller matrix elements of sd-shell nuclei relevant for stellar evolution of massive stars are calculated by using the sd-shell model wave functions of Wildenthal. Emphasis is placed on the calculations of GT transitions between excited states, which are not obtainable by experiment. Our results are compared with the previous work by Fuller et al. and are found notably different in many cases. The beta decay rates, as calculated with and without the contributions of excited states, are demonstrated to be quite different under conditions of high density and high temperature.     

Four-nucleon system with Δ-isobar excitation

The four-nucleon bound state and scattering below three-body breakup threshold are described based on the realistic coupled-channel potential CD Bonn+Δ$\text{Bonn}+\mathrm{\Delta }$ which allows the excitation of a single nucleon to a Δ isobar. The Coulomb repulsion between protons is included. In the four-nucleon system the two-baryon coupled-channel potential yields effective two-, three- and four-nucleon forces, mediated by the Δ isobar and consistent with each other and with the underlying two-nucleon force. The effect of the four-nucleon force on the studied observables is much smaller than the effect of the three-nucleon force. The inclusion of the Δ isobar is unable to resolve the existing discrepancies with the experimental data.     

Trinucleons as multi-quark systems

A new approach to the three-nucleon system is suggested, in which it is assumed that the short-range interaction of nucleon clusters within the trinucleons is described in terms of wave functions of virtual multi-quark configurations. It is shown that the effective three-nucleon Hamiltonian contains three-body forces arising from the dynamics of overlapping bags in the trinucleons. They may, however, be eliminated by a proper redefinition of the nucleon component in a nine-quark wave function. We derive the integral equation for the three-nucleon wave function which has the form of the standard Faddeev equation but requires the phase-equivalent redefinition of the initial form of nucleon-nucleon potential in the quark-compound-bag method.     

Perturbative role in the inelastic electron scattering from <Superscript>29</Superscript>Si

Inelastic electron scattering form factors away from the closed sd -shell are investigated. This investigation covers the low-lying states in ²⁹Si , which is considered according to the many-particle configuration mixing shell model as the ¹⁶O core, plus thirteen nucleons distributed over the entire sd -shell orbits. The investigation concentrates on the perturbative role of the core, which is called core polarization effects, on the inelastic electron scattering form factors. Core polarization effects are taken into consideration through the excitation of nucleons from 1s and 1p core orbits, and also from the 2s -1d valence orbits into higher shells, with 2ℏω excitations. Core polarization matrix elements are calculated with the M3Y effective interaction. For the sd -shell model space, a new Hamiltonian, based on a renormalized G -matrix, USDB, is used. All calculations are performed without adjusting any parameters.     

Search for supersymmetry in light nuclei

The supersymmetry assumption based on a system of valence interacting bosons and odd nucleons has been checked in the second half of the nuclear sd-shell. The dynamical supersymmetric hamiltonian restricted to the linear combination of chosen second-order Casimir invariants has been applied to energy levels of several nuclei organized in supermultiplets. The supersymmetry predictions for nine nuclei are in accord, to a good approximation, with experimental energy levels up to 4–7 MeV.     

Effective Field Theory for Few Particles in a Trap

In this contribution we show applications of effective field theory (EFT) to few-particle systems trapped in a harmonic oscillator potential. The principles of EFT allows to construct interactions among the particles in a systematic and improvable manner. We first consider systems of two-component fermions and show excellent agreements with the exact solution at unitarity (for the two- and three-body problem) and results obtained by other methods (in the four-body case). We then consider trapped systems of three nucleons and extract neutron–deuteron phase shifts, and show that the quartet scattering length is in good agreement with experimental data. We also show the collapse of the system in the J ^π  = 1/2⁺, T = 1/2 (triton) channel at Leading-Order when no three-nucleon force is included.