Four-nucleon Systems Research Articles

From correlations to universal behavior in few-nucleon systems

The deuteron, the only two-nucleon bound state, has a shallow character: its binding energy is strictly related to zero-energy parameters, the triplet scattering length 3anp and triplet effective range 3rnp. This fact places the deuteron inside the universal window, a region in which systems having a large value of the two- body scattering length are located. When the scattering length is large compared to the interaction range certain types of correlations can be observed. Increasing the number of nucleons these correlations are responsible for the particular spectrum of light nuclei as for example the lack of excited states in three- and four-nucleon systems. In this presentation some constraints imposed by the large values of the singlet and triplet scattering lengths in the spectrum of light nuclear systems are discussed.

θ -dependence of light nuclei and nucleosynthesis

We investigate the impact of the QCD vacuum at nonzero $\theta$ on the properties of light nuclei, Big Bang nucleosynthesis, and stellar nucleosynthesis. Our analysis starts with a calculation of the $\theta$-dependence of the neutron-proton mass difference and neutron decay using chiral perturbation theory. We then discuss the $\theta$-dependence of the nucleon-nucleon interaction using a one-boson-exchange model and compute the properties of the two-nucleon system. Using the universal properties of four-component fermions at large scattering length, we then deduce the binding energies of the three-nucleon and four-nucleon systems. Based on these results, we discuss the implications for primordial abundances of light nuclei, the production of nuclei in stellar environments, and implications for an anthropic view of the universe.

Efimov Physics with $${1/2}$$ 1 / 2 Spin-Isospin Fermions

The structure of few-fermion systems having $1/2$ spin-isospin symmetry is studied using potential models. The strength and range of the two-body potentials are fixed to describe low energy observables in the angular momentum $L=0$ state and spin $S=0,1$ channels of the two-body system. Successively the strength of the potentials are varied in order to explore energy regions in which the two-body scattering lengths are close to the unitary limit. This study is motivated by the fact that in the nuclear system the singlet and triplet scattering lengths are both large with respect to the range of the interaction. Accordingly we expect evidence of universal behavior in the three- and four-nucleon systems that can be observed from the study of correlations between observables. In particular we concentrate in the behavior of the first excited state of the three-nucleon system as the system moves away from the unitary limit. We also analyze the dependence on the range of the three-body force of some low-energy observables in the three- and four-nucleon systems.

Few-Nucleon Research at TUNL: Probing Two- and Three-Nucleon Interactions with Neutrons

The central goal of few-nucleon research at the Triangle Universities Nuclear Laboratory (TUNL) is to perform measurements that contribute to advancing ab-initio calculations of nuclear structure and reactions. The program aims include evaluating theoretical treatments of few-nucleon reaction dynamics through strategically comparing theory predictions to data, determining properties of the neutron-neutron interaction that are not accessible in two-nucleon reactions, and searching for evidence of longrange features of three-nucleon interactions, e.g., spin and isospin dependence. This paper will review studies of three- and four-nucleon systems at TUNL conducted using unpolarized and polarized neutron beams. Measurements of neutron-induced reactions performed by groups at TUNL over the last six years are described in comparison with theory predictions. The results are discussed in the context of the program goals stated above. Measurements of vector analyzing powers for elastic scattering in A=3 and A=4 systems, differential cross sections for neutron-deuteron elastic scattering and neutrondeuteron breakup in several final-state configurations are described. The findings from these studies and plans for the coming three years are presented in the context of worldwide activities in this front, in particular, research presented in this session.

Comparative study of three-nucleon force models in nuclear matter

We calculate the energy per particle of symmetric nuclear matter and pure neutron matter using the microscopic many-body Brueckner-Hartree-Fock (BHF) approach and employing the Argonne V18 (AV18) nucleon-nucleon (NN) potential supplemented with two different three-nucleon force models recently constructed to reproduce the binding energy of $^{3}\mathrm{H},\phantom{\rule{0.16em}{0ex}}^{3}\mathrm{He}$, and $^{4}\mathrm{He}$ nuclei as well as the neutron-deuteron doublet scattering length. We find that none of these new three-nucleon force models is able to reproduce simultaneously the empirical saturation point of symmetric nuclear matter and the properties of three- and four-nucleon systems.

Three-nucleon forces

In this paper, the role of three-nucleon forces in ab initio calculations of nuclear systems is investigated. The difference between genuine and induced many-nucleon forces is emphasized. Induced forces arise in the process of solving the nuclear many-body problem as technical intermediaries toward calculationally converged results. Genuine forces make up the Hamiltonian. They represent the chosen underlying dynamics. The hierarchy of contributions arising from genuine two-, three- and many-nucleon forces is discussed. Signals for the need of the inclusion of genuine three-nucleon forces are studied in nuclear systems, technically best under control, especially in three-nucleon and four-nucleon systems. Genuine three-nucleon forces are important for details in the description of some observables. Their contributions to observables are small on the scale set by two-nucleon forces.

Excited states of 4He

The study of the 4He nucleus is important because it is the most basic sub-unit (cluster) in nuclei. We have investigated the structures and the reaction mechanisms in 4He by using the correlated Gaussian basis function with the global vector representation. In order to treat the boundary condition for the ab-initio calculation of the four nucleons, we employ the Microscopic R-matrix Method (MRM) and the Complex Scaling Method (CSM) . Elastic-scattering phase shifts for four-nucleon systems are studied in an ab-initio type cluster model with MRM in order to clarify the role of the tensor force and to investigate cluster distortions in low energy d+d and t+p scattering. For 1S0, the calculated phase shifts show that the t+p and h+n channels are strongly coupled to the d+d channel for the case of the realistic interaction.

Four-Nucleon Scattering with a Correlated Gaussian Basis Method

Elastic-scattering phase shifts for four-nucleon systems are studied in an $ab$-$initio$ type cluster model in order to clarify the role of the tensor force and to investigate cluster distortions in low energy $d+d$ and $t+p$ scattering. In the present method, the description of the cluster wave function is extended from a simple (0$s$) harmonic-oscillator shell model to a few-body model with a realistic interaction, in which the wave function of the subsystems are determined with the Stochastic Variational Method. In order to calculate the matrix elements of the four-body system, we have developed a Triple Global Vector Representation method for the correlated Gaussian basis functions. To compare effects of the cluster distortion with realistic and effective interactions, we employ the AV8$^{\prime}$ potential as a realistic interaction and the Minnesota potential as an effective interaction. Especially for $^1S_0$, the calculated phase shifts show that the $t+p$ and $h+n$ channels are strongly coupled to the $d+d$ channel for the case of the realistic interaction. On the contrary, the coupling of these channels plays a relatively minor role for the case of the effective interaction. This difference between both potentials originates from the tensor term in the realistic interaction. Furthermore, the tensor interaction makes the energy splitting of the negative parity states of $^4$He consistent with experiments. No such splitting is however reproduced with the effective interaction.

Selected Topics in Three- and Four-Nucleon Systems

Two different aspects of the description of three- and four-nucleon systems are addressed. The use of bound state like wave functions to describe scattering states in $N-d$ collisions at low energies and the effects of some of the widely used three-nucleon force models in selected polarization observables in the three- and four-nucleon systems are discussed.

Few-nucleon physics

Recent progress in few-nucleon physics achieved by Italian research groups is described. Results for relativistic effects in elastic three-nucleon form factors (Rome group), hadronic and electromagnetic observables in three- and four-nucleon systems with special emphasis on three-nucleon force effects (Pisa and Trento groups), and spectra of nuclei with more than 4 nucleons (Padua group) are presented.

Density matrix renormalization group approach to two-fluid open many-fermion systems

We have extended the density matrix renormalization group (DMRG) approach to two-fluid open many-fermion systems governed by complex-symmetric Hamiltonians. The applications are carried out for three- and four-nucleon (proton-neutron) systems within the Gamow shell model (GSM) in the complex-energy plane. We study necessary and sufficient conditions for the GSM+DMRG method to yield the correct ground-state eigenvalue and discuss different truncation schemes within the DMRG. The proposed approach will enable configuration interaction studies of weakly bound and unbound strongly interacting complex systems, which, because of a prohibitively large size of Fock space, cannot be treated by means of the direct diagonalization.

Global-vector representation of the angular motion of few-particle systems II

The angular motion of a few-body system is described with global vectors which depend on the positions of the particles. The previous study using a single global vector is extended to make it possible to describe both natural and unnatural parity states. Numerical examples include three- and four-nucleon systems interacting via nucleon-nucleon potentials of AV8 type and a 3α system with a nonlocal αα potential. The results using the explicitly correlated Gaussian basis with the global vectors are shown to be in good agreement with those of other methods. A unique role of the unnatural parity component, caused by the tensor force, is clarified in the 0− 1 state of 4He. The two-particle correlation function is calculated in the coordinate and momentum spaces to show different characteristics of the interactions employed.

Variational Description of Bound States in Three- and Four-Nucleon Systems

The hyperspherical harmonic basis is used to describe the bound states of the three- and four-nucleon systems. Modern nucleon-nucleon potentials plus three-nucleon interactions are considered in configuration space as well as in momentum space. The corresponding binding energies have been calculated with accuracy at the level of 1% or better. The convergence with respect to the number of states included in the expansion is much faster for the momentum space than for the momentum space potentials, due to a less repulsive core at short distances.

Low-momentum interaction in few-nucleon systems

The effective low-momentum interaction Vlowk is applied to three- and four-nucleon systems. We investigate the 3H, 3He and 4He binding energies for a wide range of the momentum cutoffs. By construction, all low-energy two-body observables are cutoff-independent, and therefore, any cutoff dependence is due to missing three-body or higher-body forces. We argue that for reasonable cutoffs Vlowk is similar to high-order interactions derived from chiral effective field theory. This motivates augmenting Vlowk by corresponding three-nucleon forces. The set of low-momentum twoand three-nucleon forces can be used in calculations of nuclear structure and reactions.

Testing nonlocal nucleon-nucleon interactions in four-nucleon systems

The Faddeev-Yakubovski equations are solved in configuration space for the $% \alpha$-particle and n-$^3$H continuum states. We test the ability of nonlocal nucleon-nucleon interaction models to describe 3N and 4N systems.

Ab-Initio Calculations of Four-Nucleon Elastic Scattering

We present microscopic calculations of low-energy scattering observables in all possible four-nucleon systems: n-3H, p-3He, and p-3H. Results were obtained by solving Faddeev-Yakubovski equations in configuration space, appropriately modified to include Coulomb and three-nucleon forces.

Few-nuclon physics based on chiral dynamics

After a brief review of results in few-nucleon physics based on conventional nuclear forces the steps towards nuclear forces in the effective field theory approach constrained by chiral symmetry are indicated. Several low-energy constants are adjusted to nucleon-nucleon phase shift values and in the three-nucleon system to the triton binding energy and the doublet nd scattering length. Applications based on NNLO nuclear forces to the three- and four-nucleon systems are very promissing. Finally, a new regularization scheme is described which leads to a nice convergence of the chiral expansion.

Parameter-free effective field theory calculation for the solar proton-fusion and hep processes

Spurred by the recent complete determination of the weak currents in two-nucleon systems up to $\mathcal{O}{(Q}^{3})$ in heavy-baryon chiral perturbation theory, we carry out a parameter-free calculation of the threshold S factors for the solar $\mathrm{pp}$ (proton-fusion) and hep processes in an effective field theory (EFT) that combines the merits of the standard nuclear physics method and systematic chiral expansion. The power of the EFT adopted here is that one can correlate in a unified formalism the weak-current matrix elements of two-, three-, and four-nucleon systems. Using the tritium $\ensuremath{\beta}$-decay rate as an input to fix the only unknown parameter in the theory, we can evaluate the threshold S factors with drastically improved precision; the results are ${S}_{\mathrm{pp}}(0)=3.94\ifmmode\times\else\texttimes\fi{}(1\ifmmode\pm\else\textpm\fi{}0.004)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}\mathrm{MeV}\mathrm{}\mathrm{b}$ and ${S}_{\mathrm{hep}}(0)=(8.6\ifmmode\pm\else\textpm\fi{}1.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\mathrm{keV}\mathrm{}\mathrm{b}.$ The dependence of the calculated S factors on the momentum cutoff parameter $\ensuremath{\Lambda}$ has been examined for a physically reasonable range of $\ensuremath{\Lambda}.$ This dependence is found to be extremely small for the $\mathrm{pp}$ process, and to be within acceptable levels for the hep process, substantiating the consistency of our calculational scheme.

Three- and four-nucleon systems from chiral effective field theory.

Recently developed chiral nucleon-nucleon (NN) forces at next-to-leading order (NLO), that describe NN phase shifts up to about 100 MeV fairly well, have been applied to 3N and 4N systems. Faddeev-Yakubovsky equations have been solved rigorously. The resulting 3N and 4N binding energies are in the same range as found using standard NN potentials. In addition, low-energy 3N scattering observables are very well reproduced as for standard NN forces. The long-standing A(y) puzzle is absent at NLO. The cutoff dependence of the scattering observables is rather weak.

A variational approach to three- and four-nucleon systems

The correlated Hyperspherical Harmonic technique is a powerful tool for describing few-nucleon systems. The triton and alpha-particle binding energies, calculated with different realistic potentials, are found in good agreement with the corresponding estimates of other sophisticated techniques. Accurate results for p − d and n − 3H scattering observables are obtained, as well. Interesting comparisons are done with experimental data in order to test the various potential models. Of particular importance is the correct inclusion of the Coulomb repulsion between charged particles, responsible for sizeable interference contributions. The study of the capture reaction d( p, γ) 3 He is also briefly discussed.