Light nuclei from chiral EFT interactions

Recent developments in nuclear theory allow us to make a connection between quantum chromodynamics (QCD) and low-energy nuclear physics. First, chiral effective field theory (χEFT) provides a natural hierarchy to define two-nucleon (NN), three-nucleon (NNN), and even four-nucleon interactions. Second, ab-initio methods have been developed capable to test these interactions for light nuclei. In this contribution, we discuss ab-initio no-core shell-model (NCSM) calculations for s-shell and p-shell nuclei with NN and NNN interactions derived within χEFT.     

Electromagnetic interactions in a chiral effective lagrangian for nuclei

Electromagnetic (EM) interactions are incorporated in a recently proposed effective field theory of the nuclear many-body problem. Earlier work with this effective theory exhibited EM couplings that are correct only to lowest order in both the pion fields and the electric charge. The Lorentz-invariant effective field theory contains nucleons, pions, isoscalar scalar (σ) and vector (ω) fields, and isovector vector (ρ) fields. The theory exhibits a nonlinear realization of SU(2)_L × SU(2)_R chiral symmetry and has three desirable features: it uses the same degrees of freedom to describe the currents and the strong-interaction dynamics, it satisfies the symmetries of the underlying QCD, and its parameters can be calibrated using strong-interaction phenomena, like hadron scattering or the empirical properties of finite nuclei. It has been verified that for normal nuclear systems, the effective lagrangian can be expanded systematically in powers of the meson fields (and their derivatives) and can be truncated reliably after the first few orders. The complete EM lagrangian arising from minimal substitution is derived and shown to possess the residual chiral symmetry of massless, two-flavor QCD with EM interactions. The uniqueness of the minimal EM current is proved, and the properties of the isovector vector and axial-vector currents are discussed, generalizing earlier work. The residual chiral symmetry is maintained in additional (non-minimal) EM couplings expressed as a derivative expansion and in implementing vector meson dominance. The role of chiral anomalies in the EM lagrangian is briefly discussed.     

Approaching light nuclei and hypernuclei based on chiral interactions

We report on predictions for binding energies of light nuclei and hypernuclei based on chiral nuclear interactions. We discuss the pattern of convergence with increasing orders of the chiral expansion. Especially, we study the residual dependence on the cut-offs, contributions of three-nucleon forces and first predictions for p-shell nuclei.     

Shear viscosity of neutron matter from realistic nucleon-nucleon interactions

The calculation of transport properties of Fermi liquids, based on the formalism developed by Abrikosov and Khalatnikov, requires the knowledge of the probability of collisions between quasiparticles in the vicinity of the Fermi surface. We have carried out a study of the shear viscosity of pure neutron matter, whose value plays a pivotal role in determining the stability of rotating neutron stars, in which these processes are described using a state-of-the-art nucleon-nucleon potential. Medium modifications of the scattering cross section have been consistently taken into account through an effective interaction obtained from the matrix elements of the bare interaction between correlated states. Medium effects produce a large increase of the viscosity at densities rho > or approximately0.1 fm;{-3}.     

Peripheral nucleon-nucleon phase shifts and chiral symmetry

Within the one-loop approximation of baryon chiral perturbation theory we calculate all one-pion and two-pion exchange contributions to the nucleon-nucleon interaction. In fact we construct the elastic NN-scattering amplitude up to and including third order in small momenta. The phase shifts with orbital angular momentum L ≥2 and the mixing angles with J ≥ 2 are given parameter free and thus allow for a detailed test of chiral symmetry in the two-nucleon system. We find that for the D-waves the 2π-exchange corrections are too large as compared with empirical phase shifts, signaling the increasing importance of shorter range effects in lower partial waves. For higher partial waves, especially for G-waves, the model-independent 2π-exchange corrections bring the chiral prediction close to empirical NN phase shifts. We propose to use the chiral NN phase shifts with L ≥ 3 as input in a future phase-shift analysis. Furthermore, we compute the irreducible two-pion exchange NN potentials in coordinate space. They turn out to be of van der Waals type, with exponential screening of two-pion mass range.     

Gamow-Teller strength with realistic nucleon-nucleon interactions

Two realistic nucleon-nucleon interactions are used to calculate the energy-weighted sum rules for the Gamow-Teller operators. There are no free parameters in our calculations. The two interactions give similar results for ⁴⁸Ca and ⁹⁰Zr.     

Renormalizability of leading order covariant chiral nucleon-nucleon interaction

In this work,we study the renormalization group invariance of the recently proposed covariant power counting in the case of nucleon-nucleon scattering [Chin.Phys.C 42(2018) 014103] at leading order.We show that unlike the Weinberg scheme,renormalizaion group invariance is satisfied in the ~3 P_0 channel.Another interesting feature is that the ~1 S_0 and ~3 P_1 channels are correlated.Fixing the relevant low energy constants by fitting to the ~1 S_O phase shifts at T_(lab).=10 and 25 MeV with cutoff values ∧=400-650 MeV,one can describe the ~3 p_1 phase shifts relatively well.In the limit of ∧→∞,the ~1 S_0 phase shifts become cutoff-independent,whereas the ~3 P_1 phase shifts do not.This is consistent with the Wigner bound and previous observations that the ~3 P_1 channel is best treated perturbatively.As for the ~1 P_1 and ~3 S_1-~3 D_1 channels,renormalization group invariance is satisfied.     

Helium halo nuclei from low-momentum interactions

We present ground-state energies of helium halo nuclei based on chiral low-momentum interactions, using the hyperspherical-harmonics method for ⁶He and coupled-cluster theory for ⁸He , with correct asymptotics for the extended halo structure.     

QCD sum rules for nucleon-nucleon and hyperon-nucleon interactions

The QCD sum rules for spin-dependent nucleon-nucleon (N N) and hyperon-nucleon (Y N) interactions are formulated and their physical implications are clarified. A dispersion integral around the nucleon threshold can be identified as a measure of interaction strength. Calculating the operator product expansion (OPE) of the correlation function, we have found that the spin-dependent operators are related to the axial and tensor charges. The obtained sum rules relate the interaction strengths to the nucleon matrix elements of the quark-gluon operators. The spin-dependent parts are smaller than the spin-independent parts in the N N and the Y N channels. The spin-independent N N interaction strength is greater than the spin-independent Y N interaction strengths. The results are consistent with the empirical result in the N N channel.     

Effective nucleon-nucleon forces and interaction of light exotic nuclei with stable nuclei at low energies

The effect of the density dependence of effective nucleon-nucleon forces on the folded potential of the interactions of the light exotic nuclei ⁶He, ¹¹Li, ¹¹Be, and ⁸B with the stable nucleus ¹²C is studied, and the corresponding experimental data on the total reaction cross sections and on elastic scattering are analyzed. A semimicroscopic double-folding model featuring various density-dependent forces based on the M3Y interaction is used together with the nucleon densities as calculated within the density-functional method by using a unified set of parameters for all the above nuclei. It is shown that the angular distributions recently measured for elastic ⁶He scattering on ¹²C at an energy of 41.6 MeV per projectile nucleon and for elastic ¹¹Be scattering on ¹²C at an energy of 49.3 MeV per projectile nucleon can be described satisfactorily if the real part of the optical folded potential is supplemented with a surface term mimicking the contribution of the dynamical polarization potential.     

Effective nucleon-nucleon interactions and nuclear matter equation of state

Nuclear matter equations of state based on Skyrme, Myers-Swiatecki and Tondeur interactions are written as polynomials of the cubic root of density, with coefficients that are functions of the relative neutron excess δ. In the extrapolation toward states far away from the standard one, it is shown that the asymmetry dependence of the critical point ( ,) depends on the model used. However, when the equations of state are fitted to the same standard state, the value of is almost the same in Skyrme and in Myers-Swiatecki interactions, while is much lower in Tondeur interaction. Furthermore, does not depend sensitively on the choice of the parameter γ in Skyrme interaction. Received: 5 May 2000 / Accepted: 16 January 2001     

Perturbative chiral nucleon-nucleon potential for the 3P0 partial wave

We study perturbativeness of chiral nuclear forces in the ³P₀ channel. In previous works, the focus has been on the one-pion exchange, and the applicable window of perturbative pion exchanges has been shown to span from the threshold to center-of-mass momentum k≃180 MeV. We will examine, instead, whether the cancellation of short- and long-range parts can sufficiently soften the ³P₀ chiral force to make it more amenable to perturbation theory. The result is encouraging, as the combined ³P₀ force is shown to be perturbative up to k≃280 MeV, covering many nuclear-structure calculations.     

Folded diagrams and 1s-Od effective interactions derived from Reid and Paris nucleon-nucleon potentials

The sd-shell effective-interaction matrix elements are derived from the Paris and Reid potentials using a microscopic folded-diagram effective-interaction theory. A comparison of these matrix elements is carried out by calculating spectra and energy centroids for nuclei of mass 18 to 24. The folded diagrams were included by both solving for the energy-dependent effective interaction self-consistently and by including the folded diagrams explicitly. In the latter case the folded diagrams were grouped either according to the number of folds or as prescribed by the Lee and Suzuki iteration technique; the Lee-Suzuki method was found to converge better and yield the more reliable results. Special attention was given to the proper treatment of one-body connected diagrams in the calculation of the two-body effective interaction.We first calculate the (energy-dependent) G-matrix appropriate for the sd-shell for both potentials using a momentum-space matrix-inversion method which treats the Pauli exclusion operator essentially exactly. This G-matrix interaction is then used to calculate the irreducible and non- folded diagrams contained in the $\text{Q}\text{?}\text{-}\text{box}$. The effective-interaction matrix elements are obtained by evaluating a $\text{Q}\text{?}\text{-}\text{box}$ folded diagram series. We considered four approximations for the basic $\text{Q}\text{?}\text{-}\text{box}$. These were (C1) the inclusion of diagrams up to 2nd order in G, (C2) 2nd order plus hole-hole phonons, (C3) 2nd order plus (bare TDA) particle-hole phonons, and (C4) 2nd order plus both hole-hole and particle-hole phonons.The contribution of the folded diagrams was found to be quite large, typically about 30%, and to weaken the interaction. Also, due to the greater energy dependence of higher-order diagrams, the effect of folded diagrams was much greater in higher orders. That is, the contribution from higher-order diagrams for most cases was greatly reduced by the folded diagrams. The convergence of the folded-diagram series deteriorates with the inclusion of higher-order $\text{Q}\text{?}\text{-}\text{box}$ processes in the method which groups diagrams by the number of folds, but remains excellent in the Lee-Suzuki method.Whereas the inclusion of the particle-hole phonon was essential to obtain agreement with experiment in earlier work, when the folded diagrams are included the effect of the particle-hole phonon is to reduce the amount of binding. All four approximations to both potentials produce interactions which badly underbind nuclei. The excitation spectra given by these interactions are, however, all rather similar to each other. The Paris interaction produces more binding than does the Reid, but differences between results obtained with the two interactions were often less than differences obtained in the four approximations. Essentially no difference was found between the effective non-central interactions from the Reid and Paris potentials after including the folded diagrams, although these two potentials themselves are quite different, especially in the strength of the tensor force.Comparisons between.calculated spectra and experiment were done for ¹⁸O, ¹⁸F, ¹⁹F, ²⁰O, ²⁰Ne, ²²Ne, ²²Na and ²⁴Mg.