Realistic nuclear Hamiltonian: Ab exitu approach

Abstract

Fully-microscopic No-core Shell Model (NCSM) calculations of all stable s and p shell nuclei are used to determine a realistic N N interaction, JISP16, describing not only the two-nucleon data but the binding energies and spectra of nuclei with A ≤ 16 as well. The JISP16 interaction, providing rapid convergence of the NCSM calculations, is obtained in an ab exitu approach by phase-equivalent transformations of the JISP6 N N interaction. To complement the successful but computationally intensive 'ab initio' No-core Shell Model (NCSM) [1], we introduce the 'ab exitu' NCSM. While the former has proven very successful for light nuclei when one includes three-body (N N N ) forces [2,3], the computational complexity motivates us to introduce an approach that simultaneously minimizes N N N forces while providing more rapid convergence with a pure nucleon-nucleon (N N ) force. We invoke directly an end-goal of nuclear theory (hence the term 'ab exitu'), a successful description of nuclear properties, including the available N N data, to develop a new class of N N potentials that provide accurate descriptions of a broad range of nuclear data. PACSTo achieve this, we form a union of two recent techniques -the J-matrix inverse scattering [4,5,6] and the NCSM [1]. A major ingredient of our approach is the form of the N N interaction (a small matrix in the oscillator basis), which is chosen to provide rapid convergence of manybody observables within the NCSM. Indeed, we show below that results up through A = 16 obtained directly with the bare interaction (one that accurately describes the N N data) are close to those obtained with the effective interaction and are very useful to establish the confidence region for the binding energy.Since this is a departure from the more traditional approach, we motivate our development with observations concerning the successful ab initio approaches to light nuclei. Indeed several promising microscopic approaches have been introduced and tested extensively with realistic N N interactions (see [7] and references therein) and with realistic N N + N N N interactions [8,2,3]. Progress towards heavier nuclei appears limited only by scientific manpower and by available computers. However, all approaches face the exponentially rising computational complexity inherent in the quantum many-body problem with increasing particle number and novel schemes are needed to minimize the computational burden without sacrificing realism and precision.The earliest and most successful in reaching nuclei beyond A = 4 is the Green's-function Monte Carlo (GFMC) approach [8] whose power has been used to determine a sequence of everimproving N N N interactions [8,9,10], in conjunction with highly precise N N interactions [11] that 1

In-medium similarity renormalization group for closed and open-shell nuclei

“…The first interaction optimized with this protocol is NNLO sat [26], which is able to accurately describe the ground-state energies and charge radii of 40,48 Ca at the same time. Following the same philosophy but not the same approach, Shirokov et al have produced Daejeon16, a softened chiral N N interaction that has been tuned for the description of light nuclei without explicit 3N forces [27][28][29][30].…”

Properties of nuclear matter within the JISP16NNinteraction

“…[1,2] is constructed in the J-matrix inverse scattering approach [3]. It is known to provide an excellent description of np scattering data with χ 2 /datum ≈ 1 [4].…”

“…The interaction was fitted in Ref. [1] by means of phaseequivalent transformations to the binding energies of nuclei with A ≤ 16, and it provides a good description of bindings and spectra of light nuclei without referring to three-nucleon forces [1,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In particular, the binding energy and spectrum of exotic proton-excess nucleus 14 F have been predicted [9] in No-core Full Configuration Calculations [7] with the JISP16 N N interaction.…”

“…The conventional JISP16 interaction of Refs. [1,2] is defined in N N partial waves with J ≤ 4 only; just these J ≤ 4 results were presented in Fig. 1.…”

“…However, the JISP16 saturation point is still overbound at too high a density as compared to conventional extrapolations to the infinite mass limit of heavy nuclei properties. The main idea of the JISP-type interaction is to utilize an ab exitu approach [1,39,40] in the N N force design, i. e., first the J-matrix inverse scattering approach [3] is used to construct an N N interaction perfectly describing the two-nucleon data (deuteron properties and N N scattering), next the interaction is modified by phase-equivalent transformations in order to achieve a reasonable description of many-body nuclear systems. Following this route, the JISP6 interaction fitted to nuclei with A ≤ 6 was proposed in Refs.…”