Ab initio Translationally Invariant Nonlocal One-body Densities from No-core Shell-model Theory

Abstract

[Background:] It is well known that effective nuclear interactions are in general nonlocal. Thus if nuclear densities obtained from {\it ab initio} no-core-shell-model (NCSM) calculations are to be used in reaction calculations, translationally invariant nonlocal densities must be available. [Purpose:] Though it is standard to extract translationally invariant one-body local densities from NCSM calculations to calculate local nuclear observables like radii and transition amplitudes, the corresponding nonlocal one-body densities have not been considered so far. A major reason for this is that the procedure for removing the center-of-mass component from NCSM wavefunctions up to now has only been developed for local densities. [Results:] A formulation for removing center-of-mass contributions from nonlocal one-body densities obtained from NCSM and symmetry-adapted NCSM (SA-NCSM) calculations is derived, and applied to the ground state densities of ${}^4$He, ${}^6$Li, ${}^{12}$C, and ${}^{16}$O. The nonlocality is studied as a function of angular momentum components in momentum as well as coordinate space [Conclusions:] We find that the nonlocality for the ground state densities of the nuclei under consideration increases as a function of the angular momentum. The relative magnitude of those contributions decreases with increasing angular momentum. In general, the nonlocal structure of the one-body density matrices we studied is given by the shell structure of the nucleus, and can not be described with simple functional forms.

13 pages, 11 Figures

References in corpus (9)

• Recent developments in no-core shell-model calculations
• Ab Initio Many-Body Calculations of n-3H, n-4He, p-{3,4}He, and n-10Be Scattering
• Ab initio no-core full configuration calculations of light nuclei
• Symmetry-guided large-scale shell-model theory
• Corrections to nuclear energies and radii in finite oscillator spaces
• Universal properties of infrared oscillator basis extrapolations
• Optical potential from first principles
• Infrared length scale and extrapolations for the no-core shell model
• Electron-scattering form factors for 6Li in the ab initio symmetry-guided framework

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