Turning the nuclear energy density functional method into a proper effective field theory: reflections

Abstract

Nuclear energy density functionals (EDFs) have a long history of success in reproducing properties of nuclei across the table of the nuclides. They capture quantitatively the emergent features of bound nuclei, such as nuclear saturation and pairing, yet greater accuracy and improved uncertainty quantification are actively sought. Implementations of phenomenological EDFs are suggestive of effective field theory (EFT) formulations and there are hints of an underlying power counting. Multiple paths are possible in trying to turn the nuclear EDF method into a proper EFT. I comment on the current situation and speculate on how to proceed using an effective action formulation.

Probing ab initio emergence of nuclear rotation

“…where the Coriolis decoupling parameter a depends upon the structure of the rotational intrinsic state. The excitation spectra obtained in NCCI calculations for the odd-mass isotopes 7,9,11 Be are shown in Figs. 1-3, with energies against an angular momentum axis scaled as J(J + 1), as appropriate for rotational energy analysis.…”

“…These degrees of freedom are traditionally the domain of phenomenological models [1][2][3][4][5], yet their description may be placed on a more fundamental footing if viewed in terms of effective theories built on a microscopic description. Indeed, the emergent phenomena of nuclear structure may be viewed as simply the topmost tier in a tower of effective theories of nuclear physics beginning at the subnucleonic level [6,7].…”

“…To explore the physical structure of emergent rotation in some of the lightest nuclei, and to gain some insight into the nature of the relevant effective degrees of freedom, we consider here a few illustrative "case studies" of rotational bands in ab initio no-core configuration interation (NCCI) [17], or no-core shell model (NCSM), calculations of the odd-mass Be isotopes, specificially, 7,9,11 Be.…”

“…For the illustrative case of emergent rotational bands in the Be isotopes, we establish an understanding of the underlying oscillator space and angular momentum (orbital and spin) structure. We consider no-core configuration interaction (NCCI) calculations for 7,9,11 Be with the Dae-jeon16 internucleon interaction. Although shell model or rotational degrees of freedom are not assumed in the ab initio theory, the NCCI results are suggestive of the emergence of effective shell model degrees of freedom (0 ω and 2 ω excitations) and LS-scheme rotational degrees of freedom, consistent with an Elliott-Wilsdon SU(3) description.…”

Model nuclear energy density functionals derived from ab initio calculations

“…In this article, we aim to explore a complementary approach, which is based on explicitly bridging the ab initio methods with the nuclear EDFs. Formal connections between the two approaches are the subject of recent studies [25,26]. Furthermore, in Ref.…”