Translationally invariant matrix elements of general one-body operators

Abstract

Precision tests of the Standard Model and searches for beyond the Standard Model physics often require nuclear structure input. There has been a tremendous progress in the development of nuclear ab initio techniques capable of providing accurate nuclear wave functions. For the calculation of observables, matrix elements of complicated operators need to be evaluated. Typically, these matrix elements would contain spurious contributions from the center-of-mass (COM) motion. This could be problematic when precision results are sought. Here, we derive a transformation relying on properties of harmonic oscillator wave functions that allows an exact removal of the COM motion contamination applicable to any one-body operator depending on nucleon coordinates and momenta. Resulting many-nucleon matrix elements are translationally invariant provided that the nuclear eigenfunctions factorize as products of the intrinsic and COM components as is the case, e.g., in the no-core shell model approach. An application of the transformation has been recently demonstrated in calculations of the nuclear structure recoil corrections for the beta-decay of 6He.

arXiv comment7 pages, matches version accepted for publication

References in corpus (25)

• The Effective Field Theory of Dark Matter Direct Detection
• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Properties of ${}^{12}$C in the {\it ab initio} nuclear shell-model
• Recent developments in no-core shell-model calculations
• Discrepancy between experimental and theoretical $\beta$-decay rates resolved from first principles
• In-Medium Similarity Renormalization Group for Nuclei
• Non-Empirical Interactions for the Nuclear Shell Model: An Update
• Few-nucleon systems in translationally invariant harmonic oscillator basis
• New physics searches in nuclear and neutron $\beta$ decay
• Beta Decays and Non-Standard Interactions in the LHC Era
• Single electron detection and spectroscopy via relativistic cyclotron radiation
• Comprehensive analysis of beta decays within and beyond the Standard Model
• Solution of the center-of-mass problem in nuclear structure calculations
• Emergent properties of nuclei from ab initio coupled-cluster calculations
• Microscopic optical potentials derived from ab initio translationally invariant nonlocal one-body densities
• Ab initio nuclear response functions for dark matter searches
• Isospin-forbidden electric-dipole capture and the $\alpha (d,\gamma {)}^6$Li reaction
• A Mathematica script for harmonic oscillator nuclear matrix elements arising in semileptonic electroweak interactions
• Weak interaction studies at SARAF
• Intrinsic operators for the translationally-invariant many-body problem
• Precision Beta Decay as a Probe of New Physics
• Consistent description of angular correlations in $\beta$ decay for Beyond Standard Model physics searches
• Nuclear spin features relevant to ab initio nucleon-nucleus elastic scattering
• Nuclear kinetic density from ab initio theory
• Constraining new physics with a novel measurement of the ${}^{23}$Ne $\beta$-decay branching ratio

Cited by in corpus (4)

• Natural orbitals for the ab initio no-core configuration interaction approach
• Ab initio no-core shell model description of ${}^{10-14}$C isotopes
• Muon Capture on ${}^6$Li, ${}^{12}$C, and ${}^{16}$O from $AbInitio$ Nuclear Theory
• Chiral uncertainties in ab initio nucleon-nucleus elastic scattering