Intrinsic operators for the translationally-invariant many-body problem

Abstract

The need to enforce fermionic antisymmetry in the nuclear many-body problem commonly requires use of single-particle coordinates, defined relative to some fixed origin. To obtain physical operators which nonetheless act on the nuclear many-body system in a Galilean-invariant fashion, thereby avoiding spurious center-of-mass contributions to observables, it is necessary to express these operators with respect to the translational intrinsic frame. Several commonly-encountered operators in nuclear many-body calculations, including the magnetic dipole and electric quadrupole operators (in the impulse approximation) and generators of SU(3) and Sp(3,R) symmetry groups, are bilinear in the coordinates and momenta of the nucleons and, when expressed in intrinsic form, become two-body operators. To work with such operators in a second-quantized many-body calculation, it is necessary to relate three distinct forms: the defining intrinsic-frame expression, an explicitly two-body expression in terms of two-particle relative coordinates, and a decomposition into one-body and separable two-body parts. We establish the relations between these forms, for general (non-scalar and non-isoscalar) operators bilinear in coordinates and momenta.

arXiv comment48 pages, 2 figures

References in corpus (22)

• Recent developments in no-core shell-model calculations
• Ab initio coupled-cluster approach to nuclear structure with modern nucleon-nucleon interactions
• Nuclear Sizes and the Isotope Shift
• Collective Modes in Light Nuclei from First Principles
• Solution of the center-of-mass problem in nuclear structure calculations
• Benchmarks of the full configuration interaction, Monte Carlo shell model, and no-core full configuration methods
• Lithium isotopes within the ab intio no-core full configuration approach
• Coulomb-Sturmian basis for the nuclear many-body problem
• Matter and charge radius of 6He in the hyperspherical-harmonics approach
• Efficacy of the SU(3) scheme for ab initio large-scale calculations beyond the lightest nuclei
• Dual algebraic structures for the two-level pairing model
• Confined One Dimensional Harmonic Oscillator as a Two-Mode System
• Halo nuclei 6He and 8He with the Coulomb-Sturmian basis
• Emergent Sp(3,R) dynamical symmetry in the nuclear many-body system from an ab initio description
• Application of the coherent state formalism to multiply excited states
• Natural orbital description of the halo nucleus 6He
• Spurious states in the Faddeev formalism for few-body systems
• Isoscalar Hamiltonians for light atomic nuclei
• Partial Dynamical Symmetry in the Symplectic Shell Model
• Algebraic evaluation of matrix elements in the Laguerre function basis
• Construction of the center-of-mass free space for the SU(3) no-core shell model
• Perspectives on Nuclear Structure and Scattering with the Ab Initio No-Core Shell Model

Cited by in corpus (11)

• Emergent Sp(3,R) dynamical symmetry in the nuclear many-body system from an ab initio description
• Quadrupole moments and proton-neutron structure in p-shell mirror nuclei
• Natural orbitals for the ab initio no-core configuration interaction approach
• Rotational bands beyond the Elliott model
• Magnetic moments of $A=3$ nuclei with chiral effective field theory operators
• Translationally invariant matrix elements of general one-body operators
• Robust ab initio predictions for dimensionless ratios of E2 and radius observables. II. Estimation of E2 transition strengths by calibration to the charge radius
• Direct ab initio calculation of the ${}^4$He nuclear electric dipole polarizability
• Robust ab initio predictions for dimensionless ratios of E2 and radius observables. I. Electric quadrupole moments and deformation
• Halo structure of ${}^6$He from $\text{ab initio}$ two-nucleon spatial correlations
• Deformed natural orbitals for ab initio calculations