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 U(3) and 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.
Caprio, Mark A., et al. "Intrinsic operators for the translationally-invariant many-body problem." Journal of Physics. G, Nuclear and Particle Physics, vol. 47, no. 12, Oct. 2020. https://doi.org/10.1088/1361-6471/ab9d38
Caprio, Mark A., McCoy, Anna E., & Fasano, Patrick J. (2020). Intrinsic operators for the translationally-invariant many-body problem. Journal of Physics. G, Nuclear and Particle Physics, 47(12). https://doi.org/10.1088/1361-6471/ab9d38
Caprio, Mark A., McCoy, Anna E., and Fasano, Patrick J., "Intrinsic operators for the translationally-invariant many-body problem," Journal of Physics. G, Nuclear and Particle Physics 47, no. 12 (2020), https://doi.org/10.1088/1361-6471/ab9d38
@article{osti_1850095,
author = {Caprio, Mark A. and McCoy, Anna E. and Fasano, Patrick J.},
title = {Intrinsic operators for the translationally-invariant many-body problem},
annote = {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 U(3) andSp(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.},
doi = {10.1088/1361-6471/ab9d38},
url = {https://www.osti.gov/biblio/1850095},
journal = {Journal of Physics. G, Nuclear and Particle Physics},
issn = {ISSN 0954-3899},
number = {12},
volume = {47},
place = {United States},
publisher = {IOP Publishing},
year = {2020},
month = {10}}
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