Abstract
In this paper we describe a procedure to obtain the general operator form of two-nucleon (2N) potentials and apply it to the case of the 2N potential that has an additional dependence on the total momentum of the system. This violates Galilean invariance but terms including the total momentum appear in some relativistic approaches. In operator form, the potential is expressed as a linear combination of a fixed number of known spin-momentum operators and scalar functions of momenta. Since the scalar functions effectively define the potentials, using the operator form significantly reduces the number of parameters that are needed in numerical implementations. The proposed operator form explicitly obeys the usual symmetries of rotational invariance, particle exchange, time reflection and parity.
Highlights
In this paper we describe a procedure to obtain the general operator form of two-nucleon (2N) potentials and apply it to the case of the 2N potential that has an additional dependence on the total momentum of the system
This, nonrelativistic, limitation is justified for few-nucleon forces, including the newest models derived from Chiral Effective Field Theory [1,2,3,4], since they are constructed to accurately describe the experimental data primarily at low energies
We considered the properties of the scalar functions α under time reversal, particle exchange and Hermitian conjugation
Summary
We consider quantum mechanical potential operators for a 2N system in the non-relativistic domain. This, nonrelativistic, limitation is justified for few-nucleon forces, including the newest models derived from Chiral Effective Field Theory [1,2,3,4], since they are constructed to accurately describe the experimental data primarily at low energies. More interesting is the rotational invariance since it involves both the momentum and spin degrees of freedom of the system. This symmetry will be considered in detail in the sect. 2. We assume the potential to be Hermitian and invariant under parity, time reversal and particle exchange. We assume the potential to be Hermitian and invariant under parity, time reversal and particle exchange All these symmetry conditions are discussed in sect. It should be noted that rotational invariance and discrete symmetries can be considered separately since the respective transformations commute with each other
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
