On the structure of the Galilean and translationally invariant operator algebra describing intrinsic properties of finite nuclear systems
The structure of the Galilean and translationally invariant operator algebra for finite systems of fermions is investigated. After performing the decomposition of the Fock space into Hilbert spaces for the center-of-mass motion and the intrinsic motion, “intrinsic” field operators are defined and their commutation relations established. These relations deviate in a certain particle number-dependent way from the usual fermion relations. It is shown that the operators corresponding to the intrinsic (e.g. nuclear) observables can be represented in the familiar way, the usual field operators being replaced by the intrinsic ones. In this theory the normal shell model calculations appear as the approximation performed by treating matrix elements of nuclear observables as if the intrinsic field operators were satisfying the exact Fermi commutation relations.