The standard model (SM) calculations of electroweak processes in nuclei relies on nuclear structure approximations. Ref [1] offers a review on the related problem of setting up limits on the parameters for non-trivial extensions of the SM. In this paper we study the consequences of symmetry violations on the calculation of nuclear matrix elements corresponding to electroweak operators. In particular, we focus our attention on the restoration of the translational and Galilean invariance of the nuclear hamiltonian. The case of spurious center of mass (c.m.) motion is a well studied example of a broken symmetry in nuclear hamiltonian. The calculation of E1 matrix elements in nuclei is hampered by the use of an independent-particle description, which quite generally implies the violation of translation symmetry.
[1] M.K. Moe and P. Vogel, Ann. Rev. Nucl. Part. Sci. 44 (1994) 247.