Towards gauge-independent treatment of radiative capture in nuclear reactions: Applications to low-energy cluster-cluster collisions

Our departure point in describing electromagnetic (EM) interactions with nuclei (in general, bound systems of charged particles) is to use the Fock-Weyl criterion and a generalization of the Siegert theorem. It is shown how one can meet the gauge invariance principle (GIP) in all orders in the charge and construct the corresponding EM interaction operators in case of nuclear forces arbitrarily dependent on velocity. Along the guideline we have derived the conserved current density operator for a dicluster system (more precisely, the system of two finite-size clusters with many-body interaction effects included). In the context, we are addressing the current clusterization as a first step when accounting for possible cluster excitations. Being expressed through the electric and magnetic field strengths and matrix elements of the so-called generalized electric and magnetic dipole moments of the system, associated with the conserved current, the single-photon transition amplitude attains a manifestly gauge-independent (GI) form. The latter is essentially simplified at low energies.