Induced pairing interaction in nuclei and in neutron stars

For an electron going from X to Y, the pole of the propagator for a free particle is p(2) = m(2). However, making measurements at X and Y one could not tell if the electron had emitted or absorbed any number of photons. Such process, the simplest of which corresponds to emission and subsequent absorption of a photon (self-energy process) causes a shift in the position of' the pole. Physically, this means that nothing is really free and that what one measures, the experimental mass, is not the "bare inass" but something else which includes the effect of virtual processes mentioned above. If this is true for electrons moving in vacuum it is even more true in the case of nucleons moving inside a nucleus. Bouncing inelastically off the nuclear surface, a nucleon can set it into vibrations exciting a normal mode of the system which it can reabsorb at a later time. The density of levels at the Fermi energy reflects this interweaving between fermionic and bosonic degrees of freedom and the resulting effective nucleon mass. If the vibration is reabsorbed by a second nucleon it leads to an exchange of bosons and thus to an effective interaction, e.g. in the pairing channel. Within the scenario discussed above, both quantum electrodynainics (QED) and nuclear field theory (NFT), are effective field theories. Now, while the photon is an elementary particle and the exchange of photons can be accurately parametrized in terms of the Coulomb interaction, collective surface vibrations do not exist outside the nucleus and there is no simple neither accurate parametrization of the pairing induced interaction, let alone of the (1)So NN-potential in terms of quarks and gluons. On the other hand, NFT based on effective interactions and HFB plus QRPA, provide a remarkably detailed picture of the induced pairing interaction, with which, together with e.g. the upsilon(14) NN-potential, one is able to calculate rather accurately the pairing gap of superfluid systems, including compact objects like (the inner crust of) neutron stars. The corresponding results are likely to provide the basis of a DFT of pairing in nuclei.