Neutron-proton pairing in the BCS approach

We investigate the BCS treatment of neutron-proton pairing involving time-reversed orbits. We conclude that an isospin-symmetric Hamiltonian, treated with the help of the generalized Bogolyubov transformation, fails to describe the ground state pairing properties correctly. In order for the $\mathrm{np}$ isovector pairs to coexist with the like-particle pairs, one has to break the isospin symmetry of the Hamiltonian by artificially increasing the strength of the $\mathrm{np}$ pairing interaction above its isospin-symmetric value. We briefly discuss the prescription how to choose the coupling constant of this auxiliary isospin-breaking pairing force.