Sc41 - Ca41 Coulomb displacement energy

The Coulomb displacement energy in the $^{41}\mathrm{Sc}$-$^{41}\mathrm{Ca}$ system is calculated using three different methods. All three methods make use of Hartree-Fock densities at some stage. The Hartree-Fock calculations are performed with the SIII and SIV Skyrme-type forces. The results from all three methods are in agreement with each other. The resulting Coulomb displacement energy is less than 4 or less than 6 percent smaller than the experimental one depending on the force employed. Higher order Coulomb corrections are evaluated and it is found that they can be very large (of the order of 1 MeV) and depend on the approach taken. The use of the analog state defined with the ${T}_{\ensuremath{-}}$ operator as a representation of the physical analog leads to an overestimate of the Coulomb displacement energy by more than 0.5 MeV. The inclusion of Coulomb distortion terms restores the result by reducing the Coulomb displacement energy. One can also conclude from the present study that the mechanism of treating higher order Coulomb corrections by taking the giant isovector monopole as the only important intermediate state is in fact the correct one and gives precise results.NUCLEAR STRUCTURE Coulomb displacement energy, $^{41}\mathrm{Sc}$-$^{41}\mathrm{Ca}$ system.