Finite rank approximation for random phase approximation calculations with Skyrme interactions: An application to Ar isotopes

Starting from an effective interaction of Skyrme type, a finite rank separable approximation is proposed for the residual particle-hole interaction with the aim to allow one to perform structure calculations in very large particle-hole spaces. The approximation is checked on a specific example by calculating isoscalar quadrupole and isovector dipole modes in a finite nucleus using the random phase approximation. It is found that the finite rank approximation is very accurate in the isoscalar channel and it reproduces reasonably well the isovector channel. The use of the finite rank interaction is illustrated by calculating the evolution of the dipole strength distribution along the Ar isotope chain, from $A=32\mathrm{}$ to $A=52.\mathrm{}$