The iterative Arnoldi method is meaningful for the calculation of strength functions only if the number of iterations needed for accurate results is significantly less than the full RPA dimension. To study how many Arnoldi iterations we need for good accuracy, we calculated electromagnetic isoscalar (IS) and isovector (IV) strength functions [16] for doubly magic nuclei. All calculations were performed by implementing the RPA iterative solutions within the computer program HOSPHE [19], which solves the self-consistent equations in the spherical harmonic-oscillator (HO) basis. We studied both the convergence of smoothed strength functions as a function of number of Arnoldi iterations and as a function of the number of HO shells.
We used the same definitions of the ,
, and
transition operators as in Ref. [17] and the Skyrme functional
SLy4 of Ref. [20]. The function we used
to smooth the strength functions was also the same as
in [16], with
fm. Because the HF ground
state of
is spherically symmetric, our approximate
RPA phonons have good angular momentum. We tested the use of large
basis sets up to
HO shells. The HF ground state energies were
well converged for all double magic nuclei when
HO shells were
used. Below, we present the results only for
.