Figure 5 compares the
strength functions of our iterative method (solid line) with the strength functions
from Ref. [17] (dashed line). The solid line shows
the IS strength calculated when the generated Arnoldi basis is
orthogonalized against spurious mode during iteration and dotted line
corresponds to similar iterative calculation without orthogonalization. The
low-lying state at 0.72MeV, which has a large overlap with the spurious
IS
mode disappears when the orthogonalization method of
Eqs. (22)-(24) is used. Also for the
strength function, 100-120 Arnoldi iterations were needed to
produce reasonably accurate results, see Fig. 6.
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When no orthogonalization is made against the spurious mode, the obtained excitations contain small components of the spurious mode. This affects the physical part of the IS strength distribution, especially around 20-30MeV. The standard RPA strength function of Ref. [17] has not been corrected for the spuriosity but only the strength of the lowest-lying state that has a large overlap with the spurious IS mode has been omitted. At 20-30MeV, this strength agrees well with our uncorrected strength.
The orthogonalization method improves the convergence of the strength
function, because now the 8.3MeV excitation is lowest in energy and
thus converges first. Without orthogonalization against the spurious mode,
we need 140 iterations instead of 100 to get acceptably
converged strength function.