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Thus far we have chosen not to let C_{1}^{s} depend
on the density. Little is known about the empirical density dependence
of the timeodd energy functional, and timeodd Landau parameters
calculated from a ``realistic'' oneboson exchange potential in DBHF
show only a very weak density dependence [64]. Because the
kinetic spin term
,
when evaluated in INM, also contributes to the density dependence
of the Landau parameters, the densitydependence of that term must
either be small or nearly canceled by other timeodd terms.
In any event, in the following, we investigate what happens when C_{1}^{s}
depends on the (isoscalar) density in the ``standard" way (10).
All nuclei we look at have finite neutron excess, which means that
the central density should be slightly smaller than .
Figure 8:
Variation of the GT resonance energy and the strength
in the resonance when the ratio
xC_{1}^{s}[0]/
of parameters
defining the density dependence of
in
Eq. (10) is varied. Symbols and scales
are as in Fig. 6.

If g_{0}' and g_{1}' are fixed in saturated INM, there is one free
parameter, C_{1}^{s}[0], with which one can vary the density
dependence (10). (
is
fixed by the value
=1.2, and we
set the exponent =0.25, as it is in the timeeven energy
functional SkO'.) We continue here to assume that gauge invariance
holds, and that
.
We vary the parameter C_{1}^{s}[0] between
and
.
Figure 7 shows the spatial
dependence of
for several values of the ratio
xC_{1}^{s}[0]/
.
By changing
C_{1}^{s}[0], one can change both the GT resonance energy and the amount
of the lowlying strength, even with
kept
constant. As Fig. 8 shows, an increase of
C_{1}^{s}[0] for a given g_{0}' has almost the same effect as an
increase of g_{0}' for a given C_{1}^{s}[0]. Thus, the INM Landau
parameters do not tell the whole story in a finite nucleus.
Figures 7 and 8 show that the spinspin
coupling has the largest effect on the GT resonance when it is located
at or even slightly outside the nuclear radius.
Next: Study of .
Up: GT resonances from generalized
Previous: Study of .
Jacek Dobaczewski
20020315