Next: Study of C_{1}^{s} [0].
Up: GT resonances from generalized
Previous: GT resonances from generalized
We begin with the simplest case, assuming that
(i) the functional is gauge invariant,
(ii) all timeodd coupling constants are densityindependent, and
(iii) the spinsurface term can be neglected, i.e.,
.
The only remaining free parameter in the spinisospin channel
is C_{1}^{s}, which is directly related to the Landau parameters
via Eqs. (16) and (18):

(19) 
where g_{1}' is fixed by C_{1}^{T} [also in Eq. (18)].
Figure 6 shows results for the GT resonance energy when
g_{0}' is systematically varied from its SkO' value by altering C_{1}^{s}.
We have chosen only nuclei that can be expected to exhibit a collective
response to GT excitations. Noncollective contributions may show up,
however, when the coupling constants are changed. In ^{124}Sn,
for example, a state below the resonance collects a lot of strength for
small values of g_{0}'. Only by increasing g_{0}' does one push that
strength into the resonance. Similarly, in ^{112}Sn a
state about 5MeV above the resonance increasingly collects
strength as g_{0}' grows.
As the underlying singleparticle spectra are the same for all the cases
in Fig. 6, the differences are due entirely to the
value of g_{0}'. With increasing g_{0}', the resonance energy increases
and more strength is pushed into the resonance. The increase of
is nearly linear, but the lines for different nuclei have
different slopes. It is gratifying that the curves for
all have a zero around the same point,
.
This value is much smaller than the
empirical value
derived earlier
[63,51,52] for at least two reasons: (i) the
influence of the singleparticle spectrum, and (ii) the
inclusion in the residual interaction of a pwave force characterized
by g_{1}'. The latter means that g_{0}'=0 does not correspond to
a vanishing interaction in the spinisospin channel.
Figure 7:
Spatial dependence of
for various values
of xC_{1}^{s}[0]/
,
cf. Eq. (10), and g_{0}' fixed at 1.2. The value
x=1 corresponds to no density dependence. For larger values
of x, the residual interaction becomes more repulsive outside
the nucleus than inside. When x=0,
vanishes
at large distances, and for negative values of x, the residual
interaction becomes attractive outside the nucleus. The density profile
used in this plot corresponds
to ^{208}Pb.

Next: Study of C_{1}^{s} [0].
Up: GT resonances from generalized
Previous: GT resonances from generalized
Jacek Dobaczewski
20020315