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Nonselfconsistent calculations often use the residual
LandauMigdal interaction in the spinisospin channel:


= 

(13) 
where N_{0} is a normalization factor [see Eq. (69)] and
and
are defined in Appendix 8.
In most applications, only the swave interaction with strength g_{0}'
is used, and the matrix elements of the force are not antisymmetrized.
The underlying singleparticle spectra are usually taken from
a parameterized potential, e.g., the WoodsSaxon potential.
Typical values for g_{0}', obtained from fits to GTresonance
systematics, are
[45,46,47]. (See Ref. [48] for an early
compilation of data.) Sometimes this approach is formulated in terms
of the residual interaction between antisymmetrized states. The results
are similar, e.g., g_{0}' = 1.54 in the doubledecay
calculations by Engel et al. [49]. More complicated residual
interactions, like bosonexchange potentials, have been used as well;
see, e.g., Refs. [50,51,52]. Borzov et al. use
a renormalized onepion exchange potential in connection with a
LandauMigdal interaction of type
(13) [53].
A much simpler residual interaction in the GT channel is
a separable (or ``schematic") interaction,
,
where the strength
has to be a function of A. This interaction
is widely used in global calculations of nuclear decay
[54,55]. Sarriguren et al. [56]
use it for a description of the GT resonances in deformed
nuclei with quasiparticle energies obtained from selfconsistent
HF+BCS calculations. They estimate
from the Landau
parameters of their Skyrme interaction. (The same prescription is used
in their calculations of M1 resonances [57].)
But however useful this approach may be from a technical point of
view, it is not selfconsistent. Nor is it equivalent to using the
original residual Skyrme interaction; see, e.g., the
discussion in [46].
A truly selfconsistent calculation, by contrast, should interpret
the QRPA as the smallamplitude limit of timedependent HFB theory.
The Skyrme energy functional used in the HFB should then determine
the residual interaction between unsymmetrized states in the QRPA:

(14) 
The actual form of the residual interaction that contributes to the
QRPA matrix elements of 1^{+} states is outlined in Appendix
12.
Table 1:
Landau parameters for various Skyrme interactions from relations
(34) and the Gogny forces D1 and D1s.
Missing entries are zero by construction.
Force 
g_{0} 
g_{1} 
g_{2} 
g_{0}' 
g_{1}' 
g_{2}' 
SkM* 
0.33 


0.94 


SGII 
0.62 


0.93 


SkP 
0.23 
0.18 

0.06 
0.97 

SkI3 
1.89 


0.85 


SkI4 
1.77 


0.88 


SLy4 
1.39 


0.90 


SLy5 
1.14 
0.24 

0.15 
1.05 

SLy6 
1.41 


0.90 


SLy7 
0.94 
0.47 

0.02 
0.88 

SkO 
0.48 


0.98 


SkO' 
1.61 
2.16 

0.79 
0.19 

SkX 
0.63 
0.18 

0.51 
0.53 

D1 
0.47 
0.06 
0.12 
0.60 
0.34 
0.08 
D1s 
0.48 
0.19 
0.25 
0.62 
0.62 
0.04 
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Jacek Dobaczewski
20020315