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In our SHF+BCS approach, we use the Skyrme energy density
functional in its SLy4
parameterization[11] in the particlehole channel, whereas
two different pairing schemes were implemented in the
particleparticle channel. The SHF+BCS(G) scheme
employs the seniority pairing force with strength parameters defined
as in Ref.[12], i.e.,

(1) 
additionally scaled by

(2) 
In the
SHF+BCS() scheme, we apply the
statedependent interaction[13] with commonly used
parameterization variants,[14] which are summarized as

(3) 
where
and

(4) 
The scaling factors of Eq. (2), and , and
pairing strengths
MeV,
MeV (DI),
MeV,
MeV (DDDI), and
MeV,
MeV (MIX) were
adjusted to reproduce the experimental[15] neutron
(
MeV) and proton (
MeV) pairing
gaps in Fm. As we deal with contact interactions, we use
a finite pairingactive space defined by including
lowest singleparticle states for neutrons and protons, respectively.
In the SHF+BCS() approach, the pairing gap is state dependent.
Therefore, the average (spectral) gaps,

(5) 
were
used as measures of experimental pairing gaps deduced from the
oddeven mass staggering. In Eq. (5)
and are the BCS occupation amplitudes (see, e.g.,
Ref.[16] for a more detailed discussion).
Figure:
(A) The total binding energies
(lefthand side scale) and mass hexadecapole moments
(righthand side scale) along the fission paths of
Rf calculated with the SLy4 interaction and four
different pairing interactions: MIX, DDDI, and DI
interaction, and seniority pairing (G). (B) The
neutron and proton pairing gaps along the
fission paths shown above.

The calculations were carried out using the code HFODD
(v.2.19l)[17,18,19] that solves selfconsistent HF
equations by using a Cartesian 3D deformed harmonicoscillator
finite basis. In the calculations, we took the lowest 1140
singleparticle states for the basis. This corresponds to 17
oscillator shells at the spherical limit.
Next: Comparison of pairing models
Up: Theoretical framework and results
Previous: Theoretical framework and results
Jacek Dobaczewski
20061210