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In terms of the density matrix
and pairing tensor
,
defined as
![$\displaystyle \rho =V^{\ast }V^{T},\quad \kappa =V^{\ast }U^{T}=-UV^{\dagger },$](img35.png) |
(7) |
the HFB energy is expressed as an energy functional:
where
The variation of the HFB energy (8) with respect to
and
yields the HFB equations:
![$\displaystyle {\cal H}\left( \begin{array}{c} U_k \\ V_k \end{array} \right) =E_k\left( \begin{array}{c} U_k \\ V_k \end{array} \right) ,$](img43.png) |
(11) |
where
![$\displaystyle {\cal H}=\left( \begin{array}{cc} e+\Gamma -\lambda & \Delta \\ -\Delta^{\ast } & -(e+\Gamma )^{\ast }+\lambda \end{array} \right) ,$](img44.png) |
(12) |
and
are the
th columns of matrices
and
,
respectively, and
is a positive quasiparticle energy eigenvalue.
Since the HFB state
violates the particle-number symmetry,
the Fermi energy
is introduced to fix the average particle number.
Next: The Skyrme HFB method
Up: The HFB method
Previous: The HFB method
Jacek Dobaczewski
2006-10-13