Next: The Skyrme energy functional
Up: A generalized Skyrme energy
Previous: A generalized Skyrme energy
Many calculations performed with the Skyrme interaction can be viewed as
energydensity theory in the spirit of the HohenbergKohnSham
approach [15], originally introduced for manyelectron
systems. Nowadays, energy density theory is a standard tool in atomic,
molecular, cluster, and solidstate physics [16], as well
as in nuclear physics [17]. The starting point is an energy
functional
of all local densities and currents ,
,
,
,
,
and
that can
be constructed from the most general singleparticle density matrix

(1) 
(see Appendix 7 for more details), where ,
,
and t are the spatial, spin, and isospin coordinates of the
wave function. The HohenbergKohnSham approach maps the nuclear
manybody problem for the ``real'' highly correlated manybody wave
function on a system of independent particles in socalled KohnSham
orbitals .
The equations of motion for
are derived
from the variational principle

(2) 
where the singleparticle Hamiltonian
is the sum of the
kinetic term
and the selfconsistent potential
that is calculated from the density matrix

(3) 
The existence theorem for the effective energy functional makes no
statement about its structure. The theoretical challenge is to find an
energy functional that incorporates all relevant physics with as few
free parameters as possible. The density functional approach as used
here is equivalent to the local density approximation to the
nuclear G matrix [18].
The energy functional investigated here in detail describes the
particlehole channel of the effective interaction only.
For the treatment of pairing correlations, the energy functional has
to be complemented by an effective particleparticle interaction
that is constructed in a similar way from the pairing density matrix;
see [19] for details. We use here the simplest functional
proportional to the square of the local pair density with the
coupling constants given in [11].
Next: The Skyrme energy functional
Up: A generalized Skyrme energy
Previous: A generalized Skyrme energy
Jacek Dobaczewski
20020315