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In INM
.
We choose pure neutron and proton states, which leads to
,
,
and similarly for all
other densities. We take the z axis as the quantization axis for
the spin, i.e.,
s_{t, x} = s_{t, y} = 0,
s_{t} := s_{t, z}, and for
the kinetic spin density .
As discussed in Refs. [72],
this breaks the isotropy of INM, leading to an axially deformed Fermi
surface, an effect which we neglect. Adding the kinetic term, the total
energy per nucleon (i.e. the ``equation of state'') for the energy
functional (7) and (8) is given by
For unpolarized INM one has
which
recovers the expression given in Ref.[23].
An interesting special case is polarized neutron matter, which
is discussed in [70] for the Skyrme interactions. A stability
criterion derived there from the twobody force point of view
as outlined in Appendix 8 was used to constrain
the parameters of the
SLyx forces [23,24]. In this limiting case, one has
,
,
which is equivalent
to
and leads to
Expressions (34) for an antisymmetrized Skyrme force imply that
,
and

(47) 
The stability of polarized neutron matter for all densities requires
[70], so the SLyx interactions take
[23,24]. However, from the energydensityfunctional
point of view, the coupling constants are independent, and the second
term in Eq. (50) also contributes to the
stability condition.
Next: Pressure, Incompressibility and Asymmetry
Up: Infinite Nuclear Matter
Previous: Fermi surfaces and kinetic
Jacek Dobaczewski
20020315