Landau Parameters from the Skyrme energy functional

= | (55) | ||

= | (56) | ||

= | (57) | ||

= | (58) |

The kinetic densities are given by
,
.
The Landau-Migdal
interaction is defined as

= | |||

= | |||

(59) |

The isoscalar-scalar, isovector-scalar, isoscalar-vector, and isovector-vector channels of the residual interaction are given by

= | (60) | ||

= | (61) | ||

= | (62) | ||

= | (63) |

Assuming that only states at the Fermi surface contribute, i.e., , , , , and depend on the angle between and only, and can be expanded into Legendre polynomials, e.g.

(64) |

A variety of definitions of the normalization factor

f_{0} |
= | ||

f_{0}' |
= | ||

g_{0} |
= | ||

g_{0} |
= | ||

f_{1} |
= | ||

f_{1}' |
= | ||

g_{1} |
= | ||

g_{1}' |
= | (66) |

Higher-order Landau parameters vanish for the second-order energy functional (12), but not for finite-range interactions as the Gogny force discussed in the next Appendix. The Landau parameters provide a stability criterion for symmetric unpolarized INM: It becomes unstable for a given interaction when either , , , or is less than .