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# Landau Parameters from the Skyrme energy functional

A simple and instructive description of the residual interaction in homogeneous INM is given by the Landau interaction developed in the context of Fermi-liquid theory [50]. Landau parameters corresponding to the Skyrme forces are discussed in Refs. [21,27,36,37,38,73]. Starting from the full density matrix in (relative) momentum space , the various densities are defined as
 = (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)

The normalization factor N0 is the level density at the Fermi surface
 (65)

A variety of definitions of the normalization factor N0 are used in the literature and great care has to be taken when comparing values from different groups; see, e.g., Ref.[50] for a detailed discussion. We use the convention defined in [38]. The Landau parameters corresponding to the general energy functional (6) are
 f0 = f0' = g0 = g0 = f1 = f1' = g1 = g1' = (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 .

Next: Landau Parameters from the Up: Gamow-Teller strength and the Previous: Pressure, Incompressibility and Asymmetry
Jacek Dobaczewski
2002-03-15