Shulga S. Theory of superfluid states with singlet and triplet types of pairing in Fermi liquid.

The thesis is devoted to the study of superfluid states in a Fermi liquid. The work is carried out on the basis of the Fermi liquid approach which is a generalization to superfluidity of the normal Fermi liquid theory by L. Landau and V. Silin. A common method of the description of superfluid spiral state is formulated, under which simultaneously with the phase invariance, the translation invariance and the invariance relatively rotations in the spin space are broken. Self-consistent equations are obtained and solved analytically and numerically. Analytical formulas are obtained for the transition temperature and the order parameter at zero temperature as a function of the spiral parameter. It is shown that in considered model the spiral states realize with triplet symmetry. It is shown that medium spin of system does not depend on the spiral parameter, however there is a dependency of the spin correlation function on the spiral parameter. Superfluidity in symmetrical nuclear matter with superposition of singlet and triplet states is considered. A system of self consistent equations is obtained and solved. The conditions for interaction and density of the system which are necessary for the existence of studied states are defined. Thermodynamic potential of the system is studied and the conclusions about stability of such states are drawn. The problem of existence of unitary superfluid states with the superposition of singlet and triplet superfluidity at the presence of asymmetry of the nuclear matter is studied.