The adiabatic $S$-matrix and quasiparticles

A study is made of the adiabatic $S$-matrix $S_\alpha$ for a normal Fermi system. Expressions are obtained for its matrix elements for small values of $\alpha$. The connection is established between the operator $S_\alpha$ and the physical scattering matrix for quasiparticles. A unitary operator is found which transforms the Hamiltonian considered into the Hamiltonian of an ideal gas to within terms which are unimportant in a consideration of lowlying excited states.