  We provide detailed analysis of strong field ionization of degenerate valence
p orbitals by circularly polarized fields. Our analytical approach is
conceptually equivalent to the Perelomov, Popov, and Terent'ev (PPT) theory and
is virtually exact for short range potentials. After benchmarking our results
against the PPT theory for s orbitals, we obtain the results for p orbitals. We
also show that, as long as the dipole approximation is valid, both the PPT
method and our results are gauge invariant, in contrast with widely used strong
field approximation (SFA). Our main result, which has already been briefly
outlined in [I. Barth and O. Smirnova, Phys. Rev. A 84, 063415 (2011)], is that
strong field ionization preferentially removes electrons counter-rotating to
the circularly polarized laser field. The result is illustrated using the
example of Kr atom. Strong, up to one order of magnitude, sensitivity of strong
field ionization to the sense of electron rotation in the initial state is one
of the key signatures of non-adiabatic regime of strong field ionization.
