The distorted axi-planar superfluid phase of $^3$He in the “nematically ordered” aerogel

Stimulated by the results of NMR experiments with superfluid $^3$He in “nematically ordered” aerogel (R. Sh. Askhadullin, V. V. Dmitriev, D. A. Krasnikhin et al., Pis`ma v ZHETF, 95, 355 (2012)) we report on the results of phenomenological analysis of stability of different phases of superfluid $^3$He subjected to a strong homogeneous uniaxial anisotropy. On a basis of this analysis we suggest a form of the order parameter for the new ESP2 phase observed in the quoted experiments. In the weak coupling limit the suggested order parameter approaches that of the axi-planar phase. We discuss a possible experimental check of the proposed identification of the new phase.