The virial theorem for the translation invariant theory of a polaron [3] is discussed. It is shown that, in [3], Tulub made a nonoptimal choice of variational parameters in the strong coupling limit, which led to the violation of the virial relations. The introduction of an additional variational parameter to the test function reduces the polaron energy and makes it possible to satisfy the relations of the virial theorem for a strong coupling polaron (the Pekar 1 : 2 : 3 : 4 theorem).

Bipolaron energy is calculated for various distances between the centers of polarization wells of two polarons with accounting the electron correlations. A singlet bipolaron is stable at a rather high energy of ion binding h h m % 0:143, h ¼ e 1 =e 0 (e 1 and e 0 are the high-frequency and static dielectric constants, respectively). The unique energy minimum corresponds to a one-center bipolaron (analog of a helium atom). The bipolaron binding energy constitutes up to 25.8 % of a double polaron energy at h ! 0. A triplet bipolaron (analog of ortho-helium) is energetically disadvantageous. The one-center configuration of a triplet bipolaron corresponds to a maximum on the distance dependence of the total energy J Bp ðRÞ. The exchange interaction between polarons has antiferromagnetic character. A prediction is made about a possibility of Wigner crystallization of a polaron gas, which occurs with antiferromagnetic ordering in the polaron system.

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