On hypothesis of partial conservation of the axial-vector current in nuclear matter

Expressions extending the vacuum relations of the axial-vector current conservation (PCAC) to the case of infinite nuclear matter are obtained. It is shown that the account of the S wave πN interaction results in a modification of PCAC in the matter. The weak axial and the pion-nucleon vertices in the nuclear matter are obtained basing on the theory of finite Fermi systems. Contributions from transitions far from the Fermi surface are taken into account by means of the corresponding phenomenological constants. The pion decay amplitude in the matter is found, as well as its time component. Relation of the renormalization of the pion decay amplitude in the matter to the problem of the pion-condensate instability of the nuclear matter is discussed