On extended supersymmetries in nuclear physics

We prove that N = 2 SUSY of the system describing interaction of pseudoscalar isovector pionic field with nucleon field can be extended to N = 3,4,5 SUSYs. Discrete symmetries of this equation are studied when external field has definite parities. It is shown that for some classes of interaction the problem possesses a parasupersymmetry (PSUSY) with two parasupercharges.