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We calculate the transverse muon polarization in the decay K ± → π 0 µ ± ν induced by the electromagnetic two-photon final-state interaction. For the central part of the Dalitz plot the typical value of this polarization is about 4 × 10 −6 .

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Relativistic calculations for the S wave pion production cross sections of the reactions p+p__,p+p+nO and p+p--,d+zc + are carried out. Importance of the small components of the deutron relativistic wave functions in the description of the p+p~d+~ + cross section is studied. The problem of the relativistic description of a bound state is discussed.

The pion-nucleon a term value is calculated using pion-nuclear scattering lengths extracted from the data on pionic atoms with A<24 and isospin I=0. The renormalization of the soft-pion ~rN amplitude in nuclear matter is taken into account. The Adependence of the pion-nuclear scattering lengths is studied. Comparison with other results for a term leads to the conclusion that the most probable interval for it is 30-50 MeV. The dispersive part of the S-wave pion-nuclear potential is discussed. The Sum Rule for the Pion-Nuclear AmplitudesOne of the methods for determination of the pionnucleon a term value (%N) is utilization of the sum rule [1] which connects the pion-nuclear iso-symmetric amplitude on the physical threshold T+ (m~) with the same amplitude in the soft-pion limit (so called Weinberg point) T +(0):Here m= and f~ denote the pion mass and the charged pion decay constant (=0,94 m=) respectively, /) -+ are the axial current divergences, IB> is the nuclear ground state, j+ are the pion source functions; the intermediate state In) runs over all states allowed by the selection rules (actually, the authors of [1] limited the set of states In> to the ground or excited nuclear states without pions or with only one pion; for our approach such a restriction is not necessary); E, and P, are energy and momentum of the intermediate system; c.t. stands for the crossed term q2 ~J+, E,-E B ~-E B-E,). Assuming validity of PCAC the commutator in the right-hand side of (1) is equal to zero. Then, if in the sum (1) we separate the coherent rescattering terms, i.e. In>=lB~>, we obtain (see [13)instead of (1) m2 d3q 2 2). T+(m~)=TB+ q (2=)32mAY~(21T,,q] +lTo~ ] (2)Here m A is the mass of the nucleus, q and (Oq are the intermediate pion momentum and energy; T,,q are iso-symmetric and iso-antisymmetric parts of the coherent scattering amplitudeand fl being isotopic indices, and the state IB(-q) ~(q)> being off-shell. As it is shown in [13 the quantitiy T + includes the soft-pion part of the pionnuclear amplitude and also terms corresponding to the incoherent rescattering (In>=lB'=>) and to the pion absorption (In>=lB'>). It was proved [1] that in the nonrelativistic potential model the quantity TB + is nothing but the Born iso-symmetric amplitude of the pion-nuclear scattering. In the framework of that model the expression for the pion-nuclear scattering length has the same structure as (2) (see [1]), namely