On the Theory of Meson Decay

Abstract

A new derivation of the meson lifetime and of the $\beta$-decay formula according to Yukawa's theory is given in which the meson field equations are used in their unquantized form. The vectorial meson theory leads to a Fermi $\beta$-decay theory with the Gamow-Teller selection rules as required by experiment. It is, however, not possible to obtain a quantitative agreement for both meson decay and $\beta$-decay. When the constants are so adjusted as to give the observed lifetime for $\beta$-decay, the resulting lifetime of the meson is of the order ${10}^{-8\mathrm{}}$ sec., as compared with about ${10}^{-6\mathrm{}}$ sec. from cosmic-ray observations. It is shown that the uncertainties in nuclear theory do not greatly influence this result, and that most of the conceivable changes in the theory make the theoretical lifetime of the meson shorter and thus the discrepancy greater.