Mass-Ratio Method Applied to the Measurement ofL-Meson Masses and the Energy Balance in Pion Decay

We report a comprehensive series of measurements made on the masses of $L$-mesons produced by the 184-inch cyclotron. A general ratio principle of measurement is employed which largely eliminates systematic errors. The particular method that we have developed is described in detail. The theory of nonequilibrium particle orbits in the cyclotron field is worked out to provide formulas from which momenta may be calculated, and to obtain the momentum distribution functions determined by the target and detector dimensions. The energy-loss processes in nuclear track emulsion, which is used as a stopping material and detector, are studied and the range-momentum exponent $q$ is found. Several small corrections to the mean range are made. A number of range straggling effects are evaluated. The theoretical distribution of the quantity $R{p}^{-q}$ ($R$ being the range and $p$ the momentum) is studied, and the first three moments of the distribution are calculated explicitly. The distribution is found to be closely gaussian. From the theory of the distribution of $R{p}^{-q}$, the best estimate and the statistical uncertainty of the mass ratio (e.g., of meson to proton) are evaluated. A number of effects influencing the ratio are studied, but all the corrections found are very small. The measurement of the momentum acquired by the muon when a pion decays has also been treated. Several important relations connecting this quantity with the particle masses are then introduced. Apparatus developed for the application of the ratio principle is described. A number of experiments in which mesons and protons of similar velocities were detected in the same nuclear track plate are reported. Each experiment was repeated a number of times. The measurements of particle ranges and orbit parameters, the magnetic field measurements, the dimensional tolerances, the calculations, and other important details are discussed.