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

Abstract

was evinced. It was concluded that the half-life obtained was due to pileup of pulses with lower energy; such pileup should display a half-life of one-half the 7.7-min half-life.The lack of an observed internal conversion line indicates that the 0+, T=l level 2 probably lies above the 7=3, T-0 level. This would require a positron end point for the 0.95-sec activity in K 38 of energy > 4.84 Mev. In any case the above argument indicates that the energy of the transition is greater than 4.76 Mev. CONCLUSIONSThe experimental results reported in this paper together with the half-life measurement of Kline andWe 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 Rp~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 Rp~g, 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 * This work was done under the auspices of the U. S. Atomic Energy Commission. 1 Many of the earlier measurements are reviewed in: J. A. ); Koslov, Fitch, and Rainwater, Phys. Rev. 95, 625 (A) (1954); Camac, Piatt, and Schulte, Phys. Rev. 89, 905 (A) (1953); 88, 134 (1952); A. D. McGuire et al., Phys. Rev. 95, 625 (1954).

Charged particle motion in a highly ionized plasma

“…Powers of the dimension bearing electric charge must appear in either a quantum-mechanical parameter η or in the classical plasma coupling parameter g, with g 2 bringing in a factor of the plasma density. Long ago, Barkas et al [17] 5 Whenη pb is small, the function G has a term of order lnη pb that adds to the ln g pb , giving ln(g pb /η pb ) = ln(β κ bvpb ) which converts the classical short-distance cutoff into a quantum cutoff. This is in keeping with the remark above that quantum effects may become important whenη pb becomes small.…”

“…In these cases, the quantum parameters defined in (3.1), 17) are large. In the energy loss problem, these are the only independent dimensionless parameters that entail the quantum unit, Planck's constant .…”

“…To make contact with this line of development, we consider a distribution function f peaked 17 To make our sign conventions explicit, we note that we have defined dE/dt and dP/dt as the time rate of energy and momentum transferred to the background plasma from the moving projectile. Thus, as the projectile slows down, dE/dt and v · dP/dt are positive.…”

Contribution of close collisions to the Barkas effect: The classical picture

“…The discovery of different penetration ranges for positive and negative pions in matter made by Barkas and co-workers [1] was the first evidence of deviations of the stopping power of energetic particles from the quadratic dependence on projectile charge Z 1 predicted by the Bethe theory [2]. The origin of this difference, as proposed by Barkas, is due to higher-order terms in the perturbative Born series.…”

“…The ARB model [3] was based on the classical harmonic-oscillator model. The treatment was similar to the Bohr model [7] but the analysis was extended to secondorder ͑Z 1 3 ͒ terms, corresponding to the polarization of the atomic oscillators, in the approximation of distant collisions. They showed that the Barkas effect is characterized by the classical parameter gZ 1 0 / v 3 , where Z 1 is the bare-ion charge, 0 the oscillator frequency, v the particle velocity, and g a numerical constant.…”