The phenomenological description of a relativistic three-particle emission

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The Phenomenological Description of a Relativistic Three-Particle Emission. N. KARAYIANIS, Diamond Or. Fuze Labs., Bldg. 92, Rm. IN7, Connecticut & Van Ness Sts., N.W. Washington 25, D.C. A relativistic, phenomenological analysis of an arbitrary three-particle emission is made consistent with energy momentum and angular momentum conservation. The analysis parallels the general approach to the calculation of a decay rate from an interaction matrix with the unknown matrix elements serving as the arbitrary expansion coefficients. In this manner, the Lorentz invariants of the problem are easily traced. The result is specialized to a localized interaction for an emission of three spin one-half particles. It is shown that, in order to be consistent with Lorentz invariance, the emission must necessarily involve correlations between the momenta of the emitted particles. In the limit of three massless emitted particles, the most general energy spectrum for one of the product particles is calculated. The spectrum thus obtained is identical in form to the parametrized Michel spectra for the electron in muon decay, demonstrating that the Michel spectra have a fundamental origin. It is also shown that merely the added assumption of specific helicities for the emitted particles leads to results for muon decay identical to those obtained from the V-A law. The Deformation STANLEY SWIATECKI,

Energy of a Charged Drop: Part Argonne National Laboratory, Lawrence Radiation Laboratory,

COHEN,

V. Results of Electronic Computer Studies. Argonne, Illinois, AND WLADYSLAW J. University of California, Berkeley, Cali-

fornia. The results of electronic computer studies of equilibrium configurations of an idealized charged drop are presented. The symmetric family of saddle-point shapes has been traced as a function of the fissionability parameter 5. The properties of the saddle-point shapes have been tabulated in the interval z = 0.30 to 1: = 1.00 in steps of 0.02. The appearance of these shapes changes from dumbbell-like for 5 5 0.67 to cylinder-like for z 2 0.67. The transition is fairly rapid, but not discontinuous. The properties tabulated include the energies, moments of inertia and quadrupole moments of the saddle-point shapes. In addition, the elastic constants (stiffnesses) of the symmetric sale-point shapes for different types of symmetric and asymmetric distortions have been determined. The shapes were found to be stable against asymmetry down to r = 0.3g4, at which point an asymmetric family of equilibrium shapes bifurcates. A simple formula is given which reproduces the calculated liquid-drop thresholds with fair accuracy. New Concept of Representation of versita, Viale Taranelli, Pavia, A new, more general, concept emerged from a group-theoretical the example of the three-dimentional

a Lie Algebra. A. LOINQER, Italy. of (operator) representation study of classical mechanics, homogeneous rotation

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The Neutron Strength Function and the Shell Model. BARRY BLOCK AND H. FESHBACH, Princeton University, Department of Physics, Princeton, N. J., and CERN Geneva 23, Switzerland. The projection operator-equivalent potential method is employed for the study of neutron