Theory of the pionic decay of sigma hyperons in the bound state model

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OF PHYSICS:

Abstracts

16: 467468

(1961)

of Papers

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Quantum Theory of Measureme&. RICHARD A. MO~LD. When a quantum mechanical measurement is made, the initial wave which otherwise evolves continuously under a time dependent Schrodinger process collapses discontinuousl) to the measured state. Van Neumann formalized this process by defining the general transformation whereby a pure state is converted discontinuously into a stat’istical mixture in a measurement interaction. It is concluded by von Neumann and others that the continuous Schrodinger process and the mixture conversion process are both fundamental theoretical necessities, and that they together represent a nonclassical relationship between observer and t,he observed. The present paper shows that’ the more intuitive classical observer-observed relationship can be made consistent with quantum mechanical measurement, and that when this is done the Schrodinger theory is entirely sufficient to account for measurement processes without ‘essent,ial’ discontinuity. This requires, however, that, t,he notion of boundary conditions be est,ended to include four-volume qualifications of a kind that w-ere not necessary in classical physics, and that the task of the theory be given a special formulation. The scheme is shown to make a sound and natural connection with mixture theory for the purpose of handling inaccurate and (or) incomplete boundary observations. In addition, the assumptions of the scheme are compared with t,he classical and current assumptions, and some comments are added bearing on further theoret,ical study. Theory of the Pionic Decay of Sigma Hyperons i?~ the Bound State Model. L3.4~1~ BARSHAY. A study of the three pionic decay modes of sigma hyperons is carried out within the framework of a model in which the sigma hyperon is considered as a bound S-state of a pion and a lambda hyperon. A previous study is modified so as to include an explicit estimate of all of the simplest, dynamical mechanisms which may contribute to the decays in this model. A relat,ively unique and simple dynamical t,heory of t,he decays is formulated which has t,he following features: (1) The near zero asymmetry parameters in the decay modes S- -II+ ‘n and 2+ -+]I+ + 12 seem to follow essentially from a certain relationship between the mass of the nucleon, the mass of the sigma, and the mass of the Y1*; (2) the nearly maximal asymmeky parameter in the decay mode 2’ --tTI” + p and the approximate equality of the three decay rates follow naturally from (1) and the zl = 1x6 rule, which is assumed; (3) the asymmetry parameter for the mode Z+ -II” + p is predicted to be opposite in sign and comparable in magnitude to the asymmet’ry parameter in the pionic decay of the lambda hyperon; (4) the decayz+II+ n is predicted to be essentially pure P-wave and the decay 2+ 4II+ + 71 to be essentially pure S-wave. The above-mentioned relationship between the masses of nucleon, sigma, and 1 -I* is shown to be most reasonable if we assume that the I*,* is a bound state of a l? and a nucleon with about the same binding energy as the hypothesized bound-state sigma. Indeed, the relationship can he utilized to give an estimate of the K-meson mass in terms of the pion mass. s- and Sear

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