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Measurability of the spin density matrix
ANNALS OF PHYSICS:49, 339-340 (1968)
Abstracts
of Papers
to Appear
in Future
Issues
Measurability of the Spin Density Matrix. ROGER G. NEWTON AND BING-LIN YOUNG. Indiana University, Bloomington, Indiana. The spin density matrix for particles of arbitrary intrinsic angular momentum is explicitly expressed in terms of directly measurable quantities. The latter are taken to be either expectation values of components of multipole moments, or the relative weights of partial beams split up by a Stern-Gerlach apparatus according to eigenvalues of dipole projections in several directions. Potential Model Calculation for Coplanar and Noncoplanar, Proton-Proton Bremsstrahlung. DIETER DRECHSEL AND L. C. MAXIMON. The Catholic University of America and National Bureau of Standards, Washington DC. The cross section for proton-proton bremsstrahlung is calculated for both coplanar and noncoplanar events using the Hamada-Johnston and Reid (soft-core) potentials. Agreement is obtained with the experimental data for angular distributions and cross sections integrated over the photon directions. We present a detailed analysis of the kinematics, the phase space and the matrix element in the neighborhood of the kinematic limit of noncoplanarity. We find a rapid decrease of the cross section integrated over photon angles as this limit is approached. This is due, not to a strong variation of the phase space, which is essentially constant, but to the fact that near the kinematic limit for noncoplanarity of the protons, the photon is restricted to angles for which the probability for emission is small. For low energies (530 MeV) of the incident proton, we give analytic expressions for the scattering amplitude, valid for coplanar as well as for noncoplanar events. Generalization of Distortion Operator Method. B. MICHALIK. Institute of Plasma Physics, Czechoslovak Academy of Sciences, Prague, Czechoslovakia. A set of new objects is introduced into the theory, the nth term of which is called “the distortion operator of nth kind”. The distortion operator of 0th kind is identical to the transition (or reaction) operator, the distortion operator of 1st kind is the previously introduced distortion operator. Equations for the new operators are deduced and shown to be nonsingular for all n > 1. The radius and speed of convergence of the Neumann series following from these equations increase with increasing n. The transition and reaction operators are expressed in terms of the distortion operator of the nth kind; in the first approximation of the second distortion approach unitarity is satisfied (as well as in the first order of the first distortion approach). In the partial wave momentum representation, separable approximations of a given interaction are then obtained. Finally, the convergence when going from the first to the second distortion approach is tested and found to be very rapid. Charge Qaantization and Nonintegrable Lie Algebras. C. A. HURST. Center for Theoretical Studies, University of Miami, Coral Gables, Florida. The Schrodinger equation for the motion of an electric charge in the field of a magnetic monopole is examined to see how the quantization of the interaction constant follows from the requirement of rotational invariance. It is shown that the Hamiltonian can be extended 339
Abstracts
of Papers
to Appear
in Future
Issues
Measurability of the Spin Density Matrix. ROGER G. NEWTON AND BING-LIN YOUNG. Indiana University, Bloomington, Indiana. The spin density matrix for particles of arbitrary intrinsic angular momentum is explicitly expressed in terms of directly measurable quantities. The latter are taken to be either expectation values of components of multipole moments, or the relative weights of partial beams split up by a Stern-Gerlach apparatus according to eigenvalues of dipole projections in several directions. Potential Model Calculation for Coplanar and Noncoplanar, Proton-Proton Bremsstrahlung. DIETER DRECHSEL AND L. C. MAXIMON. The Catholic University of America and National Bureau of Standards, Washington DC. The cross section for proton-proton bremsstrahlung is calculated for both coplanar and noncoplanar events using the Hamada-Johnston and Reid (soft-core) potentials. Agreement is obtained with the experimental data for angular distributions and cross sections integrated over the photon directions. We present a detailed analysis of the kinematics, the phase space and the matrix element in the neighborhood of the kinematic limit of noncoplanarity. We find a rapid decrease of the cross section integrated over photon angles as this limit is approached. This is due, not to a strong variation of the phase space, which is essentially constant, but to the fact that near the kinematic limit for noncoplanarity of the protons, the photon is restricted to angles for which the probability for emission is small. For low energies (530 MeV) of the incident proton, we give analytic expressions for the scattering amplitude, valid for coplanar as well as for noncoplanar events. Generalization of Distortion Operator Method. B. MICHALIK. Institute of Plasma Physics, Czechoslovak Academy of Sciences, Prague, Czechoslovakia. A set of new objects is introduced into the theory, the nth term of which is called “the distortion operator of nth kind”. The distortion operator of 0th kind is identical to the transition (or reaction) operator, the distortion operator of 1st kind is the previously introduced distortion operator. Equations for the new operators are deduced and shown to be nonsingular for all n > 1. The radius and speed of convergence of the Neumann series following from these equations increase with increasing n. The transition and reaction operators are expressed in terms of the distortion operator of the nth kind; in the first approximation of the second distortion approach unitarity is satisfied (as well as in the first order of the first distortion approach). In the partial wave momentum representation, separable approximations of a given interaction are then obtained. Finally, the convergence when going from the first to the second distortion approach is tested and found to be very rapid. Charge Qaantization and Nonintegrable Lie Algebras. C. A. HURST. Center for Theoretical Studies, University of Miami, Coral Gables, Florida. The Schrodinger equation for the motion of an electric charge in the field of a magnetic monopole is examined to see how the quantization of the interaction constant follows from the requirement of rotational invariance. It is shown that the Hamiltonian can be extended 339