Transport in Dilute Gases and Chemical Forces

It is shown that the theory of transport phenomena in gases may be so formulated that the potentials characterizing the cross sections, which account for intractions between molecules in the binary collision limit, are the same as those conventionally employed in investigations of molecular structure. Thus it is indicated that at least some of the essential features of chemical forces may be conveniently introduced into the description of such phenomena.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69736/2/JCPSA6-32-6-1817-1.pd

Nonlinear Bremsstrahlung

A computation of the probability per unit path per photon for an arbitrary number of photons to be emitted or absorbed by an electron passing through the field of an ion is presented. The results provide a qualitative estimate of the conditions for the onset of nonlinear processes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86150/1/PhysRevA.5.1660-RKO.pd

Kinetic Equations for Fully Ionized, Inhomogenous Plasmas

It is shown that, in the sense of certain procedures for successively approximating the quantum Liouville equation, the Boltzmann-Vlasov-Maxwell equations for the description of the fully ionized plasma are a natural first approximation. The nature of some of the approximations inherent in the use of such a description of the plasma is indicated, but little attention is given to their quantitative evaluation. An H theorem for the particle-photon system is demonstrated.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86128/1/PhysRev.130.2142-RKO.pd

Small-Energy Rotational Transitions in Slow-Neutron Scattering by Water

A model which treats one rotational degree of freedom as hindered and the other as free and all translational degrees of freedom as hindered has been employed to calculate neutron differential scattering cross section of water in the region of small-energy transfers. The distribution is found to be sensitive to the presence of free-rotation transitions. It is suggested that such transitions present additional complexities in the study of molecular center-of-mass motions from high-resolution scattering data.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86122/1/PhysRev.131.2547-RKO.pd

The Phenornenological Theory of Exchange Currents in Nuclei

As was first pointed out by Siegert, the existence of exchange forces in nuclei implies the existence of accompanying exchange currents. Sachs has calculated an expression for these, by making the Hamiltonian containing exchange potentials gauge-invariant, and has applied it to the calculations of exchange magnetic moments in H3 and He3. The Hamiltonian obtained by Sachs is not the most general admissible one. More generally, the exchange current density is found to depend on a vector function whose irrotational part is completely determined by gauge-invariance but whose solenoidal part is arbitrary except for the requirements (following from conditions of translational invariance and symmetry in all nucleons on the Hamiltonian) that it be translationally invariant and antisymmetric under the exchange of the spin and space coordinates of each pair of nucleons. Making use of these conditions on the Hamiltonian, the explicit form of the dependence of the solenoidal part of the exchange current upon the spin and isotopic spin coordinates of the nucleons has been derived. In the resultant exchange moments, the irrotational part leads to the expression obtained by Sachs, while the solenoidal term contribution contains the spin operators of the nucleons in particular combinations, together with arbitrary functions of the nucleon separation. Villars' exchange moment expression, as obtained from meson theory, is included as a special case and hence the exchange contributions to the moments of H3 and He3 are explicable on a phenomenological basis, contrary to the results obtained in Sachs' special case. The generality and significance of the results are discussed in relation to the various meson theories.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86129/1/PhysRev.79.795-RKO.pd

The Scattering of Neutrons by Macroscopic Systems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86137/1/osborn-scattering_neutrons.pd

Effects of Lattice Vibrations on Angular Correlations

A theory of the influence of the environment on ?-? angular correlation is presented. The theory is formulated by using the damping theory, and the perturbation factor of the perturbed angular-correlation function, which contains the effects of the changes of the states of the environment on the angular correlation, is obtained. In the solid environment, the effects of the lattice vibrations on the electric quadrupole coupling have been analyzed by using the normal-mode expansion of the lattice displacements; and the perturbed angular correlation function is shown to be a function of the crystal temperature. In order to determine the nuclear electric quadrupole moment in an excited state, which cannot be done by the usual microwave methods, a rotational technique is suggested and the theory has been developed for the case of asymmetric fields. For the special case of an axially symmetric crystalline field, the present theory predicts a phase shift in the rotational pattern of anisotropy.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86149/1/PhysRev.146.695-RKO.pd

Empirical Determination of Nuclear Moments of Inertia and Intrinsic Quadrupole Moments

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86148/1/PhysRev.103.833-RKO.pd

Nuclear Matrix Elements in Beta Decay

By using the j-j coupling model, all the _-decay nuclear matrix elements are calculated (in terms of radial integrals) for one- and two-nucleon configurations. The operators in terms of which one can describe the entire theory are of five types. Three of these, involving the nucleon momentum operator, replace the operators which, in the conventional representation of the theory, appeared as odd Dirac operators. The operators in the present representation, which is most naturally expressed in terms of spherical notation and angular momentum eigenfunctions are explicitly related to those which appeared in the older notation as cartesian tensor components. The results for both one- and two-nucleon configurations are expressed in terms of reduced matrix elements which, in turn, can be written in terms of Racah coefficients and other coefficients derived from them. All these coefficients, and thereby the reduced matrix elements, can be written in terms of comparatively simple algebraic formulas which cover all cases of interest. A brief discussion of the implications of these results for spectral shapes and comparative half-lives is given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86124/1/PhysRev.93.1326-RKO.pd

The Pseudoscalar Interaction and the Beta Spectrum of RaE

It is shown that the theory of forbidden beta transitions, as hitherto used, does not provide a correct treatment of the pseudoscalar interaction. This is demonstrated by the application of a canonical transformation to the Hamiltonian of interacting nucleons and leptons whereby all odd nuclear Dirac operators are eliminated from the theory. When this is done properly it is seen that the pseudoscalar interaction makes a contribution to the _-decay process only by virtue of the fact that the lepton covariants are not constant. The corresponding additional operators introduced in the other three interactions (S is pure even) are examined and it is shown that, except in one case, these make trivial corrections which would not be observed in practice. The exception occurs in second and higher forbidden transitions wherein the spin change (tensor rank, strictly speaking) is lower than the forbiddenness order. By virtue of present knowledge of the beta interaction these must be regarded as small correction terms. The possibility of calculating all nuclear matrix elements using nonrelativistic wave functions based on some coupling model is discussed. The results presented here also show that wherever P and T interactions interfere (spin change zero, first-forbidden transitions) it will be possible to obtain the ratio of coupling coefficients (gP/gT for example) by comparison with the observed spectral shapes. A method of reduction of the _-decay operators is described and it is pointed out that the same procedure is very convenient for obtaining the nuclear matrix elements. In this method the irreducible tensors are obtained automatically and the retardation expansion is a trivial operation performed at the end of the calculation rather than at the beginning. The correction factors for pseudoscalar (P) as well as P-T and P-A mixtures are obtained and the fact that the shape of the correction factor is strongly modified as compared to the customary result is observed. The correction factor is now more strongly Z dependent and this would perhaps account for the appearance of the P interaction only for heavy elements. The results of this investigation are applied to the RaE spectrum. No fit with the assumption of zero spin for RaE can be obtained. It is suggested that the spin of RaE is unity, and other evidence pointing in this direction is cited.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86125/1/PhysRev.93.1315-RKO.pd