Non-relativistic Spin Research Articles

Unrestricted Dirac-Fock theory: Relativistic determination of core polarization hyperfine interactions

The unrestricted Dirac-Fock (UDF) method is developed for determining relativistic contributions to the hyperfine interaction, notably that due to core polarization. Radial core-polarization of the one-electron ( jj-coupled) spin orbitals is obtained by relaxing the restraint in restricted Dirac-Fock (RDF) theory that the radial part be independent of the magnetic quantum number, the projection m j of j. Relativistic effects on the core polarization are obtained by comparison with results obtained from the non-relativistic spin polarized Hartree-Fock ( m s unrestricted) and spin plus orbital polarized Hartree- Fock ( m s plus m j unrestricted) calculations. For the 5d transition series ions, the relativistic core polarization enhancement factor, S s ( z), is determined to be about a factor of two and so is much smaller than the isomer shift charge density enhancement factor (≈6) found earlier for these same ions. Comparison is made with limited experimental data available to date; for the case of atomic Re, excellent agreement is obtained with experiment.

On the Bunge-Kalnay position operator for the Dirac electron

A similarity is noted between a constant of the motion for the Dirac equation, with position operators as discussed by Bunge and Kalnay, and a constant of the motion discussed by Corben in connection with a nonrelativistic spinning particle.

A New Approach to Relativistic Composite Model of Hadrons. I

A new scheme of hadron composite model is proposed. The hadron constituents are described as relativistic independent particles with Dirac's four components in a central potential. The potential is supposed to be self-consistently determined via a net effect of the media of infinite constituent-particle inside a hadron. Any hadron at rest is composed of several constituent particles, i.e., the valance constituents on the media mentioned above, which are specified with the individual “whole angular momentum” j=σ/2+l, besides other suitable quantum numbers. Our scheme possesses several desirable features of hadron dynamics. First, the successful results of SU(6) symmetry founded on the concept of the non-relativistic spin of constituents are retained. Secondly, the effect of the “small component” of constituent particles enables us to make clear the problems concerning static phenomena such as the paradox of Van Royen-Weisskopf, the GA/GV ratio deviated from the predicted value of SU(6) theory and so on. Thirdly, on account of the relativistic treatment of constituent particles, our scheme improves the results of strong decays of hadrons so far dealt with, for instance, by SU(6)W.

Relativistic Effects in the Magnetic Hyperfine Structure of the 3dN4s2 Atoms

Relativistic self-consistent-field wavefunctions have been used to calculate relativistic mean values of r-3 for the orbital, spin-dipole and spin terms of the magnetic hyperfine Hamiltonian for the 3dN4s2 atoms. These theoretical values are compared with experimental results. The relativistic contribution to the experimentally determined spin term, which is usually referred to as the Casimir contribution, has been calculated to be of the order of 5-10% for these elements. The difference between the experimental spin term and the Casimir contribution is due to the contact interaction. Semiempirical values of the contact interaction have been derived using experimental results and the theoretical values of the Casimir contribution. Experimental values of the contact term are compared with theoretical results obtained from non-relativistic spin-polarized wavefunctions and many-body perturbation calculations. New relativistic correction factors for bound and excited s states are calculated by comparing non-relativistic and relativistic spin densities obtained with restricted self-consistent-field wavefunctions. These new correction factors are compared with earlier commonly used correction factors. They have also been used to correct the theoretical non-relativistic contact contribution for relativistic effects.

Functional Quantum Theory of Scattering Processes. III

Abstract Dynamics of quantum field theory can be formulated by functional equations. To develop a complete functional quantum theory one has to describe the physical information by functional operations only. The most important physical information of elementary particle physics is the matrix. In this paper the functional S-matrix is constructed for nonrelativistic spin 1/2 fermions, as in this system a rigorous construction of operator representations is possible. The method of S-matrix derivation used in I and II is improved and the exact perturbation solution for the scattering functionals is given.

Role of Spin in the Monopole Problem

The scattering of an electric charge from a magnetic monopole is discussed in a way which explicitly incorporates conservation of angular momentum. The Dirac quantization condition for the physical charges is derived from the correspondence principle and the requirement of rotational invariance. The same discussion shows that the initial and final states of the scattering reaction contain an extra spin, which cannot be associated with either particle alone. In the classical nonrelativistic theory it is known that such an extra spin appears, and that it may be identified with the angular momentum of the electromagnetic field. A quantized version of this nonrelativistic spin theory is obtained and shown to be equivalent to the Dirac theory based on a singular vector potential. The spin approach gives an interesting perspective on the relativistic monopole problem. Among the standard $S$-matrix postulates, that of crossing symmetry must be modified or abandoned if a relativistic theory is to succeed.

Description of Pauli Matter as a Continuous Assembly of Small Rotating Bodies

The method of Kramers to represent a two-component spinor is revised and developed into a consequent formulation of the quantum mechanical theory of a non-relativistic spinning particle (§4). Furthermore the method is unified with the hydrodynamical representation of the Pauli electron theory established in the previous article, giving the picture of the Pauli field as an assembly of very small rotating bodies (distinct from usual rigid bodies) continuously distributed in space (§3). The formalistic and physical features of these new representations are considered. Also some remarks are given on the characteristics of the former hydrodynamical formulation (§2). Particularly it is pointed out that Planck's constant enters this scheme only as the constant signifying the magnitude of the spin.