Kiyomi Itabashi

On the Recoil Correction to Adiabatic Nuclear Potential

Recoil correction to adiabatic nuclear potential in the symmetrical pseudoscalar meson theory with pseudovector coupling is calculated up to the first order in the nucleon velocities by means of the F-S.T formalism!) which is formulated by taking into account the normalization condition for the TammDancoff amplitude. Divergences which appear in the course of the calculations are subtracted by a sort of non-covariant renormalization procedure. Resultant correction consists of two parts, spin-orbit coupling part and velocity-independent part. The former is found to be of the correct sign and suitable magnitude as required by the theory of nuclear shell model.

A pathology of the Landau gauge in euclidean Yang-Mills theories

It is argued that the Landau gauge in euclidean Yang-Mills theories exhibits the following pathological features similar to those of the Coulomb gauge: (1) As far as asymptotically O(3) symmetric potentials are concerned, the potential for the field configuration with |q|1 is necessarily singular, where q is the topological quantum number of the configuration. (2) If furthermore the boundary condition rA→0 as r→∞ is imposed, then even the |q|=1 configuration necesstitates singularities of the potential.

On the |ΔI| = 1/2 Rule for the Decay of Σ

Isotopic spin selection rules in the decays of strange particles have been investigated and it has been strongly suggested that in these decays the interactions of the type of STA DELTA I! = 1/2 are dominant. The branching modes of SIGMA /sup 0/ decay are partially explained by the rule STA DELTA I! = 1/2. The experimental data for the ratio of the lifetimes SIGMA /sup -/ and SIGMA / sup +/ and the branching ratio between the two modes of SIGMA /sup +/ decay are not inconsistent with the rule. This rule can never be absolute, since it can not explain the data concerning K-meson decays. (A.C.)

Parity-Nonconservation and the Spins of the Strange Particles

Taking into account possible parity-nonconservation in weak interactions, the decay angular distributions of strange particles produced by pion-nucleon collisions are re-examined. It is shown that, when the paritynonconservation effect is actually observed in the decay angular distribution of the hyperon, its spin value can be determined less ambiguously than in the case of the parity-conservation. Especially, in this case, it is possible in principle to decide completely whether the spin is 1/2 or not. The effect of the parity-nonconservation can appear also in the K/sub mu /sup 2/ - and K/sub pi /sup 3/ -modes of decay, unless the spin of K is zero. The possibility of determining the spin value of the K-meson is considernd. In this case the conclusion is not so decisive as the case of the hyperon. (auth)

On the Renormalization in Tamm-Dancoff Approximation for One-nucleon Problem, II: Subtraction of Divergences in the Generalized Tamm-Dancoff Equations

The subtraction of the divergences are carried out in the generalized Tamm-Dancoff equations , derived in the previous paper (Part 1). The essence of the method is the .extension of Fubinis procedure to the arbitrarily higher order approximation. That is, first, we construct the formal solutions which satisfy the equations in question ; they contain the infinities and accordingly are quite meaningless. Then, we separate the infinities (including the overlapping divergences) individually at each stage of the construction of these formal solutions. The forms of the nucleon propagation function or the vertex parts which have been made convergent by this method depend on the configurations to which they refer. However, this seems to be inevitable for the present approximation method,·. i. e. the reduction of the infinite set of coupied integral equations to the finite one.