arXiv subjects
Publications and source records attributed to Susumu Kinpara.
The axial-vector form factor for the decay of pion $\pi^{+} \rightarrow \gamma + e^{+} + \nu_e$ is calculated by using the pseudovector coupling pion-nucleon interaction with the non-perturbative term. The self-energy is approximated by the lowest-order constant. The parameter is significant to improve the value of the form factor as well as the vector form factor in our previous study.
The vector form factor of the decay $\pi^{+} \rightarrow \gamma + e^{+} + \nu_e$ is calculated by the method for the pseudovector pion-nucleon system. The non-perturbative term is taken into account by using the parameter for the self-energy of nucleon following our previous calculation of the pion form factor. The suppression of the anomalous interaction of proton in the loop integral is significant to understand the experimental value.
The correction of the higher-order process for the photon-pion-pion vertex is calculated by the field theoretical method of the pion-nucleon system. The non-perturbative term of the pseudovector coupling interaction is included to examine the effect of the self-energy.
The role of the suppression of the coupling constant in the pseudovector pion-nucleon interaction is examined to account for the calculation of the magnetic moment of nucleon. Among three kinds of the higher-order corrections the vacuum polarization of the pion propagator contributes to the numerical value considerably. On the other hand the lowest-order vertex correction for the pion-nucleon-nucleon vertex does not give large effect in the approximation of the on-shell momenta for nucleons.
The effect of the pion propagator on the $β$-decay of neutron is investigated to account for the ratio of the axial-vector to the vector part $g_A/g_V$ by including the pole term. A suggestion is made that the sign and the size of the vertex correction is appropriate to improve the discrepancy between the result of the model hamiltonian and the experiment.
The scattering amplitude of the photoproduction of $π^{+}$ is calculated using the helicity formalism. The pseudovector coupling $π$-N interaction with the non-perturbative term is applied to the perturbative expansion. The parameters for the self-energy are taken from the results of the $π$-N scattering in our previous study.
The scattering amplitude of the pion-nucleon elastic scattering is calculated by the lowest-order approximation of the perturbative expansion with the non-perturbative term. The self-energy of nucleon is determined so as to give the scattering parameters of the $S$-wave. It is shown that the scattering process mediated by the $σ$-meson plays a decisive role together with the pseudovector pion interaction.
The effect of the self-energy on the photon-proton elastic scattering is investigated for the backward and the forward directions. The shape of the Thomson scattering at the photon energy $ω\to 0$ is broken by taking into account the self-energy of proton. The electromagnetic polarizabilities $\barα\pm\barβ$ are calculated by the lowest-order perturbative treatment.
The effect of the non-perturbative term is investigated for the pion-nucleon scattering. Including the self-energy of nucleon the cross section of the elastic scattering results in a constant value at the laboratory momentum $p_L \to \infty$. The amplitude of the forward direction is applied to the dispersion relation.
The electromagnetic form factor of proton is studied following our previous calculation of the anomalous magnetic moment. The non-perturbative term is incorporated to correct the $Q^2$ dependence.
The anomalous part of the magnetic moment of nucleon is studied. The electromagnetic vertex of nucleon is calculated using the pseudovector coupling pion-nucleon interaction. The self-energy of nucleon suggested in the previous study is applied to the internal line.
The procedure for deriving the Ward-Takahashi identity is applied to the pseudovector coupling pion-nucleon system in which the isovector and axial-vector current does not conserved. The relation is given in closed form although it is more complicated than that of the quantum electrodynamics. The application to the propagator has revealed the interesting results.
Nucleon-nucleon potential is given in coordinate space starting from the Bethe-Salpeter equation appropriate to elastic scattering at the intermediate energy region. The next order in the potential is added to construct the scattering wave for ${}^3S_1$ state. The constant terms have an effect on the spin observables particularly at the center of mass angle $θ=90^{\circ}$
For the coefficients of the amplitude a set of simultaneous equations is derived in momentum space. By the auxiliary conditions they are equivalent to nonrelativistic equations and suitable for the investigation of two-nucleon system.
Bethe-Salpeter equation is applied to $p$-$n$ elastic scattering. The spin observables are calculated by the M matrix similar to $p$-$p$ case. The parameters of the meson-exchange model are used with the cut-off for the pion exchange interaction. Change of the M matrix indicates breaking of the charge independence in the nucleon-nucleon system.
Bethe-Salpeter equation is applied to $p$-$p$ elastic scattering. The observables of spin are calculated in the framework of the M matrix using the two-body interaction potential. The parameter of the pseudovector coupling constant is adjusted so as to reproduce the spin singlet part. It is shown that the spin rotation $R(θ)$ and $A(θ)$ are improved by the resonance effect for ${}^{\rm 1}S_{\rm 0}$.
Bethe-Salpeter equation is applied to nucleon-nucleon elastic scattering at the intermediate energy. The differential cross section and the polarization are calculated in terms of the phase shift analysis method using the two-body potential derived from the Bethe-Salpeter equation. The lowest-order Born approximation for the K-matrix is corrected by including the inverse square part of the potential.
Bethe-Salpeter equation is solved for bound state composed of two fermions mediated by pion exchange force of the pseudovector coupling. Expanding the amplitude by gamma matrices the one-dimensional integral equation is derived. It reproduces the binding energy of deuteron. The relation with the quadrupole moment is also discussed in the framework of the asymptotic approximation.