The fixed angle dispersion relations near forward direction are applied to the derivation of the integral equations of s-wave and p-wave pion-nucleon scattering amplitudes. The equations involve the contribution of annihilation process, in which the main contribution comes from the two pions intermediate state. In order to examine the effect of ππ interaction on pion-nucleon scattering, the observed values of scattering phase shifts are substituted into the equations, and the numerical calculation is given. Using the experimental informations of the form factors of the electro-magnetic structure of nucleon, and taking the square resonance energy tr=20, we obtain the I=I=1ππ scattering resonance width parameter γ=0.1. This result is consistent with the experimental data of the all three low angular momentum partial wave amplitudes, but the resonance width is small compared with the observed value.
The fixed angle dispersion relations near forward direction are applied to the derivation of the integral equations of s-wave and p-wave pion-nucleon scattering amplitudes. The equations involve the contribution of annihilation process, in which the main contribution comes from the two pions intermediate state. In order to examine the effect of ππ interaction on pion-nucleon scattering, the observed values of scattering phase shifts are substituted into the equations, and the numerical calculation is given. Using the experimental informations of the form factors of the electro-magnetic structure of nucleon, and taking the square resonance energy tr=20, we obtain the I=I=1ππ scattering resonance width parameter γ=0.1. This result is consistent with the experimental data of the all three low angular momentum partial wave amplitudes, but the resonance width is small compared with the observed value.
The extended Chew-Low equation for π-N scattering under two pion approximation is solved by neglecting contribution from the crossing terms. From rapidly increasing pion-production cross-section we calculated the elastic scattering cross-section of the D3/2 channal (T=1/2). The peak of elastic scattering cross-section in the second resonance is explained.
The extended Chew-Low equation for π-N scattering under two pion approximation is solved by neglecting contribution from the crossing terms. From rapidly increasing pion-production cross-section we calculated the elastic scattering cross-section of the D3/2 channal (T=1/2). The peak of elastic scattering cross-section in the second resonance is explained.
The s-wave π-π scattering amplitude is calculated by using the chain approximation from the nonrenormalizable interaction Lagrangian which gives rise to the same p-wave scattering amplitude as obtained by Frazer and Fulco from the dispersion relation. It is found that the s-wave amplitude contains two additional parameters. This appearance of new parameters is inevitable since the interaction is nonrenormalizable. The connection of our method of solution with that of the dispersion relation is also discussed. Our calculation gives rise to a low energy resonance in the I=0 state which may be identified as the resonance observed by Booth et al.
The s-wave π-π scattering amplitude is calculated by using the chain approximation from the nonrenormalizable interaction Lagrangian which gives rise to the same p-wave scattering amplitude as obtained by Frazer and Fulco from the dispersion relation. It is found that the s-wave amplitude contains two additional parameters. This appearance of new parameters is inevitable since the interaction is nonrenormalizable. The connection of our method of solution with that of the dispersion relation is also discussed. Our calculation gives rise to a low energy resonance in the I=0 state which may be identified as the resonance observed by Booth et al.
In ruby a Cr3+ ion and its six nearest neighbouring O2- ions form a heavily distorted octahedron. Consequently, the magnitude of odd crystal field of the higher order is comparable with the first-order odd field. Because of the site group of Cr3+ ion in ruby approximately retains C3v symmetry, the higher-order crystal field component of T2u type is very small and can be neglected, but those of T1u type and A2u type must be taken into account. The higher-order odd field components make appreciable contribution to Y band and U⊥ band, but their contribution to U‖ band is negligible.The intensities of U‖ band and Y band are discussed with proper attention paid to the odd vibrations of ions. It has been concluded that the U band absorption is mainly produced through the coupling of odd vibrations with electrons. With this point of view, the oscillator strength, the dichroism, the band shape, etc., of the absorption bands of ruby are analysed. The results are in good agreement with experimental data.
In ruby a Cr3+ ion and its six nearest neighbouring O2- ions form a heavily distorted octahedron. Consequently, the magnitude of odd crystal field of the higher order is comparable with the first-order odd field. Because of the site group of Cr3+ ion in ruby approximately retains C3v symmetry, the higher-order crystal field component of T2u type is very small and can be neglected, but those of T1u type and A2u type must be taken into account. The higher-order odd field components make appreciable contribution to Y band and U⊥ band, but their contribution to U‖ band is negligible.The intensities of U‖ band and Y band are discussed with proper attention paid to the odd vibrations of ions. It has been concluded that the U band absorption is mainly produced through the coupling of odd vibrations with electrons. With this point of view, the oscillator strength, the dichroism, the band shape, etc., of the absorption bands of ruby are analysed. The results are in good agreement with experimental data.
The effect of heat treatment on the ferromagnetic resonance of lutecium iron garnet (Lu3Fe5O12 or Lu I G) and manganese ferrite single crystals is investigated. The heat treatments are 1 hour at 700℃ in air and 10 hours at 700℃ in oxygen, used separately. It is found that these treatments have no significant influence on the values of K1/Ms and the g-factor, but the anisotropy of resonance line-width AH decreases appreciably. Although the effect of heat treatment on the △H of Lu IG is small, the AH of manganese ferrite increases several times after each treatment. The causes of the variation of △H with heat treatment are discussed. Meanwhile, X-ray diffraction patterns show that some α-Fe2O3 precipitates in the manganese ferrite sample after it is subjected to heat treatment.
The effect of heat treatment on the ferromagnetic resonance of lutecium iron garnet (Lu3Fe5O12 or Lu I G) and manganese ferrite single crystals is investigated. The heat treatments are 1 hour at 700℃ in air and 10 hours at 700℃ in oxygen, used separately. It is found that these treatments have no significant influence on the values of K1/Ms and the g-factor, but the anisotropy of resonance line-width AH decreases appreciably. Although the effect of heat treatment on the △H of Lu IG is small, the AH of manganese ferrite increases several times after each treatment. The causes of the variation of △H with heat treatment are discussed. Meanwhile, X-ray diffraction patterns show that some α-Fe2O3 precipitates in the manganese ferrite sample after it is subjected to heat treatment.