## Vol. 25, No. 5 (1976)

##### 1976-03-05

###### CONTENT

1976, 151 (5): 373-382.
doi: 10.7498/aps.25.373

Abstract +

Single crystals of the ferrimagnetie garnet Bi3-2xCa2xFe5-x-yInyVxO12 are grown by the flux method, with x = 1.35 ±0.02, y = 0-0.388. Single crystals having a dimension greater then 10mm and few inclusions can be obtained for all materials with different. In content by the technology described in this paper. The Curie temperature of all these materials is 10-30℃ higher then that of Ga-YIG with the same magnetization. The magnetic anisotropie constant drops rapidly with increase in number of the nonmagnetic indium ions. The anisotropie field falls slightly at first and then increases gradually with decrease from 530 to 200 Gauss of the saturation magnetization. The ferromagnetic resonance linewidth for the X band region increases with decreasing magnetization. It seems that there exists a relaxation mechanism which is connected with the dipole-n'arrowed model. The linewidth is about 1 to 4 Oe for the materials with the above magnetization. The best materials obtained possess an anisotropie field of 16 Oe and a linewidth of 0.7 Oe. The above results show that these materials can be employed in low frequency microwave devices.

1976, 151 (5): 383-398.
doi: 10.7498/aps.25.383

Abstract +

A short-cut method for the solution of the betatron oscillation in particle accelerators is developed to obtain its smooth term and quick oscillation term in whatever order of accuracy desired. An example is worked out in detail to show the practical application of the theory. Finally the mathematical foundation of this method is proved.

1976, 151 (5): 399-408.
doi: 10.7498/aps.25.399

Abstract +

The local stability of the Tokamak is discussed and a general approximate criteria β c obtained, where η is the longitudinal magneticwell. Furthermore, the influence of multipole' fields on the longitudinal magnetic well and the magnetic shear is discuss. It is observed that small triangular and octopole field components may considerably stabilize a Tokamak of elliptical cross-section.

1976, 151 (5): 409-414.
doi: 10.7498/aps.25.409

Abstract +

This article calculates the radiative decay process π+→e++ v + r of the π+ meson, by employing the field-current identity of the axial vector current which may be deduced from field algebra theory or the quantum theory of composite fields. The theoretical calculations are compatible with experimental results.

1976, 151 (5): 415-422.
doi: 10.7498/aps.25.415

Abstract +

On the basis of our previous report this paper discusses the structure wave functions of mesons formed from a straton and anti-straton pair. We assume that the straton is very heavy and that the interaction is the potential of a harmonic oscillator. Provided the spinor type coupling satisfies certain conditions then the following general results are obtained: (1) The equal spacing relation of the squared mass levels are obtained antomatically, and at the same time the usual difficulty of too high energy values for the ground states is avoided; (2) If the intrinsic weak current of the straton is of the V-A type, and also if its intrinsic electro-magnetic current contains no anomalous magnetic moment, then the inconsistency in the Cabibbo angle for the two body lepton decay of the pseudo-scalar meson and the difficulty in explaining the branching ratios of e+e- decay of various vector mesons may be avoided; (3) A very small SU(3) violation term is sufficient to explain the observed SU(3) mass breaking of mesons. This gives a reasonable explanation why the mass of K is 3.5 times that of the pion while SU(3) symmetry is still manifested in many situations; (4) The expansion of the equation with respect to p2/M2 gives fairly good approximation; (5) The radius of distribution of the straton and anti-straton is compatible in order of magnitude with the observed electro-magnetic radius of the meson; (6) The spinor and momentum structures of the structure wave functions are completely determined by the theory.

1976, 151 (5): 423-432.
doi: 10.7498/aps.25.423

Abstract +

Although the meson mass spectrum calculated from the simple harmonic potential by the B-S equation fits the experimental data fairly well, the wave function so obtained leads however to unreasonable results when applied to calculate the electromagnetic form factor, which turns out to be complex for space-like q2. It is argued that the reason for this lies in the fact that such a wave function does not possess the correct analytical property for the variable p0. In order to guarantee this analyti-city as well as to maintain the covariant form, it is adequate to express the wave function in the form of an integral representation according to a theorem proved by Dyson. Furthermore, some summation rules for the spectral function in the integral representation are derived with the physical condition that the wave function should be finite at x = 0.

1976, 151 (5): 433-443.
doi: 10.7498/aps.25.433

Abstract +

In this paper a theorem is proved and some of its applications discussed. The theorem gives an answer to the question: Under what conditions does the following relation εα±[Eα(N±1)-E0(N)] hold exactly? In the above relation, the εα′s are the single-particle (sp) energiesdetermined by the corresponding sp potential, E0(N) is the exact ground stateenergy of a closed-shell nucleus N, and the Eα(N±1)′s denote the exact energy eigenvalues of its neighbouring N ±1 nucleus.