## Vol. 15, No. 1 (1959)

##### 1959-01-05

###### CONTENT

1959, 46 (1): 1-12.
doi: 10.7498/aps.15.1

Abstract +

In this paper, the Fourier transtorm method is used to solve the plane problems of an elastically anisotropical crystal thai has a two-hold symmetriceal axis. The stress distribution formulas of a crystal produced by the aetion of a point force are derived. Using these formulas the stress field of a, dislocation in the crystal is obtained. As an example, it is ealculated that the twined Zn crystal can lower its elastical energy about 35 per cent.

1959, 46 (1): 13-24.
doi: 10.7498/aps.15.13

Abstract +

In industry and in laboratory work oftentimes we are confronted with the problem of electromagnetic shielding between two bodies. In many ceases it is sufficient to have electrostatic shielding, and thus the interaction between two bodies can be determined by examining the mutual capacitance between them. When the interfering body is small and can be considered as a point source, its effect in the presence of another grounded conductor (in our case, the metallic shield) can be calculated by means of the Green's function for this grounded conductor surface. As the Green's functions for various surfaces are well established so these various forms of shielding can be handled by the method proposed in this paper.Green's functions for regions bounded by surfaces of oblate spheroidal as well as prolate spheroidal coordinate system are discussed with a mind to supplement a few formulas for the Legendre function with imaginary variables which are useful in physical and technical problems and which do not seem to appear in popular literatures.The problem of a hole of arbitrary shape on a conducting surface is then discussed with emphasis on the allowable size of the hole on a conducting surface of finite dimension, verifying the experimental results in literature. Finally the formula for calculating the mutual capacitance of two small bodies, one of which is enclosed by a closed metallic shield with a hole on its surface is given.

1959, 46 (1): 25-31.
doi: 10.7498/aps.15.25

Abstract +

In this paper, we have calculated the elastic scattering of high energy electrons with nuclei C12 by phase shift calculation.We take the charge distribution of the nucleus C12 as following:(1) exponential distribution:ρ(x)=ρ0θ-x/a, (2) gaussian distribution:ρ(x)=ρ0e(-x2/a2),(3) uniform distribution: ρ(x) ={ρ0 when 0kR, where a and b are the parameters, and the constant R is the radius of the nucleus C12. The energy of the electrons is 187 Mev.The result of the calculation shows that the gaussian distribution confirms the experimental result better than the other two kinds of distributions, and gives R=(12)1/3r0, where r0=1.35×10-13 cm.

1959, 46 (1): 32-41.
doi: 10.7498/aps.15.32

Abstract +

The branching ratio of the following three modes of K+-meaon decay K+→μ++π0+ν K+→e++π0+ν K+→μ++ν is calculated by using the theory of the universal Fermi weak interaction proposed by Feymann and others. Perturbation method with cut-off is used. The ratio obtained is 1:1.5:12, which is in fair agreement with the experimental value 1:1:15. It is shown, other conbinations of Fermi interactions can not give result in agreement with experiment.

1959, 46 (1): 42-54.
doi: 10.7498/aps.15.42

Abstract +

This short papper applies a method for studying the configurational partition function of regular solutions developed by Wang, Hsu and the author to a number of special cases. In sucb concrete calculations it is seen that the method is applicable to almcst every type of solid solutions. In fact, its applicability is independent of the type of lattice which atoms of the solution inhabit, of the existence of the long distance order, of the existence of interactions between atoms more distant than nearest neighbours, and of the number of components in the solution. Since the method is actually an expansion of the configurational free energy in terms of certain coordination numbers of the lattice, the results of the calculations after ignoring the higher coordination numbers become closed expressions in terms of the Boltzmann factors and thus avoids expansions in kT or in (kT)-1. Needless to say, expansion of the results obtained here in (kT)-1 gives results identical with those obtained by Kirkwocd's method. Next we discuss quasi-chemical formulas based on the above method. We point out that if we neglect all the coordination numbers except the lowest, we obtain the usual quasichemical formula, quite independently of the number of components in the solution, (A corresponding combinatory formula is derived.) On including higher coordination numbers, we get natural extensions of the quasi-chemical formula. Thus for a binary solid solution on a face centred cubic system, the quasi-chemical formula after including the next higher coordination number becomes In the above, NθA, NθB denote the numbers of A, B atoms, X′AA, X′AB,…,X",… are numbers determined by (2), (3), (4), and their substitution into the right hand sides of (1) gives the numbers XAA XAB, XBB of AA, AB, BB pairs of nearest neighbours. It may be noted that X′ may be negative and they do not bear any direct physical significance.It is also pointed out that instead of considering the numbers of pairs of nearest neighbours, we may consider directly the numbers of pairs of triplets (ie. 3 atoms forming mutually nearest neighbours) and write down by analogy (to the usual quasi-chemical formula) new quasi-chemical equations for the different numbers of triplets. (From this, a combinatory formula is easily derived). It is shown that such a theory differs from (1)-(4) given above.