## Vol. 21, No. 4 (1965)

##### 1965-02-20

###### CONTENT

1965, 120 (4): 691-706.
doi: 10.7498/aps.21.691

Abstract +

The hyperfine interaction of the carriers in semiconductors (involving the Fermi-contact and noncontact terms) has been treated by a "pseudo-contact interaction", which acts on the effective mass wavefunction. For the Si29 nucleons and the holes in silicon, it can be represented by {S1(Jxμnx+Jyμny+Jzμnz)+S2(Jx3μnx+Jy3μny+Jz3μnz)}δ(r-rn). The coupling parameters S1 and S2 are certain integrals connecting the Bloch functions of the top of the value band, generally S2≈0. Utilizing the above formula we have treated the nuclear magnetic relaxation in p-type silicon and obtained an expression for the relaxation time; the value of the parameter S1 has been determined from the relaxation time and from the spin orbit splitting value at the valence band top.

1965, 120 (4): 714-719.
doi: 10.7498/aps.21.714

Abstract +

Using the 24-litre propane chamber, photographs from JINR π0-meson production in inelastic interactions of π--mesons of momentum 6.8 GeV/c with nucleons are examined. About 2700 pairs of stereoscopic pictures have been scanned and 1275 events of π--N inelastic interactions have been found in an effective region 29.3 cm wide. In these events, 936 π--p and 339 π--n events, 240 and 89 electron-positron pairs have been observed respectively. After taking account of the efficiency of the bubble chamber for detection of γ-photons, it is found that the mean number of π0 mesons produced per event is n(π0)=1.00±0.06 and the mean transverse momentum of the γ-photons is Pγ⊥ = 173 MeV/c. In addition, the energy distribution of the γ-photons is especially examined. Under the assumptions that the γ-photons are entirely due to π0 decays and that the energy spectrum of the π0 mesons is the same as that of the π± -mesons', an energy distribution of γ-photons can be deduced from the energy distribution of the secondary π±-mesons produced in π--N interactions at the same incident energy; the γ-photon energy distribution obtained in the present experiment is in agreement with this deduced distribution within experimental error.

1965, 120 (4): 736-747.
doi: 10.7498/aps.21.736

Abstract +

The ion-optical properties of the accerlerating tube made of a series of coaxial cylinders in a DC accerlerator have been investigated. The potential distribution in such an accerlerating tube has been found both theoretically and experimentally by means of an electrolytic trough. The field in the accerlerating tube is found to be not exactly uniform as usually considered but it should also consist of a periodic part.The paraxial-ray equation for describing the ion trajectory in such a periodic field has been solved. The profile of the ion beam does show an undulatory shape, especially in the low energy region. The periodic field produces a significant focusing effect. A formula for describing the focal length of the ion-optical system was derived. The space charge effect has also been considered.

1965, 120 (4): 765-778.
doi: 10.7498/aps.21.765

Abstract +

It is proved that for a class of nonlocal potentials, the S matrix element S(λ,k) as a function of the angular momentum λ is meromorphic in λ in the region Re λ > 0. It is proved further that as λ→∞ along the positive real axis or the negative imaginary axis, [S(λ, k)-1] exp(-iπλ)→0. Under more restrictive assumptions, it is shown that S(λ, k) is meromorphic with respect to the momentum variable k in the strip |Im k| < μ. The positions of the poles are discussed. For such potentials, the Regge poles in the right half plane do not lie necessarily in the first quadrant.

1965, 120 (4): 779-786.
doi: 10.7498/aps.21.779

Abstract +

The energy spectra of π0 in Kμ3+ and Ke3+ decays, and the energy spectrum and longitudinal polarization of μ+ in Kμ3+ decay have been calculated by the dispersion relation method on the assumptions that 1) the weak interaction is of a universal V-A form and 2) the strange vector current is not conserved. Consequently one subtraction is made for each of the dispersion relation for the form factors f0 and f1. Only the contribution of K1* (m* = 888 MeV) intermediate state is considered in the calculations. If the parameter defined in the paper is assumed to be equal to 2.1, the results agree with experiments within their limits of errors. Thus, better agreement with experiments could be achieved by abandoning the assumption of partially conserved strange vector current.

1965, 120 (4): 787-801.
doi: 10.7498/aps.21.787

Abstract +

In this paper, the effect of electron-phonon coupling on the bandwidth of impurity absorption has been considered with a one-dimensional model of crystal lattices. The eigenfunctions of lattice vibrations in the presence of an impurity have been seriously treated by using a field theoretic method. The strength of electron-phonon coupling was obtained in analytical form as a function of the wave number k of the phonon, the range of interaction λ, and the parameter P = r′/r. Here r′ and r are respectively the force constant between an impurity and its neighbours and that between the normal neighbouring atoms. The results show that an impurity which causes the force costant to change has a considerable effect on the electron-phonon coupling. Under certain conditions the contribution of an antisymmetric localized mode in an ionic crystal may be much larger than the total contributions of intra-band modes. Especially, it is possible for the so called "critical scattering" to appear in ion crystals. In that case the contribution of intra-band modes may become very small and contribution comes almost entirely from the localized mode. Conversely, in a nonpolar crystal the contribution of the localized mode is generally negligible. The possible meaning of the above result in the problem of three-dimensional crystals was discussed in the final part of this article.

1965, 120 (4): 802-816.
doi: 10.7498/aps.21.802

Abstract +

, is then studied for each of the four cases. It is found that for all cases, the value of the integral can be expressed in terms of the matrix element of a transformed matrix U by which the reducible representation has been reduced. The corresponding reducible representations Г′s are respec-tively: A) (Гki?Гk′i′)(?);B)Гki?Гk′i′;C)Гki(s)?Гk′i′(s); and D)(Гki(s)?Гk′i′(s))(?). The final form of the integral is then obtained by finding the explicit form of the transformation matrix by using the pseudo-projection operator.">It is shown that in the direct product of two wave vector stars k?k′, if k"∈k?k′, the wave vector group, Gk", may belong to any one of the following cases: A) Both Gk and Gk′ are subgroups of Gk"; B) Gk=Gk′= Gk"; C) Gk" = Gs; D) Gs is the subgroup of Gk". The reduction of an integral A=μ″i″(k″)|fμi(k)|fμ′i′(k′)>, is then studied for each of the four cases. It is found that for all cases, the value of the integral can be expressed in terms of the matrix element of a transformed matrix U by which the reducible representation has been reduced. The corresponding reducible representations Г′s are respec-tively: A) (Гki?Гk′i′)(?);B)Гki?Гk′i′;C)Гki(s)?Гk′i′(s); and D)(Гki(s)?Гk′i′(s))(?). The final form of the integral is then obtained by finding the explicit form of the transformation matrix by using the pseudo-projection operator.

1965, 120 (4): 817-823.
doi: 10.7498/aps.21.817

Abstract +

The heat capacity of Nb3Sn has been measured between 16.0°K and 20.3°K. A jump in specific heat at Tc is found with ΔC = 2.21 (±5%) joule/mole·deg. The transition temperature of the sample is Tc= 17.88°K, and the transition interval is ΔTc ≈ 0.2°K. From the measured ΔC and by using the thermodynamic relationship, the thermodynamic critical magnetic field at 0°K, H0≈5300 Oe, was obtained. Using the result of ΔC obtained in the present work, and the jump of the thermo-expansion coefficient Δα and (?Tc/(?p) from the literatures, the thermodynamic relation be-tween these quantities was found to be valid.Apparatus for measuring the specific heat is briefly described.

1965, 120 (4): 824-838.
doi: 10.7498/aps.21.824

Abstract +

A simple two-band model was used to investigate the influence of the multiconnec-tivity of the Fermi surface on the properties of superconductors. It was shown that the effect is analogous to that of anisotropy. The effect of impurity scattering was considered by the Green's function method of Абрикосов and Горъков. There is a unique energy gap for both bands in the presence of impurities. The new gap parameter is larger than the smaller one of the two gaps in the pure case. The critical temperature Tc, critical magnetic field Hc, and its temperature coefficient x near T=0°K are lowered with doping, while the jump in specific heat at the transition point is raised. The combined measurement of the relative changes of these quantities should provide a direct verification of the theoretical calculations. The properties of heavily doped two-band superconductors are identical with those in the single band case. Furthermore, the results obtained were used to discuss the tunnelling experiment on Pb films and the anomaly of critical temperature in the alloy systems of In-Sn and In-Pb.

1965, 120 (4): 839-848.
doi: 10.7498/aps.21.839

Abstract +

The ordering of the alloy AgAuZn2 has been studied by means of X-ray diffracto-metry. The specimens were quenched from 600℃ and subsequently annealed at 100℃ for various periods of time. It was shown that in the quenched condition almost all of the Zn atoms were at their appropriate lattice sites, whereas the Ag and Au atoms were comparatively less readily to occupy their right places. A very short period of annealing at 100℃ was sufficient to make all the Zn atoms take their proper positions. The ordering among Ag and Au atoms proceeded as annealing was continued, the positions of Zn atoms being unaffected.The size of antiphase domains deduced depended markedly on the indices of reflections during the early stage of domain growth. The final sizes attained in different directions, however, were practically the same. The ordering of atoms and the growth of domains took place simultaneously. However, the degree of order reached a steady value long before the domains attained the final size.

1965, 120 (4): 849-857.
doi: 10.7498/aps.21.849

Abstract +

The crystal structure of FeGa3 has been determined by means of Debye-Scherrer photographs. The unit cell is tetragonal, with a = 6.2628? and c = 6.5559? at 20℃. There are four formula units per unit cell. The space group is D4h14——P42/mnm. The four Fe atoms are situated at the 4(f) positions, while the twelve Ga atoms are situated at the 4(c) and 8(j) positions, the atomic parameters being xf=0.343,xj=0.157 and zj=0.264.This structure represents a new type of intermetallic compound.

1965, 120 (4): 858-865.
doi: 10.7498/aps.21.858

Abstract +

Starting from the discussion of analytic properties and using the Landau relation to improve the diagrammatic technique of Dzyaloshinskii, the Feynman diagrammatic technique for double time dependent causal Green's function is established. There is a correct limit of zero temperature and may be used to calculate the various dynamical properties of nonequlibrium processes.

1965, 120 (4): 866-874.
doi: 10.7498/aps.21.866

Abstract +

After systematic experimental investigations, the chief factors which influence the sensitivity, stability and resolution of the ESR spectrometer have been ascertained. Effective means of improving these characters have been worked out. As a result, the sensitivity has reached 2.7×10-12M DPPH. (RC = 2sec., microwave power into cavity ≈l0mw.). The resolution has been found to be better than 1×10-4. The baseline stability has been greatly increased. The main drawbacks inherent in this type of spectrometer has also been discussed.