Vol. 21, No. 3 (1965)
1965-02-05
CONTENT
1965, 21 (3): 481-495.
doi: 10.7498/aps.21.481
Abstract +
For considering the electron-phonon coupling in the problem of impurity absorption band, a set of normal modes of lattice vibration were formed by the linear combination of plane (running) waves in order to present fully the site symmetry of the impurity. The symmetric (standing) waves of a definite type are characterized by an irreducible representation of the site group. The frequency distribution function of the phonons of a certain symmetry type is that of the lattice vibration divided by a constant. The phonons involved in the transition of an absorption band are restricted to certain symmetry types but no selection on the frequency may be found. The configuration coordinate approximation of Williams et al. was critically examined at this stage. The dependence of the coupling strength on the frequency of phonons was qualitatively discussed and the possible importance of the critical points of the frequency distribution was remarked. The mathematical analysis of symmetric standing waves was given in details. The relation between this set of normal modes of lattice vibration and those of an isolated cluster containing a central ion and the ligands was demonstrated.
1965, 21 (3): 503-507.
doi: 10.7498/aps.21.503
Abstract +
An X-ray method has been proposed for identifying the coalescence sequences in silicon carbide crystals containing several polytypes in coalescence. The platelet of single crystal silicon carbide is ground layer by layer by ultrasonic technique, and two Laue patterns are taken before and after every layer was ground off. Thus with the aid of these Laue photographs it would be found possible to determine the sequences as well as the ratios of various coalescent polytypes. The experimental results of one crystal were discussed in view of the mechanism of silicon carbide polytypism suggested by Mitchell.
1965, 21 (3): 508-518.
doi: 10.7498/aps.21.508
Abstract +
We have investigated the methods of calculating the virial coefficients in the equation of state of gases, and proposed four rules for determining the number of terms in the equation of state. These rules are: (1) Use the variation of ∑v2 (v = (pV)cal - (pV)exp); (2) each succeeding term of the polynomial should be less in numerical value than its preceding term; (3) the last term of the polynomial should be of the same order of magnitude as the experimental error; (4) the residuals v should have nearly equal numbers of positive and negative values.We advise the use of the condition A0+B0+C0+…=1, but not the condition A=RT. We have also investigated whether the expansion is better in increasing powers of pressure or of density, the omission of odd power terms, the number of significant figures in the numerical values of the virial coefficients, and the correction of some experimental data.Based on the above considerations we have recalculated the virial coefficients of hydrogen gas from two different sets of experimental data, with results differing from those of the original authors. The virial coefficients calculated from two different sources agree within twice the standard error, and differ less than those of the original authors.
1965, 21 (3): 519-525.
doi: 10.7498/aps.21.519
Abstract +
The method developed by the authors for reducing the direct product of irreducible space group representations has been extended to the reduction of the symmetrized and the antisymmetrized n th power of irreducible space group representations. The reduction coefficients for symmetrized squares of the hexagonal closed-packed and wurtzite space groups are calculated. An application of the results thus obtained in the study of the configuration instabilities is briefly discussed.
1965, 21 (3): 526-530.
doi: 10.7498/aps.21.526
Abstract +
Thin and uniform sources are always needed in β-spectroscopy. For this purpose, an apparatus of vacuum evaporation was designed, by mean of which sources such as In114,Au198 and Sm153 have been prepared. The souces of In114 were prepared respectively by the methods of drop evaporation and vacuum evaporation, and both were measured with the double focusing β-spectrometer and double lens β-spectrometer. Their internal conversion spectra were compared. The advantage of the method of vacuum evaporation is obvious. In addition, the Au198 K-conversion line of 411.8 KeV γ-ray and Sm153 K, LⅠ,LⅡ, LⅢ convertion lines of 69.67 KeV γ-ray measured with double focusing β-spectro-meter are given.
1965, 21 (3): 531-541.
doi: 10.7498/aps.21.531
Abstract +
The coherent effect inherent in particle-particle pair or particle-hole pair which is moving in a rotating weak-deformed nuclear field has been investigated. The low-lying even-parity states 0+, 2+, 4+, of O18 and odd-parity states 0-, 1-, 2-, 3-, of O16 have been calculated accordingly. Comparison with the corresponding wave-functions by the shell model classical calculation shows that there is much similarity between them. Some preliminary conclusions are obtained as follows: The main components in nuclear force are the P2 force plus certain other force with coherent property. The former is equivalent to a rotating deformed field, while the latter is essential in all calculated states except for the 0- state only.
1965, 21 (3): 542-545.
doi: 10.7498/aps.21.542
Abstract +
In a previous paper we have proposed a spatially symmetrized wave function of the two-particle system. Here we propose further a wave function of a three- and four-particle system with the same symmetrical property. Comparing our wave functions with the shell model wave functions calculated by Flowers and by Redlich, we observe the similarity between them and find that the squares of the overlap integrals of the corresponding wave functions are greater than 80%.
1965, 21 (3): 569-576.
doi: 10.7498/aps.21.569
Abstract +
Using the hypercharge-charge representation, leptonic decays of elementary particles are considered under the symmetry of the group B2. Baryons and mesons are assigned to the 4-dimensional representations of the group B2, then the 10-dimensional regular representation just contains all |△S|≤1 and |△Q|≤l baryonic currents or mesonic currents. Assumming that the weak interaction is mediated by intermediate bosons, and inserting them into the 10-dimensional representation of B2, we have calculated various leptonic decay rates of strange particles which involve both △S = + △Q and △S = - △Q processes. The results here obtained are not in contradiction to present experimental data.
1965, 21 (3): 577-582.
doi: 10.7498/aps.21.577
Abstract +
The mass formula which was derived from the theory of unitary symmetrical group seems to be somewhat different with experiments. Now we have discussed this problem from the point of view of field interaction. The results show that the mixing effects of both T = 0 states, one belongs to the one dimensional representation and the other to the eight, give a correction to the mass of each of them, and the contradiction between the theory and experiment may be explained. Finally we have discussed the K-K resonant state.
1965, 21 (3): 583-590.
doi: 10.7498/aps.21.583
Abstract +
In this paper, the analytical properties of the S matrix of nonrelativistic cut-off Coulomb potential in the complex angular momentum and complex energy planes are discussed. The Regge poles of this S matrix for four special cases are given, and the first two Regge trajectories are traced by means of numerical calculations.
1965, 21 (3): 591-607.
doi: 10.7498/aps.21.591
Abstract +
The influence of Fe2+ on the ferrimagnetic resonance properties of nickel ferrites was discussed. Since the ground state of Fe2+ in spinels is a singlet, the crystal field only slightly affects the motion of the spin magnetic moment of Fe2+. It was pointed out that due to the anisotropy of the exchange interaction between Fe2+ and Fe3+ or Ni2+ situated at the octahedral position, the longitudinal branch might play the major role in the relaxation process of nickel ferrites.The method used in Ref. [1] was extended to treat the strong exchange coupled system. It was confirmed that usually the expression for the line width coincides with that of the case of a weakly coupled system.Under the light of a reasonable model of anisotropic exchange interaction the experimental fact that the line width goes through a maximum at a definite temperature along all crystal directions except [001], was satisfactorily explained. The theoretical expression obtained for the anisotropy of the line width agrees with the experimental results.
1965, 21 (3): 608-617.
doi: 10.7498/aps.21.608
Abstract +
The positions of the absorption lines in ruby are calculated with the general electrostatic interaction parameters in the ligand-field theory. Consistence of the theory with experiment is slightly better than those obtained previously. The effects of molecular orbi-tals on these parameters are discussed. Similar results are obtained by a calculation using two covalence parameters and other known free-ion parameters. In this method, the calculated values of Nπ≌0.92 and Nσ≌0.89 are obtained. The parameters in the generalized effective Spin-Hamiltonian are calculated. It is found that the g-factor in the modified term results from the contribution of the fourth order perturbation, and its order of magnitude is about 10-5. The effective Hamiltonian which is used to describe the R line of ruby was obtained.
1965, 21 (3): 618-621.
doi: 10.7498/aps.21.618
Abstract +
The paramagnetic resonance of the Fe3+ ions in sodium borate glasses has been studied. There is a sharp and approximately symmetric resonance line at g (apparent) = 4.27. The experimental results show that the Fe3+ ion has replaced the boron ion in the tetrahedron [BO4] contacting with two sodium ions.
1965, 21 (3): 622-629.
doi: 10.7498/aps.21.622
Abstract +
Relationships between the activation energies (QA and QB) of self-diffusion of each component and the concentration CB of a completely disordered binary solid solution are derived on the basis of a quasi-chemical model. These theoretical results are compared with experimental data.When the atomic size of the two components is approximately the same, a linear relationship is obtained between(QB - QA) and CB for both f.c.c. and b.c.c. structure. This is in good agreement with the experimental results of Ag-Au system.In the low concentration range, the relationship between the activation energy QA of self-diffusion of the solvent and the concentration CB is also a straight line. The sign of the slope can be predicted from the relative magnitude of activation energy of self-diffusion of the solvent and that of impurity diffusion in the same solvent. This prediction is in good agreement with the known experimental data of self-diffusion of silver in nine different silver alloys of low alloy concentration.
1965, 21 (3): 630-635.
doi: 10.7498/aps.21.630
Abstract +
In this paper, it is shown that for negative absolute temperatures the form of the Le Chatelier's principle may not be changed, but the content of the second "force" action is opposite to that for positive absolute temperatures. Secondly, it is shown what condition is required for Maxwell's relations to fulfil the deduction of the Le Chatelier's principle.
1965, 21 (3): 636-645.
doi: 10.7498/aps.21.636
Abstract +
The design feature of a direct-reading spectro-analyser with emphasis on the electronic circuit design is presented in this paper. This instrument is stable, speedy, and accurate. The first and second order spectral ranges are respectively 2000-6000 and 2000-3000?. The mechanical construction of the optical system is so characterized that two (for first order) or four (for second order) pickups can be set exactly on the same spectral line. A line-frequency, high-voltage and high-energy spark source system is employed with adequate sensitivity. The measuring system consists of a pulse amplifier, a rectifier, an integrator, and a pulse counter. The operation of this instrument is completely automatic after the mounting of the sample. Finally, typical operational data are illustrated.
1965, 21 (3): 646-664.
doi: 10.7498/aps.21.646
Abstract +
One of the most fundamental quantities in the study of various parametric applications of the varactors is its nonlinear characteristics. The required pumping power can be greatly reduced if a varactor having much higher nonlinearity is employed. For the purpose of studying either lower pumping applications or non-sinusoidal pumping applications of the varactor, a knowledge of both the fundamental and the harmonics of the pumped time-varying parameters of the varactors is highly desirable. An analysis on the proper selection and normalization of the non-linear characteristics of the varactor is offered. A graphical method to analyze the fundamental and the harmonics of the pumped time-varying parameters was employed, and curves relating these components to the nonlinearity of the varactor γ, and the pumping voltage ratio m1 were obtained. These curves serve as one of the fundamental references in various varactor parametric applications. Sample applications are also included as illustrations.
1965, 21 (3): 665-673.
doi: 10.7498/aps.21.665
Abstract +
Account is taken of the change in the state of polarization of multiply diffracted X-rays in mosaic crystals, and a more rigorous treatment of secondary extinction is given. Separate expressions for the transmitted, and multiply diffracted power are obtained, which enable the effective absorption coefficient to be calculated.
