Vol. 14, No. 4 (1958)
1958-02-20
CONTENT
1958, 14 (4): 289-299.
doi: 10.7498/aps.14.289
Abstract +
The theory of the excitation of nuclei by electrons of intermediate energy has been studied. Cross sections for the excitation of nuclei due to the interaction of the electromagnetic field of the electron with the electric dipole, qua-drupole, and with the magnetic dipole and quadrupole moments of the nucleus have been evaluated explicitly in terms of these moments.A relationship between the electro-excitation cross section and corresponding X-ray excitation cross section is established. This relationship is independent of all properties of the nucleus except for the change in the energy, angular momentum and parity involved in the transition.The predictions of the theory are compared with the experimental measurements in the excitation of In115. It is found that no definite information about the nuclear levels is obtained by this comparison because of insufficient precise experimental results. Measurements which would lead to information about the properties of the nuclear states are suggested.
1958, 14 (4): 300-307.
doi: 10.7498/aps.14.300
Abstract +
The purpose of this short paper is to compare the two existing theories of quantization of equations of motion containing high derivatives. As well known, when the order of the derivatives of field quantities q are finite, it is possible in certain cases to express q as a linear combination of quantities Q, each of which satisfies an equation of the second order. Quantization proceeds as if the various Q are independent. On the other hand, one may, following Ostro-gradski, put the equations of motion for the variables q in canonical form and then perform a subsequent quantization. (Such a theory was also discussed by the author in an earlier paper.) It is obviously worthwhile to see if the two theories are identical.In the following it is proved that the above two theories are in fact identical, both with respect to the commutation rules between q, Q and their derivatives and with respect to the total Hamiltonian.The importance of the above result lies in:(i) just as in the first theory, the Hamiltonian in the second theory is also not positive definite. In other words, possibilities of obtaining in the second theory positive definite Hamiltonians for field equatiens of certain types are found not to exist.(ii) just as in the second theory, q and its first few derivatives commute. This implies that in extending the first theory formally to cases containing derivatives of infinite order, q and all its derivatives of finite order commute. Since this is an undesirable feature, formal extension of the two theories to cases containing derivatives of infinite order seems difficult.
1958, 14 (4): 308-316.
doi: 10.7498/aps.14.308
Abstract +
The aim of this short paper is:( i ) To provide a rigorous proof for the deduction of the well-known equation i(δψ[σ])/(δσ(x))=V(x,σ)ψ[σ] (1) from the formulation of ordinary Schroedinger wave equations for wave functions on arbitrary space-like surfaces as given by Weiss and the author, and (ii) To study under what conditions the operator V in the above equation does not contain σ explicitly.To prove (1) from Weiss's theory, all that is necessary is to transform away the free Hamiltonian in the usual way and to prove that, according to the resulting wave equation, the difference of ψ on two adjacent surfaces which are different only in a small neighbourhood of σ certain point on the surfaces is proportional to the volume included between the surfaces. This is actually achieved. The terms in V which depend explicitly on a are worked out in terms of the total Lagrangian L and the interaction Lagrangian LI, i.e. 1/2Nμ(?LI)/(?φμα) GαβNν(?LI)/(?φνβ), (2) where φ1,φ2, …are the various field quantities, φμα denotes (?φα)/?xμ,Nμ denotes the surface normal and Gαβ are quantities defined by NμNν(?2L)/(?φμα?φνβ)Gβγ=δαγ. For the special case in which there is only one φ, the condition for V not to contain σ explicitly reduces to (?LI)/(?φμ)(?LI)/(?φν)/(?LI)/(?φρ)(?LI)/(?φρ)=(?2L)/(?φμ?φν)/(?2L)/(?φρ?φρ).
1958, 14 (4): 317-334.
doi: 10.7498/aps.14.317
Abstract +
For an n-type transistor, with copper and phosphor-bronze whiskers respectively for its emitter and collector, as the result of electrical forming, the emitter should have a metal-p-n structure. In the first part of this paper, the forward characteristics of such a structure is analized for the whole range of current, with special reference to the variation of the emission ratio γ with the current. The design requirement of a flat γ-Ie curve is discussed. The second part of the paper contains an analysis of current amplification of the collector. The structure assumed is a metal-p-n junction, the diffusion of phosphorus into the structure causing a high barrier for holes at the metal contact. By combining the result of the two parts, a resultant a-Ie, relation is calculated for a typical case. The main factors affecting the performance of the transistor and means of its improvement are discussed in some detail.
1958, 14 (4): 335-345.
doi: 10.7498/aps.14.335
Abstract +
The current stablizer, reported in this paper, is part of a β-ray spectrometer. Principally, it can also be used in other apparatus requiring stablized current. The stablizer can supply a maximum current of 100 A with a degree of stablity of 0.02% in ten minutes.We adopt the principle of negative feed back sevo-control in designing the stablizer. Firstly, the error signal of the DC current passing through a standard resistance is amplified. In order to avoid the drift effect of the usual DC amplifier, we use a bridge type balanced modulator to convert DC signal into AC signal. After AC amplification, the signal is demodulated by a phase sensitive demodulator. The amplification required is about 2×l04. Concerning the amplifier, the following problems are considered in detail: to keep the output of the modulator in zero potential while there is no input signal, the effect of the carrier component of the modulator, and the distortion of the modulated signal after amplification. After power amplification, the amplified signal is used to control the field supply of the DC generator. As there are capacitance and inductance in the system, the transmission of the signal in the system has time delay. In closed system, there is the possibility of instability of the nature of low frequency oscillation, and it is necessary to insert proper network in the system to suppress the oscillation. Finally, the detailed arrangements of the different components of the stablizer, its characteristics, and result of its operation are described.
1958, 14 (4): 346-353.
doi: 10.7498/aps.14.346
Abstract +
The phase diagram of the silver-rich alloys of the ternary system of Silver-Tin-Aluminium, containing up to 30 wt% tin and up to 30wt% aluminium, has been studied by X-ray and microscopic methods.The phase section at room temperature was found to consist of four single-phase [i. e. a (cubic f. c.), μ (β-Mn), β (hexagonal) and γ (rhombohedral)] regions, five two-phase (i. e. α+β, α + μ ,β + μ ,β+γ and β+δ) regions and two three-phase (i. e. α+β+μ and β+γ+δ) regions. The four single-phase's appeared are exactly the same as those existing in the binary systems of Silver-Tin and Silver-Aluminium.
1958, 14 (4): 354-368.
doi: 10.7498/aps.14.354
Abstract +
An internal friction peak induced by carbon diffusion has been observed in f. c. c. iron-nickel alloys. At a vibrational frequency of 1.4 cycles per sec., the peak occurs at about 500°K. This peak arises from the preferential rotation of the axes of carbon pairs existed in the specimen under the influence of an alternating load. These carbon pairs were formed by the interaction between the substitutional carbon atoms and their neighboring interstitial carbon atoms. Based upon this mechanism and considering the possible redistribution of the carbon atoms amongst the frozen-in vacancies in the specimen during the course of internal friction measurement, an equation bearing the quantitative relationship between the peak height and the carbon concentration has been derived. The energy of vacancy formation as well as the binding energy of the carbon pairs have been determined.The characteristics of the carbon diffusion peak in f. c. c. metals are: (1) The internal friction curve is not symmetric with respect to the peak position, the internal friction on the high temperature side being smaller than on the low temperature side. (2) The T′Qmax-1 product varies with the peak temperature T′; the lower the peak temperature, the higher the T′Qmax-1 product. (3) The peak temperature T′ drifts with the carbon concentration as well as the quench temperature of the specimen. Either an increase of the carbon concentration or a raise of the quench temperature tends to shift the peak position toward a lower temperature. These characteristics are interpreted in terms of the carbon pair theory as given in the text.
