## Vol. 16, No. 6 (1960)

##### 1960-03-20

###### CONTENT

1960, 63 (6): 305-315.
doi: 10.7498/aps.16.305

Abstract +

From the point of view of diffraction theory of optical image formation, each frequency term in the Fourier summation is regarded as a single information carrying element. The amount of information transmitted to the image space is limited by the size of the optical pupil, and is proportional to its area, irrespective of its shape or any phase modifying device which may be present at the pupil. A quantity called "information density" is introduced. The relation between resolving power and the amount of information carried through an optical system is discussed.

1960, 63 (6): 316-323.
doi: 10.7498/aps.16.316

Abstract +

This paper gives an expression of the optical frequency response function suitable for both the incoherent and the coherent optical system. Its physical aspect reveals that the frequency response function plays the role of an information selector.The Becke phenomenon for detesting small refractive index difference between object and its surrounding medium by observing the apparent movement of the diffractional border line (Becke line) on defocusing the optical system has been explained.

1960, 63 (6): 324-330.
doi: 10.7498/aps.16.324

Abstract +

Using the invariance in rotation, refletion and time reverse, general formulae for polarization in the nucleon-deutron scattering have been obtained. The consequences are represented in turn of scattering phase shifts.

1960, 63 (6): 338-347.
doi: 10.7498/aps.16.338

Abstract +

This report summurizes the preliminary work on the average spectrum of Chinese speech investigated by the Acoustics Laboratory (1956-1959), the principle of measurements being through the analysis of speech noise, a method found to be superior in many respects to the conventional method adopted by many authors. Both field and laboratory measurements were made and the spectra are presented.The average spectrum thus obtained from laboratory measurement (in an anechoic chamber) is compared with Tarnoczy's for Hungarian speech, Dunn and White for English speech etc. While the similarities of the shapes of these spectral distribution curves support the findings of the visible speech and show that the maximum energy characterizing all these languages falls approximately within the same range of frequency, the differences may be ascribed essentially to some special linguistic and phonetic features of Chinese speech sounds such as the predominance and tonal quality of the vowel sounds etc.A somewhat detailed account of the experimental techniques is given together with factors that led to uncertainties of the result enumerated and possibilities for further refinement of the present work (e.g., more accurate measurement to be conducted above 5,000 c/s etc.) discussed.

1960, 63 (6): 348-364.
doi: 10.7498/aps.16.348

Abstract +

The Thomas-Fermi model is generalized for an approximately spherically symmetric system, to include the spin orbit coupling energy G(r)L.S and the momentum-dependent potential energy V(r, p2)=V0(r) + pV2(r)p + p2V4(r)p2 +……. The latter form fol-lows in the nuclear case as a result of the combination of the Thomas-Fermi approximation and the Brueckner's theory of infinite nucleus. The generalized Thomas-Fermi model may be considered in the nuclear case as an approximate generalization of Brueckner's theory to finite nucleus. The Hamiltonians H+ and H- of the j = l + 1/2 and the j=l-1/2 particles respectively are sufficiently approximately given by where pr and p(?) denote respectively the radial and the perpendicular components of momentum P. In the ground state, the particles occupy the whole volume H±≤ λof the μ-phase space, where A denotes the largest energy of the particles. As a first approximation, sufficient for some problems in the nuclear case, letthe bar denoting the average of momentumover all particles in the vincinity of r. The corresponding density-potential relation iswhere p(r) denotes the particle density of the+ 1), R1 and R2 are positive roots of λ - A(r) = 0 and a=0 respectively. For second and higher approximations of V(r, p2), the corresponding density-potential relations are obtained as a sum of terms of decreasing magnitude, the first term being just the -expression (3). The generalized form of the total energy as a function of Vi(r) (i=0, 2, 4......) and G(r) may be similarly obtained. By applying the variational method, thebinding energy, the functions G(r), V(r, p2) and p±r) may be obtained. The detailedsteps of determining the level density on the basis of the generalized Thomas-Fermimodel are given.The generalized form including G(r)L.S and V(r, p2) given by equation (2), ofthe Fermi equation[2] applied as an integral equation to the case of nucleus by severalauthors[3-7], is given by the two coupled integral equations,where N±ldenotes the number of particles supplied by the shell model, of orbital angular momentum l and j=l±/2, N±L2) representing number of particles with j=l?/2 and orbital angular momentum≥L, are known functions of G(r) and (λ- V1(r)) (the function V2(r) of equation (2) being determined from (± - V1(r)) and the "reduced mass" in Brueckner's theory of infinite nucleus). Equations (4) with the normalization conditionswhere n+,n- are found by the shell model, determine G(r) and (λ - μ(r)) except for one range parameter which in the nuclear case, may be determined by the energy difference 2p3/2-Is of the μ-mesonic X-ray or more simply by the relation,with r0=(1.15±.03) X 10-13 cm or=(1.18 ±.03) X 10-13 cm for proton distributions near the trapezoidal type or near the Fermi type respectively.In order to estimate the accuracy of the method, equations (4), (5), (6) are solved by neglecting the spin orbit coupling energy and the momentum dependence of potential energy. The results so obtained should not change appreciably when these factors are taken into account. The allowable variation of the central density is similar to that of Hahn from the experiment of high-energy election scattering. At the present stage two and only two parameters e.g. the radial parameter e and the surface thickness t defined by Hahn , can be determined for density distributions with nearly flat central parts. The errors for the proton system of Au197 due to the uncertainties of the data and the statistical procedures used, are estimated to be cm for c and cm for t. The effect of taking into account the momentum dependence of potential energy is to increase the surface thickness t from 1.6 X 10-13 cm to 2.1 X 10-13 cm while the radial parameter c remains unchanged ( 6.5 X 10-13 cm). The latter values of t and also c are in agreement with those of Hahn to within the estimated errors. The influence on the values of c and t due to the spin orbit coupling eneigy may probably be very small, and underlying reasons are given.