Showing papers by "Tata Institute of Fundamental Research published in 1970"

Some effects of group-velocity dispersion on parametric interactions

Abstract: Three-wave parametric interactions are studied in media exhibiting group-velocity dispersion. Under certain conditions these interactions may be described by the same equations that govern pulse propagation in a two-level resonant system. This analogy suggests the existence of steady-state pulse solutions in the three-wave parametric system. Such solutions are found, and are analogues of pi and two-pi pulses. The variety of solutions in the parametric system is greater than in the resonant case.

Bradford's law of bibliography of science: an interpretation.

Abstract: THE distribution of scientific articles in journals is known to conform closely to Bradford's law. If the journals are divided into groups, each containing the same number of articles on a given subject, then the number of journals in the succeeding groups form a geometrical progression1. The conditions for strict conformity with the law are that the bibliography be complete and of limited time span, and that it refers to a well defined subject. The law, however, seems to hold even when the conditions are not fully satisfied. An interesting discussion of the law and its application in library systems is given by Brookes2. No simple model of the mechanism responsible for the law exists2.

A single domain grain model for the low-field constricted hysteresis loops of some basaltic rocks

Abstract: Basaltic rocks contain magnetic grains oriented randomly in a nonmagnetic matrix. Experimental studies of low-field hysteresis of such rocks have shown partially and totally constricted hysteresis loops for some specimens. A possible origin of these constricted loops on the basis of interacting single domain behaviour is suggested.

Effect of Carrier Scattering on Nonlinear Optical Susceptibility due to Mobile Carriers in InSb, InAs, and GaAs

Abstract: To estimate the effect of carrier scattering on the low-frequency nonlinear optical response of mobile carriers in semiconductors, the Boltzmann transport equation is solved in a generalized relaxation-time approximation Two cases, one in which the elastic scattering of carriers by ionized impurities dominates the transport properties and the other in which inelastic scattering by longitudinal optical phonons is the most important scattering mechanism, are considered in detail for InSb, InAs, and GaAs We find that the inclusion of carrier scattering affects the third-order nonlinear susceptibility in two distinct ways First, the contribution due to nonparabolicity is modified in a nontrivial fashion This modification becomes important in the optical-frequency-mixing experiments, when the difference frequency is comparable to the "average" collision frequency Second, an additional nonlinearity arises because of the energy dependence of carrier collision frequency This is estimated to be unimportant in most cases for which detailed experimental data are available at present, but is shown to be quite important when the difference frequency becomes smaller It is found that, at low temperatures, the additional nonlinearity due to energy-dependent scattering can be significant in InSb and InAs samples, with $n\ensuremath{\approx}{10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, even for the frequencies used in the presently available experimental investigations

Effect of thermal noise on the dc Josephson effect

Abstract: An approximate analytic solution of the Fokker-Planck equation describing the effect of thermal fluctuations on the dc Josephson voltage which is valid for finite capacitance of the junction is obtained. It is shown that our solution should be applicable in the important region of experimental interest.

Scattering of X-rays from Pulsar NP 0532 by Interstellar Grains

Abstract: SLYSH1 recently considered the scattering of soft X-rays from the Crab Nebula, and suggested that although all the observed X-rays from the Crab Nebula could have originated as pulsed X-rays from the pulsar NP 0532 at the centre, only ∼10 per cent unscattered by interstellar grains are recorded as pulsed X-rays in the 1–10 keV region2–4. The remaining 90 per cent are scattered, appearing as a diffuse source about 2′ wide5,6 in which the pulses are smeared out. In this report we show that the optical depth for scattering by interstellar grains is-small in the 1–10 keV region, and that the pulsed component is reduced by ∼20 per cent at the most. Consequently the observed spectrum of the pulsed component in the 1–100 keV region2–4,7,8 should closely correspond to the spectrum of the pulsar at the source, which would not have been the case from the analysis of Slysh. The optical depth for scattering is quite insensitive to the exact model of interstellar grains.

Unitarity Upper and Lower Bounds on the Absorptive Parts of Elastic Scattering Amplitudes

Abstract: We derive upper and lower bounds on the imaginary part of the elastic scattering amplitude of two spinless particles in the physical region, in terms of the elastic cross section ${\ensuremath{\sigma}}_{\mathrm{el}}$ and the total cross section ${\ensuremath{\sigma}}_{\mathrm{tot}}$, using unitarity alone. The bounds derived are the best possible ones, given only the stated unitarity constraints. The upper bound for high energies and small values of the momentum transfer squared $t$ has a particularly simple and "universal" form, $\frac{\mathrm{Im}F(s, t)}{\mathrm{Im}F(s, 0)}l~1\ensuremath{-}\frac{1}{9}\ensuremath{\rho}+\frac{3}{8}{(\frac{\ensuremath{\rho}}{9})}^{2}\ensuremath{-}(\frac{21}{320}){(\frac{\ensuremath{\rho}}{9})}^{3}+\ensuremath{\cdots}$ if $2.5g~\ensuremath{\rho}\ensuremath{\equiv}(\ensuremath{-}\frac{t}{4\ensuremath{\pi}})\frac{{{\ensuremath{\sigma}}_{\mathrm{tot}}}^{2}(s)}{{\ensuremath{\sigma}}_{\mathrm{el}}(s)}$, which depends on the particular scattering process and on the energy and momentum transfer only through the dimensionless parameter $\ensuremath{\rho}$. We give explicit formulas and numerical values for the upper bound up to $\ensuremath{\rho}=8.42$. We compare the experimental curve of $\frac{(\frac{d\ensuremath{\sigma}}{\mathrm{dt}})}{{(\frac{d\ensuremath{\sigma}}{\mathrm{dt}})}_{t=0}}$ versus $4(\ensuremath{-}t)\frac{{(\frac{d\ensuremath{\sigma}}{\mathrm{dt}})}_{t=0}}{{\ensuremath{\sigma}}_{\mathrm{el}}}$ with the theoretical upper bound on ${[\frac{\mathrm{Im}F(s, t)}{\mathrm{Im}F(s, t=0)]}]}^{2}$ versus $\ensuremath{\rho}$. The quantities plotted in the experimental and theoretical curves are the same if the unpolarized cross sections are spin-independent and purely absorptive in the diffraction-peak region. We find that the experimental points for $\mathrm{pp}$, $\overline{p}p$, ${\ensuremath{\pi}}^{+}p$, and ${\ensuremath{\pi}}^{\ensuremath{-}}p$ scattering in the lab momentum range 6-13 GeV/c fall on a curve lying only slightly below the theoretical upper-bound curve, the difference being less than 10% for $\ensuremath{\rho}$ in the range (0,3) and less than 25% for $\ensuremath{\rho}$ in the range (3,5). We further notice that this experimental curve is universal. We also derive unitarity lower bounds on the $n\mathrm{th}$ derivatives of the absorptive part at $t=0$, and on the absorptive part for positive values of $t$ within the Lehmann-Martin ellipse, in terms of ${\ensuremath{\sigma}}_{\mathrm{el}}$ and ${\ensuremath{\sigma}}_{\mathrm{tot}}$. The corresponding bounds if ${\ensuremath{\sigma}}_{\mathrm{tot}}$ alone is known are also derived.

Numerical study of the behaviour of a system of parallel line vortices

Abstract: The dynamical behaviour of a system of parallel line vortices in an inviscid fluid is studied numerically. The initial configuration of the system is assumed to be such that the points of intersection of the line vortices with a plane normal to the vorticity form a regular polygon. The numerical experiments show that the vortex polygon is rearranged due to non-linear interactions among the line vortices in such a way as to produce a more or less uniform distribution of vortices inside the fluid with an approximately constant mean separation. The average angular velocity of the rotation of the vortex lines about the instantaneous centroid of the vortex system remains approximately constant. These results agree with the conjecture of Raja Gopal (1964). The results may prove to be of some value in a macroscopic model of liquid helium based on hydrodynamical principles.

EFFECT OF PAIRING CORRELATIONS ON $sup 22$Ne SPECTRUM.

Abstract: The effects of pairing correlations on the ground-state band of $^{22}\mathrm{Ne}$ are investigated. It is shown that the computed low-lying excited-state spectrum is significantly affected, whereas the $E2$ transition probabilities are almost unaffected by the pairing correlations.

Molecular structure of pyrimidine by NMR in the nematic phase

Abstract: The NMR spectrum of pyrimidine has been studied in the nematic phase of 4-methoxy benzylidene-4-amino-α-methyl cinnamic acid-n-propyl ester at room temperature. The ratios of all the interproton distances are determined and found to differ significantly from those obtained from microwave data. The molecule, like other aromatics, is shown to orient preferentially with its plane in the direction of the magnetic field.

Search for high energy gamma rays from four pulsars.

Abstract: IT has been suggested1,2 that high energy cosmic rays originate in pulsars. If this is true, it is conceivable that the pulsars might also be emitting ultra high energy, pulsed gamma rays with the same periodicities as observed at radio frequencies. These gamma rays might be the result of either the decay of π0-mesons or the bremsstrahlung of electrons in the regions surrounding the pulsars. There is no precise theory yet on this aspect. There have already been several searches for high energy gamma rays from pulsars3–5.