Showing papers by "Tata Institute of Fundamental Research published in 1968"

A Note on Quotients of Real Algebraic Groups by Arithmetic Subgroups

Abstract: Introduction Let G be a connected semi-simple algebraic group defined over Q. Let F be an arithmetic subgroup of G, i.e., a subgroup of G such that for some (and therefore any) faithful rational representation p: G--, GL(N, C) defined over Q, Fc~p-I(SL(N, Z)) is of finite index in both F and p-a(SL(N, Z)). Let K c G be a maximal compact subgroup of Ga, the set of real points of G. With this notation, we can state the main result of this note.

Master analytic representation: Reduction of O(2, 1) in an O(1, 1) basis

Abstract: We display the reduction of the pseudo‐orthogonal group O(2, 1) with respect to a noncompact O(1, 1) basis. After the explicit solution is obtained, we rederive the results using the method of master analytic representations.

Competence and Deoxyribonucleic Acid Uptake in Bacillus subtilis

Abstract: The distribution of uninucleate and multinucleate cells of Bacillus subtilis, fractionated by zonal centrifugation, shows that the uninucleate cells are most likely to be competent Only the competent fraction of the population incorporates deoxyribonucleic acid

ACTIVATION CROSS SECTIONS OF CALCIUM, POTASSIUM, AND ALUMINUM FOR 14.2-MeV NEUTRONS.

Abstract: The cross sections for some ($n, t$), ($n, d$), ($n, p$), ($n, \ensuremath{\alpha}$), and ($n, 2n$) reactions have been measured on the various enriched isotopes of calcium and spectroscopically pure potassium and aluminum. Powdered samples, wrapped in thin aluminum foils to act as neutron monitors, were irradiated with 14.2\ifmmode\pm\else\textpm\fi{}0.2 MeV neutrons. The induced absolute activities were measured by a calibrated and specially shielded well-type NaI(Tl) crystal. The following results (in millibarns) for the cross sections have been obtained: ${\mathrm{Al}}^{27}(n, p){\mathrm{Mg}}^{27}$, 71\ifmmode\pm\else\textpm\fi{}9; ${\mathrm{Ca}}^{40}(n, t){\mathrm{K}}^{38}$ (ground state), 0.18\ifmmode\pm\else\textpm\fi{}.02; ${\mathrm{Ca}}^{42}(n, p){\mathrm{K}}^{42}$, 190\ifmmode\pm\else\textpm\fi{}24; ${\mathrm{Ca}}^{43}(n, p){\mathrm{K}}^{43}$, 93\ifmmode\pm\else\textpm\fi{}12; ${\mathrm{Ca}}^{43}(n, d){\mathrm{K}}^{42}$, 1.3;${\mathrm{Ca}}^{44}(n, p){\mathrm{K}}^{44}$, 20\ifmmode\pm\else\textpm\fi{}8; ${\mathrm{Ca}}^{44}(n, \ensuremath{\alpha}){\mathrm{Ar}}^{41}$, 35\ifmmode\pm\else\textpm\fi{}3; ${\mathrm{Ca}}^{44}(n, d){\mathrm{K}}^{43}$, 2.6\ifmmode\pm\else\textpm\fi{}.4; ${\mathrm{Ca}}^{48}(n, 2n){\mathrm{Ca}}^{47}$, 900\ifmmode\pm\else\textpm\fi{}108; ${\mathrm{K}}^{39}(n, 2n){\mathrm{K}}^{38}$ (ground state),2.6\ifmmode\pm\else\textpm\fi{}.4; ${\mathrm{K}}^{41}(n, p){\mathrm{Ar}}^{41}$, 50\ifmmode\pm\else\textpm\fi{}6; ${\mathrm{K}}^{41}(n, \ensuremath{\alpha}){\mathrm{Cl}}^{38}$, 46\ifmmode\pm\else\textpm\fi{}6. The cross sections for the ${\mathrm{Ca}}^{43}(n, d){\mathrm{K}}^{42}$ and ${\mathrm{Ca}}^{44}(n, d){\mathrm{K}}^{43}$ reactions are reported for the first time. Other cross sections measured in this work are compared with their earlier values.

Structure of the Dirac Bracket in Classical Mechanics

Abstract: We discuss the structure of the Dirac bracket in classical mechanics. We consider a generalization of the usual Poisson bracket and show the close connection of this generalization to the Lagrange brackets of classical mechanics. We show how the Dirac bracket appears as a particular case of the generalized Poisson bracket, thus giving a simple reason why the Jacobi identity holds for the Dirac bracket. We also discuss the nature of the transformations generated via the Dirac bracket and the relation of these to canonical transformations.

Bilinear optical polarizability of silver

Abstract: The linear dielectric constant and the bilinear optical polarizability of silver are calculated in the long wavelength limit, using a simple 2-band model for the metal consisting of a completely filled flatd-band and a half-filled free-electron-like conduction band. It is shown that the results thus obtained, compare well with the experimental results for the linear dielectric constantɛ(ω), forħω between 1 eV and 5 eV. In the bilinear case, the reflectivity of the second harmonic wave, when the incident laser beam is polarized perpendicular to the plane of incidence, is shown to have a broad resonance whenɛ(2ω) becomes very small. However, there is no resonance in the reflectivity of the second harmonic wave in silver at the threshold frequency for the interband absorption of this wave.

Binding energy and π + decay of light hyperfragments

Abstract: Binding energy values of hyperfragments from a sample of 541 uniquely identified mesic decays with mass numbers A=3 to 14 are presented. There does not seem to be any detectable difference in the binding energy value of Λ inAH4 obtained from its two-body and three-body decay modes. Within statistical error, the binding energy values of Λ inAH4 andAH4 are also the same. From a sample of 2π + decay events of hyperfragments the branching ratio ofAH4 decaying byπ + toπ − mode is found to be (1·5±1·0)%.

Rigidity spectrum of cosmic ray helium nuclei

Abstract: An experiment has been carried out using an oriented stack of nuclear emulsions to determine the rigidity spectrum of cosmic ray helium nuclei between 12 and 40 GV, by taking advantage of the variation of the geomagnetic cut-off rigidity in the east-west plane over Hyderabad, India. Altotal of 2433 identified helium nuclei recorded in the stack, has been divided into 8 angular intervals in the east-west plane corresponding to 8 different cut-off rigidities. From this the integral fluxes of helium nuclei at the top of the atmosphere have been obtained for all the 8 rigidity intervals. The vertical flux above an effective threshold rigidity of 16·73 GV has been determined with high statistical accuracy and has a value of 15·0±0·5 helium nuclei (m2.sr.sec.)−1. The rigidity spectrum of these nuclei between 12 and 40 GV can be well represented by a power law of the type N (>R) =1990 R−1.74±0.11 (m2.sr.sec.)−1 and is the first direct determination so far made in this rigidity region. The differential rigidity spectra of protons, helium nuclei and S-nuclei of the cosmic radiation in the vicinity of the earth at solar minimum (1965) have been constructed with the existing world data and it is found that for rigidities ≳ 10 GV, the three spectra have, within experimental errors, the same slope of 2·6. The ratio P/He and He/S of the differential fluxes have been studied as a function of rigidity. It is found that for R>2 GV, the ratio P/He has, within experimental errors, a constant value of 6·3; as for the ratio He/S, it seems that the experimental data above a GV is not inconsistent with a constant value of 14 over the entire rigidity interval considered here.

Electrons magnetic fields and background radio emission in the galaxy.

Abstract: Extensive data now available on the non-thermal background radio emission from different celestial directions, and recent measurements on the energy spectrum of cosmic ray electrons in the vicinity of the earth permit one to deduce information on the mean magnetic fields and cosmic electron spectra needed to exist in different regions of the Galaxy. It is found that in order to explain quantitatively the background radio brightness distributions from the Galaxy one needs (i) the same or nearly same electron spectrum that exists in the near interstellar space, to exist in almost all regions of Galactic space, (ii) a mean magnetic field close to 6×10−6 Gauss in the Disc in the direction of the Anti-centre, (iii) a mean magnetic field close to 2·5×10−6 Gauss in the radio Halo and (iv) a mean magnetic field probably close to 9·5×10−6 Gauss towards the Galactic Ridge in the direction of the Centre. Some inferences are also drawn on the confinement of cosmic rays in the Galaxy.

Low Energy Theorems to Fourth Order in e for Compton Scattering

Abstract: We prove low-energy theorems for Compton scattering, which are exact when the electromagnetic interaction is included up to fourth order and the strong interactions to all orders. These theorems give the terms of order ${\ensuremath{\omega}}^{2}\mathrm{ln}\ensuremath{\omega}$, where $\ensuremath{\omega}$ is the photon c.m. momentum, besides establishing the classical low-energy theorem to the order ${e}^{4}$.

Radio Emitting Electrons in the Galaxy and the Solar Modulation of Cosmic Rays

Abstract: The energy spectrum of electrons in interstellar space needed to explain the Galactic background radio emission has been derived. Information can then be deduced about the solar modulation of cosmic ray electrons.

Hartree--fock--bogoliubov projected spectra for finite nuclei.

Abstract: Explicit expressions convenient for numerical calculations are derived for the number- and total-spin-projected spectrum of a nucleus from its Hartree-Fock-Bogoliubov solution. Suitable approximation to such a spectrum is found. The applications of these results are also carried out.