Volume 26, Issue 1
January 1986, pages 1-83
pp 1- January 1986 Letter
Bosonic string theories with new boundary conditions
We show that the classical Nambu-Goto string inD dimensions admits Poincaré invariance ind dimensions (d⩽D) if (i)d − 2 of the transverse co-ordinatesx^{i} are periodic and the rest quasi-periodic involving a real orthogonal matrix with (D − d) (D − d − 1)/2 free parameters, or if (ii)d − 2 ofx^{i} obey Neumann and the rest obey a boundary condition involvingN free parameters, whereN=(D − d)^{2}/2 ifD − d is even, andN=[(D − d)^{2} − 1]/2 ifD − d is odd.
pp 1-8 January 1986 Gravitation Theory
Velocity-dependent inertial induction and secular retardation of the earth’s rotation
According to the model of inertial induction proposed earlier, the inertia force consists of an acceleration-dependent term which comes out as identically equal to -ma. Besides, there is a velocity-dependent term which is exceedingly small to be easily detected. However, it has been shown that this results in a cosmological red shift of light coming from distant stars and galaxies; the magnitude of the red shift agrees very well with the observed values. Though this model yields correct results when applied to photons it needs modification before applying to other bodies. A modified form of the inertial induction model is now proposed where the proposed velocity-dependent inertia forces, when applied to the solar system, yields correct order of magnitude for the secular retardation of the earth’s rotation. Moreover, a combined model using the velocity term and the tidal friction also does not suggest any close proximity of the moon to the earth in the past. When the model is applied to the case of Phobos, a secular acceleration of the order of magnitude of 10^{−3} deg yr^{−2} is obtained.
pp 9-14 January 1986 Quantum Mechanics
A determinantal identity is used to calculate the ensemble-averaged traces of the Hamiltonian. Using these averages a general expression is obtained for the Fourier transform of the single eigenvalue probability density function for all the three Gaussian ensembles for the two-dimensional case. It is shown how one can use the familiar step-up operators for the representation of a determinant. The ensemble-averaged traces are also used to derive the Fourier transform of the non-zero mean ensemble.
pp 15-20 January 1986 Statistical Physics
Study of Ising model on the rectangular-triangular lattice
The Ising model is studied on a new type of lattice which is named the rectangular-triangular lattice. The critical temperature for the ferromagnetic lattice is calculated exactly and it is shown that the antiferromagnetic lattice does not order at any temperature. Ground state properties are investigated and some features of frustration on the antiferromagnetic Ising lattice outlined.
pp 21-41 January 1986 Particle Physics
Validity of the equivalent-photon approximation for the production of massive spin-1 particles
T Jayaraman G Rajasekaran S D Rindani
We point out that the equivalent-photon approximation (EPA) for processes with massive spin-1 particles in the final state would have validity in a more restricted kinematic domain than for processes where it is commonly applied, viz., those with spin-1/2 or spin-0 particles in the final state. We obtain the criterion for the validity ofEPA for the two-photon production of a pair of charged, massive, point-like spin-1 particlesV^{±}, each of massM and with a standard magnetic moment (κ=1). In a process in which one of the photons is real and the other virtual with four-momentumq, the condition for the validity ofEPA is |q^{2}|≪M^{2}, in addition to the usual condition |q^{2}|≪W^{2},W being theV^{+}V^{−} invariant mass. In a process in which both photons are virtual (with four-momentaq andq′), our condition is |q^{2}||q′^{2}|W^{4} ≪ 16M^{8}, in addition to |q^{2}| ≪M^{2}, |q′^{2}| ≪M^{2} and |q^{2}| ≪W^{2}, |q′^{2}| ≪W^{2}. Even when these extra conditions permitting the use ofEPA are not fulfilled, convenient approximate expressions may still be obtained assuming merely |q^{2}| ≪W^{2} and |q′^{2}| ≪W^{2}.
We also discuss how the extra conditions are altered when the vector bosons are incorporated in a spontaneously broken gauge theory. Examples ofW boson production in Weinberg-Salam model are considered for which the condition |q^{2}||q′^{2}|W^{4} ≪ 16M^{8} is shown to be removed.
pp 43-53 January 1986 Nuclear Physics
Polarization parameters in systems with spin-spin interactions
The spin-spin interaction of two arbitrary spin systems is considered in some detail. The temporal evolution of the polarization parameters and the correlation parameters has been worked out. Applications of the formalism and the interpretation of the results to processes such as heavy-ion interactions, muon and nuclear repolarization and depolarization in muonic atoms and interactions of multilevel systems are outlined.
pp 55-60 January 1986 Atomic Physics
Theoretical calculations of the energies of the ∝ satellite and hypersatellite lines of magnesium
Lakshmi Natarajan A V Tankhiwale C Mande
The satellite and hypersatellite x-ray lines which lie on the high energy side of the dipole ∝_{1,2} lines are generally attributed to multiple ionization. In this paper, an attempt is made to calculate the energies of these lines in the x-ray spectrum of the magnesium atom using screened hydrogenic wavefunctions. Besides the good agreement found between our calculated values and the experimental results, our calculations give some additional lines not reported earlier.
pp 61-66 January 1986 Solid State Physics
Hemamalini Naik S V Subramanyam
The current voltage characteristics ofo-tolidine-iodine, with stoichiometry 1:1 grown from benzene, have been studied under high pressures upto 6 GPa atT=300 K andT=77 K. The characteristics show a pronounced deviation from ohmicity beyond a certain current for all pressures studied. At room temperature, beyond a threshold field the system switches from a low conductingOFF state to a high conductingON state with σ_{ON}/σ_{OFF} ∼ 10^{3}. TheOFF state can be restored by the application of an a.c. pulse of low frequency. The temperature dependence of the two states studied indicates that theOFF state is semiconducting while theON state, beyond a certain applied pressure is metallic. The characteristics atT=77 K do not show any switching.
pp 67-72 January 1986 Solid State Physics
Unified study and transport properties of simple metals
The resistivity, thermoelectric power at the melting points and temperature variation of resistivity of the liquid alkali metals are studied with local Heine-Abarenkov and the modified Ashcroft pseudopotentials. The parameters of the model potentials are obtained from a unified study of the static and dynamic properties of the metals. The effect of different dielectric function and structure factor on the transport properties is discussed. It is shown that the simple modified Ashcroft pseudopotential reproduces the result fairly well except for Li and Cs.
pp 73-78 January 1986 Solid State Physics
Residual resistivity in Ni-Fe-Cr/V alloys and the two-current model
The resistivity of a large number of Ni-Fe-Cr/V alloys has been measured at 77 K. An attempt has been made to explain the concentration dependence of resistivity in the light of Mott’s two-current model. It is seen that contrary to earlier observation, the model is applicable to a larger range of concentration for the Ni-Fe-Cr series. Appreciable deviation from the model starts for Fe concentration exceeding about 15 at. % and Cr about 7 to 8 at. %. However, for similar concentration range in Ni-Fe-V series, disagreement between the experimental and theoretical results is more pronounced.
pp 79-83 January 1986 Solid State Physics
V S Yadav S K Yadav R K Malhotra
Electron paramagnetic resonance of Gd^{3+} in Pr_{2}Zn_{3}(NO_{3})_{12} · 24H_{2}O single crystals has been studied at ∼ 9.45 GHz and at 285 K. In addition to the allowed fine structure lines (ΔM=± 1) some weak low field lines identified as ΔM = ± 2 transitions have been observed.
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