Classical limit of relativistic quantal system with attractive Coulomb interaction

Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r ²〉 − 〈r〉²]^1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.     

Effects of neutron skin on the excitation of isovector modes of neutron-rich nuclei

The existence of a neutron skin in neutron-rich nuclei is discussed in connection with the excitation of isovector dipole and quadrupole giant modes via isoscalar nuclear probes. In the case of large neutron excess, important contributions are obtained from the nuclear excitation, which may even become predominant according to proper kinematical conditions. At variance with the usual situation encountered in inelastic processes, constructive interference can be found between nuclear and Coulomb contributions.     

μSR studies of heavy fermion systems

We have performed both zero field and high transverse field measurements at dilution refrigerator temperatures on a number of heavy electron systems, examining the superconducting and magnetic properties of these interesting materials. Among the materials studied to date are UBe₁₃, URu₂Si₂ and U₆Fe. The magnetic field penetration depth in the superconducting state of UBe₁₃ is greater than 10000 Å, as no increase in the transverse field relaxation rate is observed belowT _c . A sharp increase in the precession frequency is seen, starting atT _c . This frequency shift shows little temperature dependence at low temperature; we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu₂Si₂ show the weak antiferromagnetic transition at 17.5 K. Finally, we we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu₂Si₂ show the weak antiferromagnetic transition at 17.5 K. Finally, we have observed relaxation in high transverse field due to the formation of a flux lattice in U₆Fe, a material where the electron effective mass is rather lighter than in other heavy fermion systems. The relaxation exhibits a sharp onset atT _c=3.9 K, and is flat at low temperatures as expected for a conventional superconductor.     

Kinetic study of n-heptane oxidation

The oxidation of n-heptane has been studied in a jet-stirred flow reactor in the temperature range 950–1200 K at atmospheric pressure for a wide range of fuel-oxygen equivalence ratios (0.2 to 2.0). A chemical kinetic reaction mechanism developed from previous studies on smaller hydrocarbons and extended to C₆ and C₇ species was used to reproduce the experimental data. Good agreement between computed and measured concentrations of major chemical species was obtained for the entire range of experimental conditions. Sensitivity analyses were carried out to identify the reactions having the greatest influence on the modeling results. The major reaction paths for n-heptane consumption and for the formation of the main products have been identified. In addition n-heptane ignition delays behind a reflected shock wave measured by other investigators were used to validate the present reaction mechanism at higher temperature and pressure.     

Phase dynamics of a detuned single-mode laser

We report measurements on the phase dynamics of a detuned single mode laser which has in the past shown correspondence to the complex Lorenz equation. The corresponding ranges of periodic pulsing, of detuned chaos and of windows within the chaotic domain are investigated.Invited paper     

Quantitative dependence of MR signal intensity on tissue concentration of Gd(HP-DO3A) in the nephrectomized rat.

Cardiac-gated SE 20/224 +/- 20 MR images were obtained from nephrectomized rats before and after intravenously administering 153Gd-Gd(HP-DO3A). The concentration of Gd, [Gd], was linear in dose in myocardium, skeletal muscle, and blood. Under steady-state conditions, where d[Gd]/dt = 0, image intensities (IIN) in regions of interest were compared with the measured [Gd]. IIN was linear in myocardium at less than or equal to 0.61 mumol/g-myocardium (less than or equal to 0.5 mmol/kg dose) and in skeletal muscle at less than or equal to 0.63 mumol/g-muscle (less than or equal to 0.75 mmol/kg). Above 0.6 mumol Gd/g-tissue, IIN did not increase further. The in vivo data were consistent with measured ex vivo and in vivo relaxivities. A 29% greater slope for IIN versus [Gd] in myocardium [14,439 +/- 4350 IIN (mumol/g)] than in muscle [10,258 +/- 5,296 IIN/(mumol/g)] was attributed to a significant difference in blood content: 25% versus 2% weight blood in myocardium and skeletal muscle, respectively. Two components were apparent from plots of ex vivo 1/T1 versus [Gd] in myocardium and muscle, and only one for blood.     

Deformations of complex structures on Γ/SL 2(C)

LetG be a connected complex semisimple Lie group. Let Γ be a cocompact lattice inG. In this paper, we show that whenG isSL ₂(C), nontrivial deformations of the canonical complex structure onX exist if and only if the first Betti number of the lattice Γ is non-zero. It may be remarked that for a wide class of arithmetic groups Γ, one can find a subgroup Γ′ of finite index in Γ, such that Γ′/[Γ′,Γ′] is finite (it is a conjecture of Thurston that this is true for all cocompact lattices inSL(2, C)). We also show thatG acts trivially on the coherent cohomology groupsH ⁱ(Γ/G, O) for anyi≥0.     

On composition of some general fractional integral operators

In the present paper we derive three interesting expressions for the composition of two most general fractional integral oprators whose kernels involve the product of a general class of polynomials and a multivariableH-function. By suitably specializing the coefficients and the parameters in these functions we can get a large number of (new and known) interesting expressions for the composition of fractional integral operators involving classical orthogonal polynomials and simpler special functions (involving one or more variables) which occur rather frequently in problems of mathematical physics. We have mentioned here two special cases of the first composition formula. The first involves product of a general class of polynomials and the Fox’sH-functions and is of interest in itself. The findings of Buschman [1] and Erdélyi [4] follow as simple special cases of this composition formula. The second special case involves product of the Jacobi polynomials, the Hermite polynomials and the product of two multivariableH-functions. The present study unifies and extends a large number of results lying scattered in the lierature. Its findings are general and deep.     

He-N2 radiofrequency discharge: Influence of N2 on discharge and afterglow

A diagnostic study q (energy transfer processes in a He-N₂ flowing discharge and afterglow has been performed in a radiofrequency-produced plasma cooled in a liquid nitrogen hath. Optical emission spectroscopy in the visible and infrared spectral range as well as Langrnuir probe diagnostics were used. The vibrational kinetics of CO injected in such an afterglow has been examined. It shows a slow cooling of the electrons in the afterglow regime. The electron kinetics responsible joy CO vibrahonal excitation is turned off when N₂ is added to the He discharge, while that for vibrationally excited N₂ molecules is turned on. The results are discussed on the basis of previous theorerical calculations and experiments on the He-N₂ system.