Ionization of hydrogen atoms by electron impact at 1eV, 0.5eV and 0.3eV above threshold

We present here triple differential cross sections for ionization of hydrogen atoms by electron impact at 1eV, 0.5eV and 0.3eV energy above threshold, calculated in the hyperspherical partial wave theory. The results are in very good agreement with the available semiclassical results of Deb and Crothers \cite{DC02} for these energies. With this, we are able to demonstrate that the hyperspherical partial wave theory yields good cross sections from 30 eV \cite{DPC03} down to near threshold for equal energy sharing kinematics.Comment: 6 pages, 9 figure

Mean squared error of empirical predictor

The term ``empirical predictor'' refers to a two-stage predictor of a linear combination of fixed and random effects. In the first stage, a predictor is obtained but it involves unknown parameters; thus, in the second stage, the unknown parameters are replaced by their estimators. In this paper, we consider mean squared errors (MSE) of empirical predictors under a general setup, where ML or REML estimators are used for the second stage. We obtain second-order approximation to the MSE as well as an estimator of the MSE correct to the same order. The general results are applied to mixed linear models to obtain a second-order approximation to the MSE of the empirical best linear unbiased predictor (EBLUP) of a linear mixed effect and an estimator of the MSE of EBLUP whose bias is correct to second order. The general mixed linear model includes the mixed ANOVA model and the longitudinal model as special cases

Radio Observations of the AGN and Gas in Low Surface Brightness Galaxies

LSB galaxies have low metallicities, diffuse stellar disks, and massive HI disks. We have detected molecular gas in two giant LSB galaxies, UGC 6614 and F568-6. A millimeter continuum source has been detected in UGC 6614 as well. At centimeter wavelengths we have detected and mapped the continuum emission from the giant LSB galaxy 1300+0144. The emission is extended about the nucleus and is most likely originating from the AGN in the galaxy. The HI gas distribution and velocity field in 1300+0144 was also mapped. The HI disk extends well beyond the optical disk and appears lopsided in the intensity maps.Comment: one page; submitted to proceedings of IAU Symposium 235: Galaxy Evolution across the Hubble Tim

Hyperspherical partial wave calculation for double photoionization of the helium atom at 20 eV excess energy

Hyperspherical partial wave approach has been applied here in the study of double photoionization of the helium atom for equal energy sharing geometry at 20 eV excess energy. Calculations have been done both in length and velocity gauges and are found to agree with each other, with the CCC results and with experiments and exhibit some advantages of the corresponding three particle wave function over other wave functions in use.Comment: 11 pages, 1 figure, submitted to J. Phys B: At. Mol. Opt. Phys; v2 - revised considerably, rewritten using ioplatex clas

Hyperspherical partial wave theory applied to electron hydrogen-atom ionization calculation for equal energy sharing kinematics

Hyperspherical partial wave theory has been applied here in a new way in the calculation of the triple differential cross sections for the ionization of hydrogen atoms by electron impact at low energies for various equal-energy-sharing kinematic conditions. The agreement of the cross section results with the recent absolute measurements of R\"oder \textit {et al} [51] and with the latest theoretical results of the ECS and CCC calculations [29] for different kinematic conditions at 17.6 eV is very encouraging. The other calculated results, for relatively higher energies, are also generally satisfactory, particularly for large $\Theta_{ab}$ geometries. In view of the present results, together with the fact that it is capable of describing unequal-energy-sharing kinematics [35], it may be said that the hyperspherical partial wave theory is quite appropriate for the description of ionization events of electron-hydrogen type systems. It is also clear that the present approach in the implementation of the hyperspherical partial wave theory is very appropriate.Comment: 16 pages, 9 figures, LaTeX file and EPS figures. To appear in Phys. Rev.

Comparison of perturbative expansions using different phonon bases for two-site Holstein model

The two-site single-polaron problem is studied within the perturbative expansions using different standard phonon basis obtained through the Lang Firsov (LF), modified LF (MLF) and modified LF transformation with squeezed phonon states (MLFS). The role of these convergent expansions using the above prescriptions in lowering the energy and in determining the correlation functions are compared for different values of coupling strength. The single-electron energy, oscillator wave functions and correlation functions are calculated for the same system. The applicability of different phonon basis in different regimes of the coupling strength as well as in different regimes of hopping are also discussed.Comment: 24 pages (RevTEX), 12 postscript figures, final version accepted in PRB(2000) Jornal Ref: Phys. Rev. B, 61, 4592-4602 (2000