Shifted large-N expansion for the energy levels of neutral atoms

Energy levels of neutral atoms have been re-examined by applying the method of shifted large-N expansion (whereN is the number of spatial dimensions) to the model Yukawa potential with a modified screening parameter. The predicted shell binding energies are found to be quite accurate over the entire range of the atomic number Z up to 84 and compare very well with those obtained within the framework of hypervirial-Padé scheme. It is observed that the large-N technique which is hitherto used in different contexts may also be applied to other areas of atomic physics.     

On screening constants in X-ray spectra

Fresh calculations of the X-ray screening constantsσ ₂ forL _II L _III,M _II M _III andM _IV M _V have been made. It has been found thatσ ₂ is not absolutely constant for differentZ. Some regular variations inσ ₂ with electronic shell structure have been noted.     

Spectrum of helium at high pressures

The effect of high pressures on an atom is frequently simulated by enclosing the atom in an impenetrable spherical box. The spectrum of such a confined helium atom placed at the centre of a spherical box is investigated. A model potential is used to calculate the energies of twelve excited states and thereby the transition wavelengths for a range of values of the radius of the confining sphere. Applications of results are discussed. Received 29 August 2002 Published online 10 December 2002 RID="a" ID="a"e-mail: ypvsj@uottawa.ca     

Valence charge density in indium arsenide

Valence charge densities of zinc-blende structure InAs calculated using an ab initio pseudopotential method are reported. It is found that as zinc-blende structure InAs is compressed, the changes in the charge density are gradual even as the volume at which it is unstable in favour of a rock salt structure is passed, and that under pressure the bond charges tend to move away from the anion sites towards the bond center sites.     

Improved condition for the absence of bound states and converging analytic bounds to critical screening parameter

Converging lower bound to the critical screening parameterD _c associated with the ground state of a two-particle system interacting through a cut-off Coulomb potential is obtained analytically using an improved condition for the absence of bound states. The predicted numerical result for the lower bound is found to be within 10⁻³% of the exact result. On the other hand, a multi-parameter variational approach yields a tight upper bound, within 0.54% of the exact result. It is shown that the critical screening parameter for the exciteds-states can also be determined in an approximate way. We obtainD _c ^ms ≈ [0.764435n ⁻²+0.617737n ⁻³]⁻¹ wheren is the principal quantum number. The predictedD _c for various quantum states (n=1 to 8) are in good agreement with the values obtained numerically by Singh and Varshni.     

Transport phenomena in nondegenerate semiconductors considering electron-electron scattering

Hall mobility and other transport properties of the electrons inn-type of semiconductors have been investigated when a magnetic field is applied, taking into account electron-electron scattering. Results have been presented for different impurity densities.     

Dipole polarizability of hydrogen atom at high pressures

Dipole polarizability of hydrogen atom at high pressures is investigated using the model of a trapped atom inside a spherical box with impenetrable surface. Both upper and lower bounds for the polarizability are obtained using accurate variational wavefunctions proposed recently. Buckingham polarizabilities calculated from the 1s state wavefunction are shown to be in good agreement with those calculated from the exact values of rⁿ for cage radii less than 2.5.     

An analytic approximation for the energy levels of neutral atoms

Using a screened coulomb potential, a simple formula is obtained for the shell binding energyE _ns of a neutral atom which gives accurate results over the entire range of the atomic number upto 84.