Affiliation:
1. Department of Mathematics, The University of Burdwan , Golapbag, Burdwan 713 104, West Bengal, India
Abstract
Structural properties of the hydrogenic atoms, embedded in a quantum plasma environment and contained in a spherical box, have been investigated theoretically. The organized effect of the quantum plasma is represented by an effective potential characterized by the quantum wave number (QWN). The corresponding Schrödinger equation has been solved variationally by employing a large wave function which takes into account the Dirichlet boundary condition (vanishing of wave function on the boundary of the box). An inclusive study is made on the combined effect of the plasma confinement and spatial confinement on the bound states of the atoms. Eigenenergies, 2k-pole oscillator strength, 2k-pole polarizability, and various geometric expectation values of the radial coordinate are calculated quite accurately for different values of the QWN and box size. For the unconstrained atom, our present results are in excellent agreement with some of the accurate results available in the literature. Special emphasis is given to report the critical values of the box size and QWN which augur the instability of the atoms. Moreover, scaling of the Hamiltonian is critically analyzed and an empirical relation is presented for calculating the critical box size for any hydrogenic atom at a given QWN from the knowledge of the critical box size of the hydrogen atom at that QWN.
Funder
Science and Engineering Research Board