Oscillator strengths of the transitions in a spherically confined hydrogen atom

Abstract

Dipole and quadrupole oscillator strengths have been calculated for the series of transitions nl → n l (n 5) in a hydrogen atom confined in the centre of a sphere with impenetrable walls. The non-monotonic dependence of the oscillator strengths on the radius of confinement has been discussed through their general forms obtained with a properly chosen radial wavefunction. It was qualitatively ascribed to variation of the radial electron density distributions of the states involved in the transitions. The effect of the confinement on the use of the dipole approximation has been studied, introducing a correction through the octupole term as well as performing the calculation with the full form of the interaction term.

Confinement approach to pressure effects on the dipole and the generalized oscillator strength of atomic hydrogen

“…Table I displays the individual DOS values obtained in this work for 1s → np (n = 2-5) transitions for a selected set of confining barrier heights (V 0 ) and radii (R 0 ). We also include in this table corresponding accurate values reported in the literature for V 0 = ∞ (R 0 = 1, 5, 10) [22,23] and for V 0 = 100 (R 0 = 1) [24]. For these latter conditions, the results of this work show excellent quantitative agreement with those from the aforementioned independent calculations for all the DOS contributions.…”

“…One of the simplest and earliest examples where these ideas have been employed is that of color centers in alkali-metal halides [18], where one or two electrons are trapped in anion vacancy sites in the ionic lattice. More recently, the spectroscopic properties (DOS) of the hydrogen atom confined by hard [19][20][21][22][23] and soft [24] spherical cavities have been reported, as well as similar studies on the optical absorption of hydrogenic impurities in semiconductor quantum dots [25].…”

“…As pointed out in the Introduction, the DOS behavior of the confined hydrogen atom has been explored mainly through the infinitely hard spherical confinement model [19,[21][22][23]. Only recently, Montgomery and Sen [24]-in their analysis of 1s static and dynamic dipole polarizabilities-have reported calculations of the DOS sums equivalent to Eq.…”

Photoionization cross sections of hydrogen impurities in spherical quantum dots using the finite-element discrete-variable representation

“…Ş ahin [15] has performed the calculations of photoionization cross sections and oscillator strengths for spherical quantum dots with hydrogenic impurity. Dipole and quadrupole oscillator strengths also have been reported recently by Stevanović [16] for the hydrogenic impurity in a spherical quantum dot with an infinite confining potential.…”

Photoionization Cross Sections of Atomic Impurities in Spherical Quantum Dots

“…The state energies of hydrogen impurity in spherical quantum dots with the infinite and finite well of rectangular potentials are explored by Chuu et al (Chuu et al (1992)), Yang et al (Yang et al (1998)), and Huang et al (Huang et al (1999)). Photoionization cross sections and oscillator strengths of hydrogenic impurities in spherical quantum dots are also obtained for the infinite and finite rectangular well models by Ham and Spector (Ham & Spector (n.d.)), Şahin (Şahin (2008)), and Stevanović (Stevanović (2010)). Recently, Lin and Ho (Lin & Ho (2011)) study the photoionization of hydrogen impurities in spherical quantum dots using the finite oscillator and Gaussian potentials.…”