Binding energy levels of a slowly moving ion in quantum plasmas

Abstract

Electrostatic potential of a slowly moving ion in quantum plasmas is studied. This potential is composed of the Debye-Hückel potential and the wake potential. The near-field-wake potential is found. The binding energy levels of one-electron bound states of the ion are calculated by use of the Ritz variation method. The trial wave function contains three variational parameters. The presence of the wake field splits the binding energy levels. This effect is analogous to the Zeeman effect. The removal of the degeneracy of binding energy levels is influenced by the speed of ion and the number density of electrons. Compared with binding energy levels of a free ion, some binding energy levels of a moving ion in quantum plasmas are "pushed up."

Precise energy eigenvalues of hydrogen-like ion moving in quantum plasmas

“…al. [32] showed that the energy of each state considered here becomes over-bound (i.e. more negative than the energy of the free ion) when the ion velocity (v) reaches a sufficiently high value.…”

“…al. [32] opined that such over-boundness occurred because of the choice of angular part of the wave function. But the angular part of the wavefunction cannot be responsible for such over-boundness as it violets the basic variational principle.…”

“…al. [32] reported that for n e = 8.0×10 23 m −3 and ion velocity v = 5000 m/s, the ground state (1s 0 ) energy of C 5+ becomes -25.60524 a.u. which is more negative than the ground state energy -18.0 a.u.…”

“…al. [32]. They [32] have found that the near field wake potential is proportional to 1 r 2 and cos θ; r being the radial distance between the moving ion and the observer while θ is the angle between the radial vector and velocity vector of the ion.…”

“…They [32] have found that the near field wake potential is proportional to 1 r 2 and cos θ; r being the radial distance between the moving ion and the observer while θ is the angle between the radial vector and velocity vector of the ion. They [32] have used Meijer's G function in deriving the analytic form of the near field wake potential, where this G function violets the condition used in its definition [33]. This results in some anomalous findings in binding energy calculations e.g.…”