1977/09/01 by Tokio Yamabe, Akitomo Tachibana, Harris J. Silverstone · 4 citations
Physics and Astronomy · #Atomic and Molecular Physics #Advanced Chemical Physics Studies #Cold Atom Physics and Bose-Einstein Condensates #Physics #Ionization #Hydrogen atom #Atomic physics #Energy (signal processing) #Ground state #Atom (system on chip) #Quantum mechanics #Ion
paper · doi:10.1103/physreva.16.877
openalex publication_date 1977/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The theory of the field ionization of the hydrogen atom is developed analytically. The leading term of an asymptotic expansion for the ionization rate---the reciprocal lifetime---is derived. In the weak-field limit, the formula for the ionization rate reduces to \frac1\ensuremathτ=n^\ensuremath-3[n2!(n2+|m|)!]^\ensuremath-1 (n\frac3F4)^\ensuremath-2n2\ensuremath-|m|_\ensuremath-1\ifmmode×\else\texttimes\fiexp[3(n1\ensuremath-n2)\frac\ensuremath-2(3n3F)], where n, m, and n1 and n2 are the usual principal, magnetic, and parabolic quantum numbers, respectively, and F is the field strength in atomic units. For the ground state, this formula agrees with that of Landau and Lifshitz. For all m2=1 states, the formula agrees asymptotically for large n2 with that of Lanczos after correction of the latter for an error. It is in disagreement with the result of Oppenheimer and with the low-field result of Rice and Good. Significantly better agreement with numerical calculations of Alexander, of Hehenberger, McIntosh, and Br"andas, of Damburg and Kolosov, and of Bailey, Hiskes, and Riviere is obtained with a formula for not quite such small F, \frac1\ensuremathτ=(\ensuremath-2ReE)(3)/(2)[n2!(n2+|m|)!]^\ensuremath-1f^\ensuremath-Bexp[\ensuremath-(1)/((6f))], where E is the perturbed energy, where f=\frac[(\ensuremath-2E)^\ensuremath-(3)/(2)F]4, and where (B)/(2)=\ensuremathβ_2,n2 is the usual perturbed separation constant [\ensuremathβ2\ensuremath→\fracn2+|m|2+(1)/(2), as F\ensuremath→0].