TY - JOUR
T1 - The hydrogen atom in strong electric fields
T2 - Summation of the weak field series expansion
AU - Hiraizumi, Ken Ichi
AU - Ohshima, Yoshihisa
AU - Suzuki, Hiroshi
PY - 1996/6/17
Y1 - 1996/6/17
N2 - The order dependent mapping method, whose convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for the Stark effect of the hydrogen atom. We perform a numerical experiment up to the 50th order of the perturbation expansion. A simple mapping, suggested by the analytic structure and the strong field behavior, gives an excellent agreement with the exact value for an intermediate range of the electric field, 0.03 (a.u.) ≤ E ≤ 0.25 (a.u.). The imaginary part of the energy (the decay width) as well as the real part of the energy is reproduced from the standard perturbation series.
AB - The order dependent mapping method, whose convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for the Stark effect of the hydrogen atom. We perform a numerical experiment up to the 50th order of the perturbation expansion. A simple mapping, suggested by the analytic structure and the strong field behavior, gives an excellent agreement with the exact value for an intermediate range of the electric field, 0.03 (a.u.) ≤ E ≤ 0.25 (a.u.). The imaginary part of the energy (the decay width) as well as the real part of the energy is reproduced from the standard perturbation series.
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U2 - 10.1016/0375-9601(96)00243-5
DO - 10.1016/0375-9601(96)00243-5
M3 - Article
AN - SCOPUS:0010803614
VL - 216
SP - 117
EP - 124
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
SN - 0375-9601
IS - 1-5
ER -