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radiative mean lifetimes for the hydrogen atom (n,l)

Version 2 2016-01-08, 14:32
Version 1 2014-10-16, 19:08
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posted on 2016-01-08, 14:32 authored by James BabbJames Babb

For the hydrogen atom, the table gives the radiative mean lifetime in seconds for
a state (n,l). The tabulation goes up to n=70.
The decay width of the level is hbar/lifetime.

I used the quantum-mechanical expressions given by H. C. Goldwire, Ap.J. Suppl. 152 (1968) 445,

DOI: 10.1086/190180

The numbers agree with, where data are available, Table I (last
column) of L.J. Curtis, JOSA 63 (1973) 105-7, DOI: 10.1364/JOSA.63.000105
and Table I (last column) of H. Marxer and L. Spruch, Phys. Rev. A
43 (1991), 1268-74, DOI: 10.1103/PhysRevA.43.1268
The numbers are also in good agreement
with the semiclassical values given by K. Omidvar Phys. Rev. 26 (1982), 3053,
Table III, up to n=25.
As a check, the tabulated
value for the lifetime of n=70,l=69 agrees with the value from the
asymptotic formula for the width given in "Relativistic and radiative
energy shifts for Rydberg states," U.D. Jentschura, E.-O. Le Bigot,
J. Evers, P. J. Mohr, and C.H. Keitel, J. Phys. B 38 (2005), S97
doi: 10.1088/0953-4075/38/2/008

Curtis and Marxer & Spruch (and others) also investigated semi-classical formulae
for the lifetimes. See the review,  "Asymptotic methods for
Rydberg transitions,", D.P. Dewangan, Phys. Rep. 511 (2012), 1-142,
DOI: 10.1103/PhysRevA.43.1268

 

 

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