An expansion formula for Stark effect transition probabilities is derived in terms of field-free (spherical) transition probabilities. Expansion coefficients are squares of Clebsch-Gordan coefficients from the SO(4) = SU(2) \ifmmode\times\else\texttimes\fi{} SU(2) description of the hydrogen atom. The method provides new sum rules for Stark transitions which explain regularities in previous calculations. Accurate formulas for average Stark transition probabilities obtain from application of the method to an empirical model for field-free transition probabilities. The approximation permits estimation of Stark lifetimes in the large- $n$ regime.An expansion formula for Stark effect transition probabilities is derived in terms of field-free (spherical) transition probabilities. Expansion coefficients are squares of Clebsch-Gordan coefficients from the SO(4) = SU(2) \ifmmode\times\else\texttimes\fi{} SU(2) description of the hydrogen atom. The method provides new sum rules for Stark transitions which explain regularities in previous calculations. Accurate formulas for average Stark transition probabilities obtain from application of the method to an empirical model for field-free transition probabilities. The approximation permits estimation of Stark lifetimes in the large-$n$ regime.

Physical Review ANov 1, 197524 citations

Stark Lifetimes for the Hydrogen Atom

John R. Hiskes, C. Bruce Tarter, D. A. Moody

The radiative transition probabilities in hydrogen have been calculated for all Stark transitions through $n=25$ . In general, the total transition probability and lifetime of a particular state are a function of the parabolic quantum numbers ${n}_{1}$ , ${n}_{2}$ , and $m$ . For $m>0$ and to within an error of the order of one percent the radiative lifetimes are functions only of $n$ , $m$ . The radiative lifetimes are presented graphically for all states from $n=2$ through $n=25$ .The radiative transition probabilities in hydrogen have been calculated for all Stark transitions through $n=25$. In general, the total transition probability and lifetime of a particular state are a function of the parabolic quantum numbers ${n}_{1}$, ${n}_{2}$, and $m$. For $m>0$ and to within an error of the order of one percent the radiative lifetimes are functions only of $n$, $m$. The radiative lifetimes are presented graphically for all states from $n=2$ through $n=25$.

Physical ReviewJan 20, 196449 citations

n

regime.

The radiative transition probabilities in hydrogen have been calculated for all Stark transitions through

n=25

. In general, the total transition probability and lifetime of a particular state are a function of the parabolic quantum numbers

{n}_{1}

{n}_{2}

, and

m

. For

m>0

and to within an error of the order of one percent the radiative lifetimes are functions only of

n

m

. The radiative lifetimes are presented graphically for all states from

n=2

through

n=25