Effect of blackbody radiation on the hydrogen spectrum

Abstract

The partition function of a single hydrogen atom diverges. While the astrophysical solution to this dilemma is the introduction of a density dependent alteration of the partition function, the question of what happens in an arbitrarily rarefied gas remains open. It is argued that in this case blackbody radiation changes the atom’s spectrum. A unified derivation including these effects and the nonrelativistic Lamb shift and spontaneous emission is presented. Then recent numerical calculations performed by workers in the field of Rydberg atom spectroscopy are utilized to estimate the principal quantum number for which blackbody radiation significantly alters the spectrum.