Reconciliation of Experimental Lamb Shifts

We develop a detailed analysis of the metastable quenching problem encountered in our recent level-crossing measurements in the $n=2\mathrm{}$ state of atomic hydrogen. The analysis allows calculation of a previously unaccounted systematic correction to the value of the Lamb shift $\mathcal{S}$ derived from these measurements. This correction, together with refinements in the calculation of $\mathcal{S}$ from a measured crossing, decreases our value to $\mathcal{S}=1057.86\mathrm{}\pm 0.10$ MHz. Within experimental error, this value agrees with the original result as measured by Lamb and collaborators. In addition, the analysis allows the calculation of a new upper limit to the parity impurity amplitude in the $2S$ state of atomic hydrogen, namely ${\left|a_0\right|}^2\le 8\times {10}^{-9\mathrm{}}$, at zero magnetic field.