Isotope shift and hyperfine splitting of the $4s\to 5p$ transition in potassium

We have investigated $4s{}^2{S}_{1\mathrm{/}2}\to 5p{}^2{P}_{1\mathrm{/}2}$ transition ($D_1$ line) of the potassium isotopes ${}^{39}$K, ${}^{40}$K, and ${}^{41}$K using Doppler-free laser saturation spectroscopy. Our measurements reveal the hyperfine splitting of the $5p{}^2{P}_{1\mathrm{/}2}$ state of ${}^{40}$K and we have determined the specific mass shift and the nuclear field shift constants for the blue $D_1$ line.