Experimental and theoretical study of the nf-level lifetimes of potassium

The theoretical and experimental values of the 5f, 6f, 7f, and 8f radiative lifetimes τ of neutral potassium are reported. The reduced matrix elements for all allowed electric-dipole nf_5∕2-n^′d_5∕2, nf_5∕2-n^′d_3∕2, and nf_7∕2-n^′d_5∕2 transitions with n=5–8 in K are calculated using the relativistic linearized coupled-cluster method with single and double excitations of Dirac-Fock wave functions included to all orders in many-body perturbation theory. The resulting electric-dipole matrix elements are used to evaluate the lifetimes of the 5f, 6f, 7f, and 8f states in neutral K and their uncertainties. The contributions from the nf_5∕2-n^′g_7∕2, nf_7∕2-n^′g_7∕2, and nf_7∕2-n^′g_9∕2 transitions to the lifetimes of the 6f, 7f, and 8f states are evaluated using the third-order many-body perturbation theory and are found to be very small. The theoretical results are τ_5f=117(4) ns, τ_6f=195(4) ns, τ_7f=301(6) ns, and τ_8f=441(9) ns. The experiment is performed in a cell using time-resolved fluorescence spectroscopy. The nf states are excited stepwise, 4s→4p→nf, using two pulsed synchronous dye lasers for the dipole and quadrupole transitions, respectively. The measured values τ_5f=117(3) ns, τ_6f=190(6) ns, τ_7f=309(8) ns, and τ_8f=428(10) ns are in excellent agreement with the present theoretical calculations.