High-accuracy calculation of energies, lifetimes, hyperfine constants, multipole polarizabilities, and blackbody radiation shift in ³⁹K

Excitation energies of the ns, np_j, nd_j, nf_j, and ng_j states with n⩽7 in neutral potassium are evaluated. First-, second-, third-, and all-order Coulomb energies and first- and second-order Coulomb-Breit energies are calculated. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for levels up to n=9–12. Electric-dipole (4s_1∕2-np_j, n=4–26), electric-quadrupole (4s_1∕2-nd_j, n=3–26), and electric-octupole (4s_1∕2-nf_j, n=4–26) matrix elements are calculated to obtain the ground state E₁, E₂, and E₃ static polarizabilities. Scalar and tensor polarizabilities for the 4p_j excited state in K I are also calculated. All the above-mentioned matrix elements are determined using the all-order method. We also investigate the hyperfine structure in ³⁹K. The hyperfine A values are determined for the first low-lying levels up to n=7. The quadratic Stark effect on hyperfine structure levels of the ³⁹K ground state is investigated. The calculated shift for the (F=2,M=0)↔(F=1,M=0) transition is found to be −0.0746 Hz∕(kV∕cm)², in agreement with the experimental value −0.071±0.002 Hz∕(kV∕cm)². These calculations provide a theoretical benchmark for comparison with experiment and theory.