Isotope shifts and transition frequencies for the S and P states of lithium: Bethe logarithms and second-order relativistic recoil

Isotope shifts and total transition frequencies are calculated for the 20.16em0ex²S-30.16em0ex²S transition of the lithium isotopes ⁶Li, ⁷Li, ⁸Li, ⁹Li, and the halo nucleus ¹¹Li. The accuracy is improved for previously calculated relativistic and quantum electrodynamic corrections, and in particular a disagreement for the Bethe logarithm is resolved for the ground ²S state. Our previous result is confirmed for the 20.16em0ex²P state. We use the pseudostate expansion method to perform the sum over virtual intermediate states. Results for the second-order relativistic recoil term of order α²(μ/M)² Ry are shown to make a significant contribution relative to the theoretical uncertainty, but because of accidental cancellations the final result for the isotope shift is nearly unchanged. However, the spin-orbit term makes an unexpectedly large contribution to the splitting isotope shift (SIS) for the 20.16em0ex²P1/2-20.16em0ex²P3/2 fine structure, increasing the theoretical value for the ⁶Li-⁷Li isotopes to 0.5560.16em0ex31(7)±0.001 MHz. A comparison is made with high-precision measurements and other calculations for the SIS and for the total 20.16em0ex²S-30.16em0ex²S transition frequency.