Isotope shift factors with quantum electrodynamics effects for many-electron systems: A study of the nuclear charge radius of ^26mAl

A method for calculating the field shift contribution to isotope shifts in many-electron atoms, incorporating quantum electrodynamics (QED) effects, is introduced. We also implement the model QED approach to incorporate QED contribution to the nuclear recoil effect at the high-order correlation effects treatment level. The proposed computational scheme is used to revise the value of the root-mean-square (rms) nuclear charge radius of the isomer of aluminium-26, ^26mAl. This radius is important for the global analysis of the V_ud element of the Cabibbo-Kobayashi-Maskawa matrix. The difference in mean-square nuclear charge radii of ^27Al and ^26mAl, obtained by combining the calculated atomic factors with recently measured isotope shift (IS) of the 3s^23p ^2P_3/2→ 3s^24s ^2S_1/2 transition in Al, is 0.443(44)(19)  fm^2, where the first and second uncertainties are experimental and theoretical ones, respectively. The latter is reduced by a factor of 4 with respect to the previous study. Using this value and the known value of the rms charge radius of ^27Al, the resultant value R_c(^26mAl) = 3.132(10) fm is obtained. With the improved accuracy of the calculated IS factors the error in R_c(^26mAl) is now dominated by the experimental uncertainty. Similar revision of rms charge radii is made for the ^28Al, ^29Al, ^30Al, ^31Al and ^32Al isotopes using existing IS measurements. Additionally, atomic factors are computed for the 3s^23p ^2P_3/2→ 3s^24s ^2S_1/2, 3s^23p ^2P_1/2→ 3s^25s ^2S_1/2 and 3s^23p ^2P_3/2→ 3s^25s ^2S_1/2 transitions in Al, which can be used in future experimental studies.