Isotope-shift factors with quantum electrodynamics effects for many-electron systems: A study of the nuclear charge radius of Al26m

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, 26m Al.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 27 Al and 26m Al, obtained by combining the calculated atomic factors with recently measured isotope shift (IS) of the 3s 2 3p 2 P 3/2 → 3s 2 4s 2 S 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 27 Al, the resultant value Rc( 26m Al) = 3.132(10) fm is obtained.With the improved accuracy of the calculated IS factors the error in Rc( 26m Al) is now dominated by the experimental uncertainty.Similar revision of rms charge radii is made for the 28 Al, 29 Al, 30 Al, 31 Al and 32 Al isotopes using existing IS measurements.Additionally, atomic factors are computed for the 3s 2 3p 2 P 3/2 → 3s 2 4s 2 S 1/2 , 3s 2 3p