Isotope-shift factors with quantum electrodynamics effects for many-electron systems: A study of the nuclear charge radius of <mmultiscripts> Al <mprescripts/> <none/> 26 m </mmultiscripts>

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 Vud 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 3s²3p~²P3/2 → 3s²4s~²S1/2 transition in Al, is 0.443(44)(19)~ fm², 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 Rc(²⁶ᵐAl) = 3.132(10)~fm is obtained. With the improved accuracy of the calculated IS factors the error in Rc(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 3s²3p~²P3/2 → 3s²4s~²S1/2, 3s²3p~²P1/2 → 3s²5s~²S1/2 and 3s²3p~²P3/2 → 3s²5s~²S1/2 transitions in Al, which can be used in future experimental studies.