Isotopic Shift of Be−like Highly Charged U⁸⁸⁺, Th⁸⁶⁺ Ions

The wavefunctions and eigenvalues of the 1s^22s^2-1s^22s2p ^1P_1 transitions for the highly charged ions ²³⁸U⁸⁸⁺ and ²³²Th⁸⁶⁺ were calculated using relativistic Multi-Configuration Dirac-Hartree-Fock (MCDHF) methods. The influence of nuclear recoil effects, the Breit effect, and quantum electrodynamics (QED) corrections — including self-energy (SE) and vacuum polarization (VP) — on transition energies is comprehensively analyzed. Additionally, mass shift and field shift parameters for isotopes ²³⁶U, ²³⁵U, ²³⁴U, ²³⁶U, ²³⁰Th, ²²⁹Th, ²²⁸Th, ²²⁷Th were also calculated, and the Contribution of each effect on the isotope shifts was thoroughly analyzed. The current results show good agreement with both experimental and theoretical data, with an accuracy within 10⁻² eV in transition energy and within 10⁻² meV in isotopic shifts.