Exchange and core-polarization effects on Rydberg-transition electric-dipole matrix elements in Rb and Cs

Abstract

Microwave electric-field measurements with Rydberg atoms require accurate Rydberg-transition electric-dipole matrix elements. We calculate these matrix elements for Rb and Cs using a Dirac-Fock plus core-polarization method, which core-valence exchange is treated explicitly and core-valence correlation is represented by a cutoff core-polarization potential. A smooth cutoff-radius model fitted to quantum-defect energies reproduces the target energies with MHz-level residuals for states up to $n=90$. Comparisons with model-potential matrix elements and internal length-velocity consistency show that the $s$-$p$ transitions are generally the most robust, whereas the $p$-$d$ and $d$-$f$ transitions show stronger atom- and branch-dependent sensitivity to short-range modeling. The largest relative differences arise from radial-integral cancellation, where short-range phase changes are amplified by the small final matrix element. These results provide a practical reliability assessment for Rydberg-transition electric-dipole matrix elements used in field-sensing applications.