Ionization potentials of beryllium-like ions from the relativistic coupled-cluster-based linear response theory

We first test our recently developed relativistic coupled-cluster-based lin ear response theory (RCCLRT) by computing the principal and the shake-up io nization potentials CTP) of highly stripped atoms. Comparison is made betwe en the IP values obtained from the relativistic and non-relativistic CCLRT calculations. The comparisons for light atoms, where the relativistic contr ibutions are negligible, provide a test of the method, while comparisons fo r heavy atoms quantify the relativistic effect. For one-valence problems su ch as ionization processes, there is a formal equivalence between the princ ipal IP values from the CCLRT and multi-reference coupled cluster (MRCC)the ory when using the Ih-Op model space. The principal IPs obtained from the C CLRT are size-extensive, but the(2h-1p) shake-up IPs are not fully size-ext ensive, where the size-inextensivity error scales as the number of valence excitations. The computed valence and shake-up ionization energies via the RCCLRT approach are in excellent agreement with experimental data. The IPs computed using the non-relativistic CCLRT also match favourably well with t he experiment only when the atomic number and ionic charge are small.