Benchmarking Many-body Approaches for the Determination of Isotope Shift Constants: Application to the Li, Be$^+$ and Ar$^{15+}$ Isoelectronic Systems

TL;DR

This paper benchmarks relativistic coupled-cluster methods for calculating isotope shift constants in light and heavy isoelectronic systems, highlighting the importance of the analytical response approach for accuracy.

Contribution

It compares different RCC-based procedures for isotope shift calculations and identifies the analytical response method as the most reliable for heavier systems.

Findings

AR approach yields more accurate IS constants

Valence triple excitations significantly affect results

Breit and QED effects are important for heavy systems

Abstract

We have applied relativistic coupled-cluster (RCC) theory to determine the isotope shift (IS) constants of the first eight low-lying states of the Li, Be$^+$ and Ar$^{15+}$ isoelectronic systems. Though the RCC theory with singles, doubles and triples approximation (RCCSDT method) is an exact method for these systems for a given set of basis functions, we notice large differences in the results from this method when various procedures in the RCC theory framework are adopted to estimate the IS constants. This has been demonstrated by presenting the IS constants of the aforementioned states from the finite-field, expectation value and analytical response (AR) approaches of the RCCSDT method. Contributions from valence triple excitations, Breit interaction and lower-order QED effects to the evaluation of these IS constants are also highlighted. Our results are compared with high-precision calculations reported using few-body methods wherever possible. We find that results from the AR procedure are more reliable than the other two approaches. This analysis is crucial for understanding the roles of electron correlation effects in the accurate determination of IS constants in the heavier atomic systems, where few-body methods cannot be applied.