Analytic response relativistic coupled-cluster theory: the first application to indium isotope shifts
B K Sahoo, A R Vernon, R F Garcia Ruiz, C L Binnersley, J Billowes, M L Bissell, T E Cocolios, G J Farooq-Smith, K T Flanagan, W Gins, R P de Groote, Á Koszorús, G Neyens, K M Lynch, F Parnefjord-Gustafsson, C M Ricketts, K D A Wendt, S G Wilkins, X F Yang
Abstract
Abstract With increasing demand for accurate calculation of isotope shifts of atomic systems for fundamental and nuclear structure research, an analytic energy derivative approach is presented in the relativistic coupled-cluster (CC) theory framework to determine the atomic field shift and mass shift (MS) factors. This approach allows the determination of expectation values of atomic operators, overcoming fundamental problems that are present in existing atomic physics methods, i.e. it satisfies the Hellmann–Feynman theorem, does not involve any non-terminating series, and is free from choice of any perturbative parameter. As a proof of concept, the developed analytic response relativistic CC theory has been applied to determine MS and field shift factors for different atomic states of indium. High-precision isotope-shift measurements of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mn>104</mml:mn> <mml:mo>−</mml:mo> <mml:mn>127</mml:mn> </mml:mrow> </mml:msup> </mml:math> In were performed in the 246.8 nm (5p 2 P 3/2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>→</mml:mo> </mml:math> 9s 2 S 1/2 ) and 246.0 nm (5p 2 P 1/2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>→</mml:mo> </mml:math> 8s 2 S 1/2 ) transitions to test our theoretical results. An excellent agreement between the theoretical and measured values is found, which is known to be challenging in multi-electron atoms. The calculated atomic factors allowed an accurate determination of the nuclear charge radii of the ground and isomeric states of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow/> <mml:mrow> <mml:mn>104</mml:mn> <mml:mo>−</mml:mo> <mml:mn>127</mml:mn> </mml:mrow> </mml:msup> </mml:math> In isotopes, providing an isotone-independent comparison of the absolute charge radii.