Reconciling mean-squared radius differences in the silver chain through improved measurement and ab initio calculations

Nuclear charge radius differences in the silver isotopic chain have been reported through different combinations of experiment and theory, exhibiting a tension of two combined standard errors. This study investigates this issue by combining high-accuracy calculations for six low-lying states of atomic silver with an improved measurement of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mn>5</a:mn><a:mi>s</a:mi><a:msup><a:mspace width="0.16em"/><a:mn>2</a:mn></a:msup><a:msub><a:mi>S</a:mi><a:mrow><a:mn>1</a:mn><a:mo>/</a:mo><a:mn>2</a:mn></a:mrow></a:msub><a:mo>−</a:mo><a:mn>5</a:mn><a:mi>p</a:mi><a:msup><a:mspace width="0.16em"/><a:mn>2</a:mn></a:msup><a:msub><a:mi>P</a:mi><a:mrow><a:mn>3</a:mn><a:mo>/</a:mo><a:mn>2</a:mn></a:mrow></a:msub></a:mrow></a:math> transition optical isotope shift. Our calculations predict measured electronic transition energies in Ag at the 0.3% level, the highest accuracy achieved in this system so far. We calculate electronic isotope shift factors by employing analytical response relativistic coupled-cluster theory and find that a consistent charge radius difference between <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mmultiscripts><d:mi>Ag</d:mi><d:mprescripts/><d:none/><d:mrow><d:mn>107</d:mn><d:mo>,</d:mo><d:mn>109</d:mn></d:mrow></d:mmultiscripts></d:math> is returned when combining our calculations with the available optical isotope shift measurements. We therefore recommend an improved value for the mean-squared charge radius difference between <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mmultiscripts><e:mi>Ag</e:mi><e:mprescripts/><e:none/><e:mn>107</e:mn></e:mmultiscripts></e:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mmultiscripts><f:mi>Ag</f:mi><f:mprescripts/><f:none/><f:mn>109</f:mn></f:mmultiscripts></f:math> as 0.207(6) <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:msup><g:mrow><g:mi>fm</g:mi></g:mrow><g:mn>2</g:mn></g:msup></g:math>, within one combined error from the value derived from muonic Ag experiments, and an updated set of charge radii differences across the isotopic chain. Published by the American Physical Society 2024