Doubly resonant coherent excitation in the x-ray regime: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1</mml:mn><mml:mi>s</mml:mi><mml:mtext>−</mml:mtext><mml:mn>3</mml:mn><mml:mi>d</mml:mi></mml:mrow></mml:math> transition in H-like <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>Ar</mml:mi></mml:mrow><mml:mrow><mml:mn>17</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math>

The $3d$ states in the $n=3$ level of H-like ${\mathrm{Ar}}^{17+}$ ions, to which direct excitation from the $1s$ ground state is optically forbidden, were prepared by the ladder-type ($1{s}_{1/2}\ensuremath{\rightarrow}2{p}_{3/2}\ensuremath{\rightarrow}3d$) double excitation with three-dimensional resonant coherent excitation (3D-RCE). 455 and 390 MeV/u ${\mathrm{Ar}}^{17+}$ ions were excited by a combination of two different crystal fields induced by the arrangement of crystal planes as they passed through a 1.0-$\textmu{}\mathrm{m}$-thick Si crystal. We observed resonance profiles in the charge-state distribution of the ions after passing through the thin crystal and in yields of Lyman $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ x rays. The $2{p}_{3/2}\ensuremath{\rightarrow}3d$ transitions were confirmed by depletion of the Lyman $\ensuremath{\alpha}$ x-ray yield. The observed resonance profile and its dependence on the polarization of the crystal field are in reasonable agreement with theoretical simulations based on the density matrix approach. These results pave the way for the formation of highly excited states of highly charged heavy ions, where the direct transition from the $1s$ ground state is optically forbidden.

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