Competition between one- and two-photon processes in Ar irradiated by the Shanghai soft x-ray free electron laser

Shanghai Soft X-ray Free Electron Laser facility has entered user operation, delivering soft x-ray pulses in self-amplified spontaneous emission mode with an intensity of the peak fluence of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>∼</a:mo><a:mn>1.0</a:mn><a:mo>×</a:mo><a:msup><a:mn>10</a:mn><a:mrow><a:mo>−</a:mo><a:mn>2</a:mn></a:mrow></a:msup><a:mspace width="0.16em"/><a:mi>µ</a:mi><a:mi mathvariant="normal">J</a:mi><a:mo>/</a:mo><a:mi>µ</a:mi><a:msup><a:mrow><a:mi mathvariant="normal">m</a:mi></a:mrow><a:mn>2</a:mn></a:msup></a:mrow></a:math> at a focus point. With these conditions, at a photon energy of 260 eV, we expect sequential processes in which <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msup><e:mrow><e:mi>Ar</e:mi></e:mrow><e:mrow><e:mn>2</e:mn><e:mo>+</e:mo></e:mrow></e:msup></e:math> created by the Auger decay following the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mn>2</f:mn><f:mrow><f:mi>p</f:mi></f:mrow></f:math> photoionization may be resonantly excited to the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mn>2</g:mn><g:msup><g:mi>p</g:mi><g:mrow><g:mo>−</g:mo><g:mn>1</g:mn></g:mrow></g:msup><g:mn>3</g:mn><g:msup><g:mi>p</g:mi><g:mrow><g:mo>−</g:mo><g:mn>2</g:mn></g:mrow></g:msup><g:mn>3</g:mn><g:mi>d</g:mi></g:mrow></g:math> inner-shell excited state and thus resonant Auger decay produces <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msup><h:mrow><h:mi>Ar</h:mi></h:mrow><h:mrow><h:mn>3</h:mn><h:mo>+</h:mo></h:mrow></h:msup></h:math>, which can also be competitively produced by the direct double Auger decay (DDAD) following the one-photon <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mn>2</i:mn><i:mrow><i:mi>p</i:mi></i:mrow></i:math> ionization of Ar. <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:msup><j:mrow><j:mi>Ar</j:mi></j:mrow><j:mrow><j:mn>4</j:mn><j:mo>+</j:mo></j:mrow></j:msup></j:math> ions dominantly arise from <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:msup><k:mrow><k:mi>Ar</k:mi></k:mrow><k:mrow><k:mn>2</k:mn><k:mo>+</k:mo></k:mrow></k:msup></k:math> with a resonant excitation and subsequent DDAD, involving two-photon absorption. The measured charge distributions as a function of the free-electron laser (FEL) fluence are well reproduced by calculations that include DDAD, normally neglected in the previous FEL studies, and resonant Auger decay. The present results demonstrate that the low peak fluence of the FEL pulses can be determined if the competition between the one- and two-photon processes is precisely described along with DDAD and resonant Auger decay.