Parts-per-million-accurate determination of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>K</mml:mi> <mml:mi>α</mml:mi> </mml:mrow> </mml:math> photoionization resonance of Be-like oxygen with resolution of its <mml

We determine with high accuracy the energy of the inner-shell transition <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>1</a:mn> <a:msup> <a:mi>s</a:mi> <a:mn>2</a:mn> </a:msup> <a:mn>2</a:mn> <a:msup> <a:mi>s</a:mi> <a:mn>2</a:mn> </a:msup> <a:mspace width="0.16em"/> <a:mmultiscripts> <a:mi>S</a:mi> <a:mn>0</a:mn> <a:none/> <a:mprescripts/> <a:none/> <a:mn>1</a:mn> </a:mmultiscripts> <a:mo>→</a:mo> <a:mn>1</a:mn> <a:mi>s</a:mi> <a:mn>2</a:mn> <a:msup> <a:mi>s</a:mi> <a:mn>2</a:mn> </a:msup> <a:mn>2</a:mn> <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:mspace width="0.16em"/> <a:mmultiscripts> <a:mi>P</a:mi> <a:mn>1</a:mn> <a:none/> <a:mprescripts/> <a:none/> <a:mn>1</a:mn> </a:mmultiscripts> <a:mmultiscripts> <a:mi mathvariant="normal">O</a:mi> <a:mrow> <a:mi>K</a:mi> <a:mi>α</a:mi> </a:mrow> <a:mrow> <a:mn>4</a:mn> <a:mo>+</a:mo> </a:mrow> <a:mprescripts/> <a:none/> <a:mn>16</a:mn> </a:mmultiscripts> </a:mrow> </a:math> at 554.372(3) eV ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>λ</e:mi> <e:mo>=</e:mo> <e:mspace width="0.16em"/> <e:mn>22.36480</e:mn> <e:mo>(</e:mo> <e:mn>12</e:mn> <e:mo>)</e:mo> <e:mspace width="0.16em"/> <e:mi>Å</e:mi> </e:mrow> </e:math> ) as well as its small shift of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mn>2.2</h:mn> <h:mo>±</h:mo> <h:mrow> <h:mn>1.3</h:mn> </h:mrow> </h:mrow> </h:math> meV ( <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mi mathvariant="normal">Δ</i:mi> <i:mi>λ</i:mi> <i:mo>=</i:mo> <i:mspace width="0.16em"/> <i:mn>0.089</i:mn> <i:mo>(</i:mo> <i:mn>52</i:mn> <i:mo>)</i:mo> <i:mspace width="0.28em"/> <i:mi mathvariant="normal">m</i:mi> <i:mi>Å</i:mi> </i:mrow> </i:math> ) for the <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mmultiscripts> <n:mi mathvariant="normal">O</n:mi> <n:mprescripts/> <n:none/> <n:mn>18</n:mn> </n:mmultiscripts> </n:math> isotope. This transition blends with a <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:mrow> <p:mi>K</p:mi> <p:mi>α</p:mi> </p:mrow> </p:math> line of <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:msup> <q:mrow> <q:mi mathvariant="normal">O</q:mi> </q:mrow> <q:mrow> <q:mn>5</q:mn> <q:mo>+</q:mo> </q:mrow> </q:msup> </q:math> used in astrophysical diagnostics, potentially affecting its reliability. In contrast to our experimental uncertainty of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"> <s:mrow> <s:mo>±</s:mo> <s:mn>3</s:mn> </s:mrow> </s:math> meV, advanced electronic structure predictions for this four-electron system, including quantum electrodynamic (QED) corrections on the order of 100 meV, still scatter by more than <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"> <t:mo>±</t:mo> <t:mn>250</t:mn> </t:math> meV. Ions generated and stored in an electron beam ion trap were excited at the ELETTRA synchrotron facility with monochromatic soft x rays, with photon energies corrected by an additional spectrometer. Upon resonant excitation of <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"> <u:msup> <u:mrow> <u:mi mathvariant="normal">O</u:mi> </u:mrow> <u:mrow> <u:mn>4</u:mn> <u:mo>+</u:mo> </u:mrow> </u:msup> </u:math> and their subsequent autoionization, we separate the photoions of each isotope by a time-of-flight measurement. This way, we resolve soft x-ray isotopic shifts of a few meV, obtain very accurate data on essential astrophysical ions, and test calculations down to the level of QED contributions.