| Summary: | The generally accepted pathway to Local Thermodynamic Equilibrium (LTE) in atomic physics, where collision rates need to be much larger than radiative decay rates, is extended to complex autoionizing states. It is demonstrated that the inclusion of the non-radiative decay (autoionization rate) on the same footing, like radiative decay, i.e., the LTE criterion <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>n</mi><mrow><mi>e</mi><mo>,</mo><mi>c</mi><mi>r</mi><mi>i</mi><mi>t</mi></mrow></msub><mo>×</mo><mi>C</mi><mo>≫</mo><mi>A</mi><mo>+</mo><mo>Γ</mo></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>n</mi><mrow><mi>e</mi><mo>,</mo><mi>c</mi><mi>r</mi><mi>i</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> is the critical electron density above which LTE holds, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>C</mi></semantics></math></inline-formula> is the collisional rate coefficient, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>A</mi></semantics></math></inline-formula> is the radiative decay rate) is inappropriate for estimating the related critical density. An analysis invoking simultaneously different atomic ionization stages identifies the LTE criteria as a theoretical limiting case, which provides orders of magnitude too high critical densities for almost all practical applications. We introduced a new criterion, where the critical densities are estimated from the non-autoionizing capture states rather than from the autoionizing states. The new criterion is more appropriate for complex autoionizing manifolds and provides order of magnitude reduced critical densities. Detailed numerical calculations are carried out for Na-like states of aluminum, where autoionization to the Ne-like ground and excited state occurrences are in excellent agreement with the new criterion. In addition, a complex multi-electron atomic-level structure and electron–electron correlation are identified as simplifying features rather than aggravating ones for the concept of thermalization.
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