Undergrad Electron capture and electron transitions.

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When a nucleus captures an electron from the innermost orbit, its proton number decreases by one, leading to a reconfiguration of the atom's energy levels. This process creates a "hole" in a low energy level, allowing electrons from higher levels to transition down, which results in the emission of electromagnetic (EM) radiation, typically in the form of X-rays. Although the change in energy levels due to the atomic number alteration is minor, the cascading effect of electron transitions is significant. Each transition emits EM waves until the atom reaches its ground state. Thus, electron capture indeed results in the emission of EM waves during these transitions.
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When a nucleus captures an electron from the innermost orbit, its proton number reduces one. Therefore, energy levels in the atom have to change accordingly, meaning all the electrons have to move lower energy levels. From this point of view, during an electron capture, can it be said that the electrons give off EM waves due to the transition between energy levels?

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oksuz_ said:
can it be said that the electrons give off EM waves due to the transition between energy levels?

Yes. The effect of changing the energies of the levels because of the change in atomic number is actually pretty small; the bigger effect is that there is now a "hole" in a low energy level, and an electron from a higher level can occupy the hole, emitting EM radiation as it does so (usually the emitted radiation is X rays). That leaves another hole that a still higher electron can occupy, etc., until the new atom is in its ground state.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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