Probabality of jumping of e in K-e capture.

[astro2cosmos]

as we know in L orbit there are two shell 2s & 2p. suppuse for an atom both shells are occupied , then what is the probabality of jumping of any electron from 2s & 2p shell to lower 1s in the process of K-electron capture process?

 

[Bob S]

Let's examine Ar=37 that decays only by electron capture.

The electron configuration in Ar-37 prior to decay is 1s(2) 2s(2) 2p(6) 3s(2) 3p(6) for a total of 18 electrons (where the number in parenthesis the number of electrons in each state). When a 1s electron is captured by the nucleus, electrons in both the 2p and the 3p states compete for the vacancy in the 1s state.

I don't have the exact answer, but for the single-electron hydrogen atom, the 2p-1s and 3p-1s transition rates are 6.25 x 10⁸ and 1.64 x 10⁸ sec^-1 respectively*. implying that the 2p-1s transition is much more likely than the 3p-1s transition. Measuring the K x-ray fine structure maybe can determine the ratio.

From page 266 in Bethe and Salpeter Quantum Mechanics of One and Two Electron Atoms.

Bob S

 

[astro2cosmos]

When a 1s electron is captured by the nucleus, electrons in both the 2p and the 3p states compete for the vacancy in the 1s state.

Bob S

ok. so does 2s or 3s also try to fill up the vacany?
during the transition from 2p & 3p screening effect is also apply?
from which i.e 2s or 2p it is readily jump to 1s?

 

[Bob S]

ok. so does 2s or 3s also try to fill up the vacany?
during the transition from 2p & 3p screening effect is also apply?
from which i.e 2s or 2p it is readily jump to 1s?

The 2s-1s and 3s-1s transitions are forbidden. Both the 2p-1s and 3p-1s transitions are partially screened by other electrons.

Bob S