Test of Invariance of the Ionization-Energy Threshold Value with Ejection Energy

Abstract

High-energy inner-shell ionization processes generate a spectrum of lower-energy shake-up lines and shake-off band satellites of a main electron energy peak, corresponding to excitations and multiple ionizations of the daughter ion. Such satellite final states give reduced screening for the ejected inner electron, and consequently the observed rise in binding energy. Experimentally we here verify the conventional view that the effective binding energy corresponding to the main peak is independent of transition energy in such fast ionizations; four transitions in $_{95}^{241}\mathrm{Am}$, one only 7 keV above the $K$ binding energy of 125 keV, gave (${L}_{1}\ensuremath{-}K$) internal-conversion electron energy differences of \ensuremath{\sim}101 keV, constant within 5 eV, over an electron energy range from 7 keV ($\frac{v}{c}=0.14$, nearly adiabatic) to 450 keV ($\frac{v}{c}=0.85$). This implied invariance of the $K$ mainline binding energy within 5 eV is contrasted to a calculated rearrangement energy value of 88 eV from a Dirac-Hartree-Fock (DHF) "frozen-orbital" eigenvalue minus the full atom-ion DHF "adiabatic" energy difference. Further, the main peak binding energy should be the threshold, adiabatic value; comparison of our (${L}_{2}\ensuremath{-}K$) electron energy difference, 102.031\ifmmode\pm\else\textpm\fi{}0.005 keV, with the $K{\ensuremath{\alpha}}_{2}$ x-ray energy, 102.033\ifmmode\pm\else\textpm\fi{}0.010 keV, verifies this to 12 eV. The displacement of the centroid of the satellite spectrum from the main peak, i.e., the mean increase in binding energy averaged over this spectrum as the transition energy increases infinitely above threshold, should equal the rearrangement energy of the ion. Based on $\ensuremath{\beta}$-decay shake-off intensity predictions for all shells of Carlson, Nestor, Tucker, and Malik, and on our experimental results for $K$ and $L$ shells at lower $Z$, we calculate a centroid shift of 89\ifmmode\pm\else\textpm\fi{}10 eV for Am.