Monotonicity of ionization energies for three electron lithium-type systems

Although it is quite obvious that an increasing amount of energy is required to remove more and more electrons from an atom, the proof of this observation seems to be a remarkably difficult problem in mathematical physics. Here, by using well-known energy bounds, we show the monotonicity of ionization energies for the simplest nontrivial system, i.e., a nucleus (with infinite mass) and three electrons, which physically corresponds to ionization in the lithium isoelectronic series via the para-channel.PHYMAT, Dept. de math. Univ. de Toulon et du Var F-83130 La Garde, France.On leave from Stranski Institut, TEL 33 Tech. Univ. Berlin D-1000 Berlin 10, F.R.G.Laboratoire propre du Centre Nationale de la Recherche Scientifique.