By I. Prigogine, Stuart A. Rice
Advances in Chemical Physics covers fresh advances on the innovative of study relative to chemical physics. The sequence, Advances in Chemical Physics, offers a discussion board for severe, authoritative reviews of advances in each region of the self-discipline.
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Extra info for Advances in Chemical Physics, Vol.125 (Wiley 2003)
The classical book by Newton  presents an excellent discussion on this subject. The nature of the resonance states, narrow or broad, crucially depends on the behavior of the corresponding bound eigenvalue in the neighborhood of the threshold. There is no rigorous definition of narrow and broad resonances, but the former has a long lifetime and is accessible for observation. For a broad resonance, the practical definition of its energy and width becomes a difficult problem . , Àn ( En ) will develop for l < lc.
Already Kato  and Hunziker  show that an atom or ion has infinitely many discrete Rydberg states if Z > N À 1, and the results of Zhislin  show that a negative ion has only finitely many discrete states if Z N À 1. Because experiment has yet to find a stable doubly negative atomic ion, Morgan and co-workers  concluded that the critical charge obeys the finite-size scaling for atomic and molecular systems 45 following inequality: N À 2 Zc N À 1. The numerical results  confirmed this inequality and show that, at most, only one electron can be added to a free atom in the gas phase.
The ratio between the ground-state energy and the second lowest eigenvalue of the two-electron atom raised to a power N as a function of l for N ¼ 6; 7; . . ; 13. As expected, the second derivative will develop a delta-function-like behavior as N is getting larger, as shown in Fig. 8c. The behavior of the ground-state energy and its first and second derivatives resembles the behavior of the free energy at a first-order phase transition. For the two-electron atoms, when l < lc the nuclear charge is large enough to bind two electrons; this situation remains until the system reaches a critical point lc , which is the maximum value of l for which the Hamiltonian has a bound state or the minimum charge necessary to bind two electrons.
Advances in Chemical Physics, Vol.125 (Wiley 2003) by I. Prigogine, Stuart A. Rice