By I. Prigogine, Stuart A. Rice
Advances in Chemical Physics covers contemporary advances on the leading edge of study relative to chemical physics. The sequence, Advances in Chemical Physics, presents a discussion board for severe, authoritative reviews of advances in each region of the self-discipline.
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Additional resources for Advances in Chemical Physics, Vol.125 (Wiley 2003)
From the variational calculations, the behavior of the energy for the triplet 2p2 3 P state as a function of l is very similar to the one found for the ground state. The curves start to bend over sharply to a constant values as N gets larger. finite-size scaling for atomic and molecular systems 39 The true excited-state energy, in the limit N ! 1, bends over sharply at lPc to become degenerate with the lowest continuum at ETP ¼ À 18 . Now, the PR equation, Eq. (55), can be applied for the excited state0 2p2 3 P ðN;N Þ to obtain a sequence of pseudocritical l as a function on N, flP g.
The corresponding eigenfunctions are nonnormalizable. 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 .
One of the most powerful tools to study resonances is complex scaling techniques (see Ref. 157 and references therein). In complex scaling the coordinate ~ x of the Hamiltonian was rotated into the complex plane; that is, Hð~ xÞ ! Hð~ x eif=2 Þ. For resonances that have yres ¼ tanÀ1 ½ImðEðresÞ Þ=Re ðresÞ ðE Þ < f the wave functions of both the bound and resonance states are represented by square-integrable functions and can be expanded in standard L2 basis functions. As an example, the Hamiltonian equation, Eq.
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