By I. Prigogine, Stuart A. Rice
Advances in Chemical Physics covers fresh 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 sector of the self-discipline.
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Additional resources for Advances in Chemical Physics, Vol.125 (Wiley 2003)
As a basis function for the finite-size scaling procedure, we used the orthonormalized eigenfunctions of the harmonic oscillator with mass equal to 1 and frequency equal to a: a1=4 1 pﬃﬃﬃ 2 pﬃﬃﬃﬃﬃﬃﬃﬃﬃ eÀax =2 Hn ð axÞ ð102Þ Én ða; xÞ ¼ n p 2 n! where Hn ðxÞ are the Hermite polynomials of order n . In order to obtain the matrix elements of the Hamiltonian equation, Eq. n! > : 0; m þ n even m þ n odd ð104Þ 56 sabre kais and pablo serra 2 The other matrix elements, hm j xk eÀax j ni for any value of k, can be evaluated using the recurrence relations between Hermite polynomials .
The potential in Eq. (101) exhibits predissociation resonances analogous to those found in diatomic molecules [160,161] and was used as a model potential to check the accuracy of different methods for the calculations of resonances [162,163]. We studied the critical behavior of the eigenfunctions and resonances of the Hamiltonian equation, Eq. (101), using the FSS method described in Section IV. As a basis function for the finite-size scaling procedure, we used the orthonormalized eigenfunctions of the harmonic oscillator with mass equal to 1 and frequency equal to a: a1=4 1 pﬃﬃﬃ 2 pﬃﬃﬃﬃﬃﬃﬃﬃﬃ eÀax =2 Hn ð axÞ ð102Þ Én ða; xÞ ¼ n p 2 n!
Three-Electron Atoms Using the finite-size scaling method, study of the analytical behavior of the energy near the critical point shows that the open-shell system, such as the lithium-like atoms, is completely different from that of a closed-shell system, such as the helium-like atoms. The transition in the closed-shell systems from a bound state to a continuum resemble a ‘‘first-order phase transition,’’ while for the open-shell system the transition of the valence electron to the continuum is a ‘‘continuous phase transition’’ .