Advances in Chemical Physics, Vol.125 (Wiley 2003) by I. Prigogine, Stuart A. Rice

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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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 [55]. 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 [55].

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’’ [9].

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