By I. Prigogine, Stuart A. Rice

ISBN-10: 0471214523

ISBN-13: 9780471214526

ISBN-10: 0471461520

ISBN-13: 9780471461524

Advances in Chemical Physics covers contemporary advances on the innovative of study relative to chemical physics. The sequence, Advances in Chemical Physics, presents a discussion board for serious, authoritative reviews of advances in each zone of the self-discipline.

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**Additional info for Advances in Chemical Physics, Vol.125 (Wiley 2003)**

**Example text**

The ABA system is stable if its energy is lower than the energy of the dissociation to AB þ A. The critical behavior and stability of the ground-state energy as a function of l for k ¼ 0 has been previously studied for the two-electron atoms [87] (with Q ¼ À1, M ¼ 1, m ¼ 1 and l ¼ 1=q ¼ 1=Z, where Z is the nuclear charge) and for the hydrogen molecule-like ions [11] (with q ¼ À1, m ¼ 1, M ¼ 1 and l ¼ j Q j ¼ ZÞ. In order to obtain the stability diagram for the three-body Coulomb systems in the ðl À kÞ-plane, one has to calculate the transition line, lc ðkÞ, which separates the stable phase from the unstable one.

60) and (71) have the scaling form as presented in Ref. [93]. For our purposes, it is convenient to write this in a slightly different form. From Eqs. (60) and (71) we have hOiðNÞ ðlc Þ $ N ÀmO =n for large values of N. 10 1/N Figure 5. aðNÞ as a function of 1=N for the ground state of the Yukawa potential. The extrapolated values are shown by dots. Because the same argument of regularity holds for the derivatives of the truncated expectation values, we have that qm hOiðNÞ qlm $ N ÀðmO ÀmÞ=n ð73Þ l¼lc hOiðNÞ is analytical in l; then using Eq.

C. Extrapolation and Basis Set Expansions To illustrate the applications of the FSS method in quantum mechanics, let us give an example of a short-range interaction, the Yukawa potential. This potential is spherically symmetric, and therefore the critical behavior can be studied for zero and nonzero angular momentum. In atomic units the Hamiltonian of the screened Coulomb potential can be written as 1 eÀr HðlÞ ¼ À r2 À l r 2 ð69Þ It is well known that the perturbation expansion in s ¼ 1=l around the Coulombic limit, s ¼ 0, is asymptotic with zero radius of convergence [91].

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

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