Atomic systems, finite-size scaling

FINITE-SIZE SCALING FOR ATOMIC AND MOLECULAR SYSTEMS... 

The above simple large-D picture helps to establish a connection to phase transitions. However, the questions which remain to be addressed are How to carry out such an analogy to the IV-electron atoms at D = 3 and what are the physical consequences of this analogy These questions will be examined in the following sections by developing the finite size scaling method for atomic and molecular systems. 

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]. 

Now, let us use the data collapse method to test the hypothesis of finite-size scaling used to obtain the critical parameter for this system and estimate the critical exponent v for the lithium-like atoms. Using data collapse to the ionization energy of the three-electron atom in its ground state, /3(A) = Eq1(A)—... 

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