Fractional phase transition in medium size metal clusters and some remarks on magic numbers in gravitationally and weakly interacting clusters

Details Fractional phase transition in medium size metal clusters and some remarks on magic numbers in gravitationally and weakly interacting clusters Fractional phase transition in medium size metal clusters and some remarks on magic numbers in gravitationally and weakly interacting clusters

2009-07-11

arxiv.org/abs/0907.1953v1

Physica A389:3307-3315,2010

Physics

General Physics

20 pages, 5 figures

Scientific paper

10.1016/j.physa.2010.03.033

Based on the Riemann- and Caputo definition of the fractional derivative we use the fractional extensions of the standard rotation group SO(3) to construct a higher dimensional representation of a fractional rotation group with mixed derivative types. An analytic extended symmetric rotor model is derived, which correctly predicts the sequence of magic numbers in metal clusters. It is demonstrated, that experimental data may be described assuming a sudden change in the fractional derivative parameter $\alpha$ which is interpreted as a second order phase transition in the region of cluster size with $200 \leq N \leq 300$. Furthermore it is demonstrated, that the four different realizations of higher dimensional fractional rotation groups may successfully be connected to the four fundamental interaction types realized in nature and may be therefore used for a prediction of magic numbers and binding energies of clusters with gravitational force and weak force respectively bound constituents. The results presented lead to the conclusion, that mixed fractional derivative operators might play a key role for a successful unified theoretical description of all four fundamental forces realized in nature.

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