Fractional phase transition in medium size metal clusters

Based on the Riemann and Caputo definition of the fractional derivative we use the fractional extensions of the standard rotation group SO(3)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 by assuming a sudden change in the fractional derivative parameter αα which is interpreted as a second order phase transition in the region of cluster size with 200≤N≤300200≤N≤300.