The experimental anomaly found in the interval between adjacent vibrational levels in the ionic C (1)Sigma(u)(+) state of the F-2 molecule is analyzed. We have calculated the vibrational states of the first (1)Sigma(u)(+) state by numerically solving the one-dimensional Schrodinger equation using the Numerov method. The Rydberg state situated at the shallow local minimum in the first (1)Sigma(u)(+) potential curve possesses a single vibrational level, which is found to be smeared out in the ionic C vibrational states, resulting in this anomaly. (c) 2005 Elsevier B.V. All rights reserved.