  We consider real eigen-functions of the Schr\"odinger operator in 2-d. The
nodal lines of separable systems form a regular grid, and the number of nodal
crossings equals the number of nodal domains. In contrast, for wave functions
of non integrable systems nodal intersections are rare, and for random waves,
the expected number of intersections in any finite area vanishes. However,
nodal lines display characteristic avoided crossings which we study in the
present work. We define a measure for the avoidance range and compute its
distribution for the random waves ensemble. We show that the avoidance range
distribution of wave functions of chaotic systems follow the expected random
wave distributions, whereas for wave functions of classically integrable but
quantum non-separable wave functions, the distribution is quite different.
Thus, the study of the avoidance distribution provides more support to the
conjecture that nodal structures of chaotic systems are reproduced by the
predictions of the random waves ensemble.
