  We study the production of a $\psi(2S)$ meson in heavy ion collisions. We
evaluate Wigner functions for the $\psi(2S)$ meson using both Gaussian and
Coulomb wave functions, and investigate the wave function dependence in the
$\psi(2S)$ meson production by recombination of charm and anti-charm quarks.
The enhanced transverse momentum distribution of $\psi(2S)$ mesons compared to
that of $J/\psi$ mesons, originated from wave function distributions of the
$\psi(2S)$ and $J/\psi$ meson in momentum space, provides a plausible
explanation for the recent measurement of the nuclear modification factor ratio
between the $\psi(2S)$ and $J/\psi$ meson.
