  We investigate the influence of a laser field, which is near-resonant to the
atomic sodium 3$^2$P$_{1/2}$ $\to$ 3$^2$D$_{3/2}$ transition, on the last bound
levels of the A$^1\Sigma^+_u$ state in Na$_2$. In a molecular beam experiment
level shifts up to $\approx$ 100 MHz and light induced line broadenings were
observed using an optical double resonance excitation scheme. Moreover, the
coupling laser can reduce the number of bound levels of the A state by one or
more units, which effectively means that in the picture of a collision of a
3$^2$S$_{1/2}$ and a 3$^2$P$_{1/2}$-atom the scattering phase is altered by
more than $\pi$. The observed effects are interpreted as light induced
couplings of the A$^1\Sigma^+_u$ state, which correlates to the
3s$_{1/2}$+3p$_{1/2}$ asymptote, to the $4^1\Sigma^+_g$ and $2^1\Pi_g$ states
at the 3s$_{1/2}$+3d$_{3/2}$ asymptote. We performed multi-channel
calculations, applying the mapped Fourier grid method, which reproduce our
experimentally observed level shifts well.
