Spectroscopic constants - explanation I'm a beginner in spectroscopy and I have troubles understanding papers describing values of spectroscopic constants. This paper, for example, describes constants $T_e, R_e, \omega_e, \omega_ex_e, B_e, \alpha_e, D_0$ and $D_e$.

I can see, that $R_e$ is an internuclear distance, but I have no idea, what are the remaining constants.

Could you provide some brief explanation? Preferably with picture of some potential energy curve(s), if possible, as I find it much easier to understand such concepts from schemes.
You can find plots and further explanations online (as I easily did). This is a homework-type question, yet I do feel that the information request for diatomic molecular spectroscopic constants warrants at least this partial answer. See this writeup for the "Vibronic Absorption Spectrum of Molecular Iodine" for more details and illustrations.

From NIST:

T$_e$ minimum electronic energy (cm$^{-1}$)

R$_e$ internuclear distance (Å)

ω$_e$ vibrational constant – first term (cm$^{-1}$)

ω$_e$x$_e$  vibrational constant – second term (cm$^{-1}$)

B$_e$ rotational constant in equilibrium position (cm$^{-1}$)

α$_e$ rotational constant – first term (cm$^{-1}$)

D$_e$ centrifugal distortion constant (cm$^{-1}$)

β$_e$ rotational constant – first term, centrifugal force (cm$^{-1}$)

From Wikipedia:

D$_0$ dissociation energy (cm$^{-1}$)