I'm reading about papers about atom-ion interaction. There are some states as showned above. The notations of the states look like molecular orbital since $\Sigma$ and $\Pi$ is usually used in orbital hybridization to denote the different alignments of wavefunctions. But the letters before $\Sigma$ and $\Pi$ and the superscripts are confusing me.
What are the letters (both lower and upper case) and all the superscript (numbers and +)?
This is molecular term symbol notation. Large greek letters are used because this labels the whole electronic state, and not just a one-electron orbital for which small greek letters are used. The roman alphabet letters are just enumerating the states, where $X^1$ is the singlet ground state, followed by $A^1,B^1,C^1$... for the excited states of same multiplicity as they are observed in the experiment. The small roman letters $a^3,b^3,c^3,...$ are used to enumerate excited states of different multiplicity to the ground state, in this case triplets. One should also note that these roman letters are not referring to irreducible representations.
See also Why is there no Sigma-minus ground state for molecular hydrogen ion?
