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The PHENIX Collaboration has measured the ratio of the yields of $\psi(2S)$to $\psi(1S)$ mesons produced in $p$$+$$p$, $p$$+$Al, $p$$+$Au, and$^{3}$He$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV over the forward andbackward rapidity intervals $1.2<|y|<2.2$. We find that the ratio in $p$$+$$p$collisions is consistent with measurements at other collision energies. Incollisions with nuclei, we find that in the forward ($p$-going or$^{3}$He-going) direction, the relative yield of $\psi(2S)$ mesons to$\psi(1S)$ mesons is consistent with the value measured in \pp collisions.However, in the backward (nucleus-going) direction, the $\psi(2S)$ ispreferentially suppressed by a factor of $\sim$2. This suppression isattributed in some models to breakup of the weakly-bound $\psi(2S)$ throughfinal state interactions with comoving particles, which have a higher densityin the nucleus-going direction. These breakup effects may compete with colorscreening in a deconfined quark-gluon plasma to produce sequential suppressionof excited quarkonia states.

physical review. c

Measurement of the relative yields of $\psi(2S)$ to $\psi(1S)$ mesons  produced at forward and backward rapidity in $p$$+$$p$, $p$$+$Al, $p$$+$Au,  and $^{3}$He$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV