# Spectroscopic notation problem

## Homework Statement

Consider a $^3D_X$ where $X=3/2$ state.

a) What are the possible values of $S, L, J$ and $J_z$?

## Homework Equations

Spectroscopic notation for this LS coupling is $^YL_J$ where $Y=2S+1$. $J$ ranges from$|L-S|$ to $|L+S|$

## The Attempt at a Solution

Since $L=2$ and $S$ must be equal to $1$, how can $J$ be a fraction? Shouldn't $J$ be either $1, 2, 3$?