# Spin and parity transition levels gamma radiation

Just a quick question regarding spin and parity. I am studying nuclear physics and I am just a tad confused with a concept about gamma radiation.

Say I have ${^{20}_{10}Ne}$

And the lowest electric multipole of gamma transition between some excited states, such as from 5.00Mev to 4Mev levels is E3.

What is the possible value(s) for the spin and parity of the 4 MeV level, if the 5Mev is $2^-$?

I know since it is an E3 transition then there is is a parity change, since $E_{l_\gamma}=(-1)^{l_\gamma}$

But for the spins, is there not a lot of possible number of values?

Since $l_\gamma = |J_i-J_f|,|J_i-J_f|+1,...,(J_i-J_f)-1,(J_i-J_f)$ and $J_i = 2$ and $l_\gamma = 3$

I think this solves out to be:

It could be $J_f = 1^+,2^+,3^+,4^+,5^+$ ???

This is just an example - but think I could extrapolate from it.