# Do different eigenstates of total angular momentum have necessarily different energies?

Let $$H$$ be the Hamiltonian of a specific atom (not hydrogen) and $$J$$ the total angular momentum. Since $$H$$ and $$J$$ commute, they have common eigenstate. So we can label the atomic states by their energy and total angular momentum $$\phi_E^J$$.

My question is, suppose we have a state $$\phi_E^J$$ and another state $$\phi_{E'}^{J'}$$, do we have necessarily that $$E\neq E'$$, that is, do states with different total angular momentum have necessarily different energies?