= Solution
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In <LS coupling>, first add the individual <orbital angular momentum>[orbital angular momenta] and <spins> separately, then add their totals:
$$
\mathbf L=\sum_i\mathbf l_i,\qquad \mathbf S=\sum_i\mathbf s_i,\qquad \mathbf J=\mathbf L+\mathbf S.
$$
The <Coulomb interaction> between <electrons> must separate different <atomic terms> more strongly than the <spin-orbit interaction> mixes them. Then $L,S,J,M_J$ are useful <quantum numbers>, with $J=|L-S|,\ldots,L+S$. This approximation is usually better for lighter <chemical atoms> and well-separated <atomic terms>; strong <configuration interaction> or strong <spin-orbit coupling> can spoil it. The <term symbol> is $^{2S+1}L_J$.
The general <electric-dipole selection rules>, for isolated <chemical atoms> with definite <parity> and total electronic <angular momentum>, are a change of <parity>, $\Delta J=0,\pm1$ excluding $J=0\leftrightarrow0$, and $\Delta M_J=0,\pm1$, with the accessible <magnetic sublevels> determined by the light's <polarization>. In pure <LS coupling>, the additional <selection rules> are $\Delta S=0$ and $\Delta L=0,\pm1$, excluding $L=0\leftrightarrow0$. In a one-<electron> description the <electric dipole operator> also requires $\Delta l=\pm1$ for the active <electron>. These latter statements can fail as exact labels when <atomic terms> mix; the general <parity> and total-<angular momentum> restrictions still apply. Unresolved <hyperfine structure> is neglected here.
For <strontium>, the closed core contributes $L=S=0$. The <Pauli exclusion principle> makes the two equivalent $5s$ <electrons> a <singlet state>. Different radial <orbitals> permit both a <singlet state> and a <triplet state>. Thus the complete lists of <atomic fine-structure levels> are
$$
\boxed{\begin{array}{c|c|c}
\text{configuration}&\text{terms}&\text{levels}\\\hline
5s^2&{}^1S&{}^1S_0\\
5s5p&{}^1P,{}^3P&{}^1P_1,{}^3P_0,{}^3P_1,{}^3P_2\\
5s6s&{}^1S,{}^3S&{}^1S_0,{}^3S_1
\end{array}}
$$
The $5s5p$ <electron configuration> has odd <parity>; the other two <electron configurations> have even <parity>.
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