Compute the canonical partition function and Boltzmann populations of He's ground and excited states using the RealQM-computed total energies. Each state is a different multiphase configuration (halfspace pair for 1¹S; nested 1s + outer for ortho/para excited states):

P_n(T) = exp(−β·E_n) / Z(T),
Z(T) = Σ_n exp(−β·E_n),    β = 1/(k_B T)

At room T the ground state dominates (gaps are ~20 eV); at plasma temperatures (10⁴–10⁵ K) excited states become populated.

Spectrum (Ha) — RealQM total energies

Term	E (Ha)	Topology
1¹S (ground)	−2.904	halfspace pair (para)
2³S	−2.175	nested 1s + 2s (ortho)
2¹S	−2.146	split 1s/2s (para)
2³P	−2.133	nested 1s + 2p (ortho)
2¹P	−2.124	split 1s/2p (para)
3³S	−2.069	nested 1s + 3s (ortho)
3¹S	−2.061	split 1s/3s (para)
He⁺ (ionized)	−2.000	1 electron

Populations vs T

T (K)	k_B T (eV)	P(1¹S)	P(2³S)	P(2¹S)	P(2³P)	Σ excited