Distortion of the CMB spectrum by the first molecules of the Dark Ages

Open Access

Table 1.

Values of spontaneous rovibrational transitions permitted by quantum selection rules, including frequencies and energies for the lowest rovibrational energy levels of para- and ortho-s H₂, HD, and HeH⁺.

Species	Transitions ^(a)	A_ul	Frequency ν_ul	E_u
	j_u–j_l	[s⁻¹]	[GHz]	[K]
	(v_u, j_u)–(v_l, j_l)
Ortho–H₂	1–	–	–	170
	3–1	4.76 × 10⁻¹⁰	17 594	1015
	5–3	9.83 × 10⁻⁹	31 011	2503
	7–5	5.88 × 10⁻⁸	43 388	4586
Para–H₂	2–0	2.94 × 10⁻¹¹	10 621	510
	4–2	2.75 × 10⁻⁹	24 410	1681
	6–4	2.64 × 10⁻⁸	37 357	3475
	8–6	1.14 × 10⁻⁷	49 077	5830
HD	(0,1)–(0,0)	5.41 × 10⁻⁸	2675	128
	(0,2)–(0,1)	5.13 × 10⁻⁷	5332	384
	(0,3)–(0,2)	1.80 × 10⁻⁶	7952	766
	(0,4)–(0,3)	4.31 × 10⁻⁶	10 518	1271
	(0,5)–(0,4)	8.35 × 10⁻⁶	13 015	1895
	(0,6)–(0,5)	1.40 × 10⁻⁵	15 429	2636
	(0,7)–(0,6)	2.14 × 10⁻⁵	17 746	3487
	(0,8)–(0,7)	3.03 × 10⁻⁵	19 955	4445
	(1,0)–(0,1)	3.09 × 10⁻⁵	106 213	5226
	(1,1)–(0,2)	1.55 × 10⁻⁵	103 441	5349
	(1,1)–(0,0)	1.67 × 10⁻⁵	111 447	5349
	(0,9)–(0,8)	4.07 × 10⁻⁵	22 055	5503
	(1,2)–(0,1)	2.46 × 10⁻⁵	113 874	5594
	(1,2)–(0,3)	1.01 × 10⁻⁵	100 590	5594
	(1,3)–(0,2)	3.16 × 10⁻⁵	116 150	5959
	(1,3)–(0,4)	6.73 × 10⁻⁶	97 679	5959
	(1,4)–(0,3)	3.86 × 10⁻⁵	118 259	6442
	(1,4)–(0,5)	4.34 × 10⁻⁶	94 724	6442
	(0,10)–(0,9)	5.23 × 10⁻⁵	24 038	6657
HeH⁺	1–0	0.109	2010	96
	2–1	1.04	4009	289
	3–2	3.75	5984	576
	4–3	9.14	7925	956
	5–4	18.1	9821	1428

Notes.

^(a)

Here and in the text u means upper level, l means lower level.

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