Spin exchange rates in proton–hydrogen collisions

The spin temperature of neutral hydrogen, which determines the optical depth and brightness of the 21-cm line, is determined by the competition between radiative and collisional processes. Here, we examine the role of proton–hydrogen collisions in setting the spin temperature. We use recent fully quantum-mechanical calculations of the relevant cross-sections, which allow us to present accurate results over the entire physically relevant temperature range 1–10
⁴
  K. For kinetic temperatures T
K
≳ 100 K, the proton–hydrogen rate coefficient exceeds that for hydrogen–hydrogen collisions by about a factor of 2. However, at low temperatures (T
K
≲ 5 K) H–H
⁺
collisions become several thousand times more efficient than H–H and even more important than H–e
⁻
collisions.