The Formation of Deuterons by Proton Combination

Phys. Rev. 54, 248 – Published 15 August 1938
H. A. Bethe and C. L. Critchfield


The probability of the astrophysically important reaction H+H=D+ε+ is calculated. For the probability of positron emission, Fermi's theory is used. The penetration of the protons through their mutual potential barrier, and the transition probability to the deuteron state, can be calculated exactly, using the known interaction between two protons. The energy evolution due to the reaction is about 2 ergs per gram per second under the conditions prevailing at the center of the sun (density 80, hydrogen content 35 percent by weight, temperature 2·107 degrees). This is almost but not quite sufficient to explain the observed average energy evolution of the sun (2 ergs/g sec.) because only a small part of the sun has high temperature and density. The reaction rate depends on the temperature approximately as T3.5 for temperatures around 2·107 degrees.


  • Received 23 June 1938
  • Published in the issue dated August 1938

© 1938 The American Physical Society

Authors & Affiliations

H. A. Bethe

  • Cornell University, Ithaca, N. Y.

C. L. Critchfield

  • George Washington University, Washington, D. C.

References (Subscription Required)

Authorization Required




Log In



Article Lookup
Paste a citation or DOI

Enter a citation
  1. Enter a citation to look up or terms to search.

    Ex: "PRL 112 068103", "Phys. Rev. Lett. 112, 068103", "10.1103/PhysRevLett.112.068103"