666 



TABLE 723.— RATES OF NUCLEAR REACTIONS IN STARS AND OF ENERGY 

 PRODUCTION AT VARIOUS TEMPERATURES* 225 



Reaction Temperature: 



iOX10« 15X10° 17.5X10 6 20X10° 25X10° 30X10° 



Hi-|-H 1 ->-H ! H-e+ 6xl0 10 yr 1.2xl0 lo yr 6xl0 9 yr 4Xl0 9 yr 2XlO e yr lX10 9 yr 



H 2 4-H 1 ->-He 3 +7 15 sec 2 sec 1 sec .5 sec .2 sec .1 sec 



He 3 +He J ->-Be 7 +7 2xl0 12 yr 1.5X10 9 yr 1.2Xl0 8 yr 1.5Xl0 7 yr 5Xl0 5 yr 5X10* yr 



Be 7 ->-Li 7 -<?- 70 days 70 days 70 days 70 days 70 days 70 days 



Li 7 +FP->-He 4 +He 4 10 hr 50 min 50 sec 15 sec 2 sec .4 sec 



Mean life of hydrogen 6X10 10 yr 3Xl0 9 yr 1.5x10 s yr lXl0 9 yr 5Xl0 8 yr 3Xl0 8 yr 

 Energy production in 



ergs/ (g sec) .75 40 80 120 250 400 



Part 2. — Carbon cycle, temperatures in °K 



Relative abundances of N u : C t2 : C 13 : N 15 at a temperature of 17.5x10° °K are in the approximate ratios of 

 5,000: 200: 50: 1. 



Note that the energy-production for the carbon cycle increases much more rapidly with tem- 

 perature than for the proton-proton cycle. At very "low" temperatures (<10 7O K) the proton- 

 proton reactions are the only ones of importance. The net result at these temperatures is the for- 

 mation of He' 1 and a positron out of three H 1 nuclei, since the reaction between He 8 and He* is 

 then too slow to be important. In Table 724 the reaction times of a few other nuclear reactions 

 are given merely to show the rapid increase of the reaction time with increasing charge of the 

 interacting nuclei especially at lower temperatures. None of the reactions listed in Table 724 are 

 of importance as sources of stellar energy. 



* Tables 723 and 724 prepared by E. E. Salpeter. 



22r ' Bethe, Phys. Rev., vol. 55, p. 434, 1939; Astrophys. Journ., vol. 92, p. 118, 1940. Gamow and Critch- 



field, Theory of atomc nucleus and nuclear energy sources, Oxford Univ. Press, 1940. Fowler, W. A., and 



Hall, R. N., Phys. Rev., vol. 77, p. 197, 1950, and private communication. Christy, R. F., and O'Reilly, J., 



unpublished work. 



TABLE 724.— TIMES REQUIRED FOR SOME OTHER REACTIONS 



Reaction Temperature: 15X10° °K 20X10° °K 30X10° °K 



F^+H^CT+He 4 5X10 9 yr 1X10 7 yr 5X10 8 yr 



N ,5 +H'_»O ,0 +7 1X10 8 yr 5X10 9 yr 5X10 8 yr 



O 10 +H l _»F 17 +7 5XlO ,8 y.- 2Xl0 11 yr 1X10 8 yr 



Ne^H^Na^+v 5Xl0 ls yr 5Xl0 12 yr 5X10 8 yr 



Li 7 +He 4 _>B n -f-7 2XlO l7 yr 2XlO u yr 2Xl0 lo yr 



Be 7 +He 4 -»C u +7 5Xl0 23 yr lXlO^yr 2X10 18 yr 



All mean reaction times are proportional to the density p of the stellar material and to 

 Cn, the percentage by weight of hydrogen (except the reactions in which one of the collid- 

 ing nuclei is He 4 instead of H 1 in which case Cue replaces Cn). The figures in the above 

 tables are for Cn = 67 percent, Ciu = 30 percent, and for p = 160 g/cm 3 . The calculations 

 of Christy and O'Reilly* for the interior of the sun give these values for Cn, Cue and p as 

 well as a concentration of 1.5 percent for carbon, nitrogen, and oxygen combined and of 

 1.5 percent for all other elements combined. Their calculations predict a temperature of 

 about 17X10" C K in the interior of the sun. The mean life of all the hydrogen now present 

 and the total energy production due to the proton-proton cycle and the carbon cycle are 

 also given in Table 723. For the carbon cycle the mean life of hydrogen and the energy 

 production depend on the concentration of the isotopes of carbon and nitrogen. These ele- 

 ments play the role of a "catalyst" controlling the speed of the reaction and are reproduced 

 at the end of each cycle. The figures in Part 2 of Table 723 are for a concentration of 1 

 percent by weight for N u . 



* For reference, see footnote 225 above. 

 SMITHSONIAN PHYSICAL TABLES 



