TABLE 721.— NUCLEAR REACTIONS* 665 



If a neutron or proton (or a light nucleus) approaches a nucleus at a distance less than 

 the range of nuclear forces it may interact with the nucleus in various ways. If the kinetic 

 energy of the incident particle is not more than a few Mev it is usually first captured by 

 the nucleus, forming a compound nucleus. This compound nucleus is in an excited state 

 (having an excess energy due to the extra binding energy of the additional particle as well 

 as its initial kinetic energy) and in a short time either (a) makes a transition to its ground- 

 state releasing the excess energy in the form of photons, (b) re-emits the incident particle 

 returning to the ground-state or an excited state of the original nucleus (elastic or inelastic 

 scattering), or (c) emits some other particle (neutron, proton, deuteron or o-particle 

 usually). 



A neutron does not experience any Coulomb repulsion on approaching a nucleus and 

 hence can react with a nucleus however low its kinetic energy. However, if the incident 

 particle is a proton or deuteron (and even more so if it is an a-particle) it has to overcome 

 an energy barrier due to the electrostatic Coulomb repulsion of the nucleus. For a proton 

 incident on a light nucleus (small Z) this barrier is a few hundred Kev and increases 

 almost proportionately with Z. If the kinetic energy of an incident proton is larger than 

 this barrier it can react about as easily as a neutron. If its energy is lower it can still 

 react due to a purely quantum phenomenon called barrier penetration, but the probability 

 of such a reaction's taking place decreases extremely rapidly as the kinetic energy is 

 decreased relative to the barrier. 



Nuclear processes in stars. — There are no free neutrons in stellar interiors (any 

 produced are quickly captured by nuclei), but there is a large proportion of ionized hydro- 

 gen and helium (protons and a-particles). At a stellar temperature of, say, 2X10 7 °C the 

 mean thermal kinetic energy of a proton is less than 2 Kev which is appreciably less than 

 the Coulomb barrier of even light nuclei. This means that the reaction rate for protons 

 being captured by a nucleus in stars is in general low and decreases very rapidly with 

 increasing charge Z of the nucleus, reactions with nuclei of Z greater than 8 (oxygen) 

 being negligible for practical purposes in stars. 



Two different cycles (the carbon and proton-proton cycle respectively) are of importance 

 in connection with nuclear energy production in stars. In each of these cycles four protons 

 are captured, separately, by certain light nuclei, two of the compound nuclei thus formed, 

 beta-decay, emitting a positron and neutrino. Each positron subsequently finds an electron 

 and the pair is annihilated, accompanied by the emission of photons. The net effect in each 

 of these cycles is that four protons and two electrons have disappeared, an a-particle has 

 appeared in their place and two neutrinos have been emitted. The energy generated is the 

 total binding energy of an a-particle plus the rest-energy of two electrons which amounts 

 to about 29 Mev per cycle. About 7 percent of this energy is lost in the form of kinetic 

 energy of neutrinos, which escape without interacting any further. The remaining 93 per- 

 cent of the energy is converted into thermal kinetic energy and radiation. The photons 

 created in the original nuclear processes are absorbed after traversing only a short distance 

 in the star and a larger number of photons of lower frequency are emitted, etc., so that 

 the radiation finally leaving the star has approximately the spectral distribution of black- 

 body radiation. The rate at which these cycles take place and hence the rate of energy- 

 production increases very much for even a small increase in the stellar temperature. 



* Prepared by E. E. Salpeter. 



TABLE 722.— THE THEORETICAL DE BROGLIE WAVELENGTHS ASSOCI- 

 ATED WITH VARIOUS PARTICLES AND BODIES OF GROSS MATTER 221 



(\ = h/{mv) ) 



De Broglie 



Velocity Energy wavelengths 



Particle Mass in g cm /sec ergs A 



Slow electron 9.1 XlO" 28 1 4.5 XlO" 28 7.3X10 8 



1-volt-electron 9.1 XlO" 28 5.9 XlO 7 1.6 XlO" 12 12. 



100-volt-electron 9.1 XlO" 28 5.9 x10 s 1.6 XlO" 10 1.2 



10,000-volt-electron 9.2 XlO" 28 5.0 XlO 9 1.6 XlO" 8 .12 



H, molecule at 200° C 3.3 XlO" 24 2.4X10° 9.5x10" .82 



100-volt proton 1.67X10"" 1.38X10 7 1.6 XlO" 9 .029 



100-volt a-particle 5.6 XlO"" 6.94X10" 1.6 XlO" 12 .0143 



a-particle from radium 6.6 XlO" 24 2.1 XlO 9 1.45X10- 8 6.6X10- 6 



22 rifle bullet 1.9 32,000 9.5 XlO 8 1.1X10" 28 



Golf ball 45 3,000 2.0 XlO 8 4.9X10" 24 



Baseball 140 2,500 4.4 XlO 8 1.9X10- 24 



221 Stranathan, J. D., The particles of modern physics, Blakiston Co., 1942. Used by permission of 

 the publishers. 



SMITHSONIAN PHYSICAL TABLES 



