Sec. 4.13] PROTONS, DEUTERONS, AND ALPHA PARTICLES 95 



is the factor that determines the probability of emission through the barrier. 

 It is a sensitive function of the barrier height and width as is readily apparent 

 from the observed half-lives of the natural radioactive isotopes which range 

 from 10~ 7 sec to 10 10 years. 



Writing the expression for r in terms of logarithms, 



log r = - + B 

 v 



where A = fv 



B = log T 



If it is assumed that the nuclear radius is nearly constant for all alpha 

 emitters, A and B are then also nearly constant and the logarithm of the mean 

 life is inversely proportional to the velocity of the alpha particle. A similar 

 relation is found between the range R and the mean life. 



or 



log r = C - D log R 

 log X = E log R + F 



where X = disintegration constant 

 C, D, E, F = constants 



These important relations were first discovered empirically by Geiger and 

 Nuttal [21] when they plotted the measured values of X and R for the alpha 

 emitters of the natural radioactive series. The components of each series are 

 found to fall remarkably close to straight lines as required by the expression 

 above. 



REFERENCES FOR CHAP. 4 



1. Crane, H. R., L. A. Delsasse, W.A. Fowler, and C. C. Lauritsen: Phys. Rev., 48, 

 484(1935). 



2. Feenberg, E.: Phys. Rev., 49, 328 (1936). 



3. Bethe, H., and R. F. Bacher: Rev. Mod. Phys., 8, 82 (1936). 



4. Bethe, H.: Ann. Physik, 6, 325 (1930). 



5. Bethe, H.: Z. Physik, 76, 293 (1932). 



6. Livingston, S., and H. Bethe: Rev. Mod. Phys., 9, 263 (1937). 



7. Miller, C: Ann. Physik, 14, 531 (1932). 



8. Blackett, P. M. S.: Proc. Roy. Soc. (London), 136, 132 (1932). 



9. Duncanson.W. E.: Proc. Cambridge Phil. Soc., 30, 102 (1934). 



10. Mano, G.: Ann. Physik, 1, 407 (1934). 



11. Bloch, F.: Z. Physik, 81, 363 (1933). 



12. Mano, G.: Ann. Physik, 1, 446 (1934). 



13. Bhabha, H. J. : Proc. Roy. Soc. (London), 164, 257 (1937). 



14. Honl, H.: Z. Physik, 84, 1 (1933). 



15. Fermi, E.: Phys. Rev., 57, 485 (1940). 



16. von Taubenberg, H. R.: Z. Physik, 2, 268 (1920). 



17. Thomson, J. J.: Proc. Cambridge Phil. Soc, 13, 49 (1900). 



