A Classical Model for the Nucleus J. G. WINANS University of Wisconsin, Madison, Wisconsin December 26, 1946 W HEN the cube root of the mass number iU plotted against the square root of the atomic number for the most abundant or longest lived isotope of the elements, there is obtained a very nearly straight line extending from the neutron to curium. Hydrogen and helium are the only elements appreciably off of the line. The equation is MI-1.15=0.528Zi. To show this more accurately, (Ml - 1.15)2 is plotted against the atomic number in Fig. 1. Assuming nuclei spherical, made of protons and neutrons each of radius ro, with the protons confined to the outside giving a constant surface charge density at a depth xro below the surface, we have: 47r(r-xro)2 = KlZ7rro2 and 4/3xrr3 = K2M4/3srrol, where M is the mass number and Z is the atomic number. Combining gives MK2i 2K2' Use of K2=1.35 as for spherical close packing gives x= 1.28, and K, = 1.36. The correction factor for K, to get a value of K, corresponding to the middle of the surface particles, depends on M and Z. For holmium, for example, M=165, Z=67, and the
Physical Review – American Physical Society (APS)
Published: Mar 15, 1947
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