Molecular-Dynamics Simulation of Statistical Mechanical

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1 we list the numbers of stable nuclei for various odd or even combinations of N and Z. Immediately one is struck by the predominance of even-even nuclei and the almost complete absence of odd-odd nuclei. 1. NUMBER OF STABLE NUCLEI N Odd Odd Even Even Z Odd Even Odd Even 10 4 48 50 156 The only stable odd-odd nuclei are f Hi, 3U3, 5B5, and ^ N 7 . In Fig. 5 we plot the stable nuclei on an N versus Z plane. For fixed even A if we plot B(A, Z) against Z we obtain the typical result illustrated in Fig.

G. 90 208 ^Ca, Zr, P b ; however, the fluctuations are not nearly as great as for the light nuclei. 5 MeV in P b represents a total binding energy fluctuation of ~100 MeV, a not inconsiderable energy. A quantity closely related to the binding energy is the single particle separation energy S(A, Z) defined as the energy required to remove the least bound particle from the nucleus. 9) and the proton separation is likewise 2 2 Z - l)c -M(A, SP(A, Z) = mpc +M(A-l, 2 Z)c . 10) To the extent that the electromagnetic forces are negligible and the nuclear forces are charge independent, we should expect Sn = Sp, and they should both be approximately equal to B(A, Z)/Z.

1) we should expect a sudden and severe deviation of the measured cross-section from that given by the Rutherford formula. In Fig. 2 we reproduce some i5) plots of cross-section against a-particle energy obtained by Kerlee et al. from a-particle scattering off ^ A u n g . 4) and for Ea = E0 this is a measure of the range of interaction of the nuclear forces between the a-particle and the nucleus, or simply the sum of the radii of the nucleus and the a-particle with 6 = 90°. 6) NUCLEAR SHAPES A N D SIZES 47 r2 10 197 Au da da 10 15 20 i i i 25 30 i 35 i 40 E a( M e V ) FIG.

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