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A spherical nucleus of mass number A and of radius R is deformed into an ellipsoid. Rotational symmetry about one axis is maintained and the volume is kept constant. a = R(1+ €)is the half-length of the long axis of the ellipsoid and b R/√1 + € the half-length of the short ones (€ < 1 is a small positive number). Show that the surface term in the semi-empirical mass formula for the binding energy changes, up to the second order in €, to- E_{S}=a_{S} A^{2 / 3}\left(1+\frac{2}{5} \epsilon^{2}\right) where as is the surface term constant. S_{\text {ellipsod }}=4 \pi\left(\frac{a^{p} b^{p}+a^{p} c^{p}+b^{p} c^{p}}{3}\right)^{1 / p} where a, b, c are the half-lengths of the principal axes and p = 8/5.

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