Suppose electron scattering fixes the radius parameter at instead of the value used…

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Nuclear constituents, size and binding · Nuclear constituents, size and binding

The Nucleus Resolved, Ch How big a nucleus is, and what the mass surface knows

Problem

Suppose electron scattering fixes the radius parameter at

r_0 = 1.25\,\mathrm{fm}

instead of the value used in the refitted mass formula. ((a)) Recompute the Coulomb coefficient

a_C = \tfrac{3}{5}(e^2/4\pi\epsilon_0)/r_0

for this

r_0

. ((b)) Using this

a_C

together with the other refitted coefficients

a_V = 15.76\,\mathrm{MeV}

a_S = 17.91\,\mathrm{MeV}

a_A = 23.25\,\mathrm{MeV}

a_P = 12.51\,\mathrm{MeV}

, compute the predicted binding energy of

^{40}\mathrm{Ca}

(

Z=N=20

) from the semi-empirical mass formula

B=a_VA-a_SA^{2/3}-a_CZ(Z-1)/A^{1/3}-a_A(N-Z)^2/A+\delta

, with

\delta=+a_P/\sqrt{A}

for even-even nuclei, and compare it with the measured value

B(^{40}\mathrm{Ca}) = 342.1\,\mathrm{MeV}

to find the binding-energy residual.