Coulomb energy between 2 charge q_1, q_2 in SI unit is

\displaystyle U_c = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r}  [J]

\displaystyle U_c = \frac{e^2}{4\pi\epsilon_0} \frac{Z_1 Z_2}{r [m]} [J \cdot m] = \frac{Z_1 Z_2}{r [m]} (\frac{e^2}{4\pi \epsilon_0}) [J \cdot m] = \frac{Z_1 Z_2}{r [m]} 2.30708 \times 10^{-28} [J \cdot m]

We need to convert the SI unit into nuclear unit:

1 [J] = \frac{10^{-6}}{e} [MeV]

1 [m] = 10^{15} [fm]

Since the unit of the r depends on the nominator, the change of the unit does not need to be compensated.

\displaystyle U_c = \frac{Z_1 Z_2}{r [fm]} 1.43996 [MeV \cdot fm]

Therefore, a simple expression

\displaystyle U_c = \frac{e^2}{r} Z_1 Z_2

where e^2 = 1.44 [MeV\cdot fm]

Other useful quantities are:

  • \hbar c = 197.327 [MeV\cdot fm]
  • e^2/\hbar c = 1/137.036
  • \hbar = 6.58212 [MeV\cdot s]
  • c = 2.99792458\times 10^{23} [fm/s]
Advertisements