I went back to my home town for visa renewal and read few books on history ( american revolution, early islam, modern chinese). After I got the visa a back to US, a lot of work has to be done and waiting for me….


The Coulomb displacement energy is the energy difference between isobaric analog states with same isospin. For example, the ground state energy different between 15O and 15N. The only difference between 15O and 15N is the proton in 0p1/2 shell replaced by a 0p1/2 neutron. Both ground state is in isospin T=1/2. The Coulomb displacement energy is defined as,

\displaystyle \Delta = BE(A, Z-1) - BE(A,Z) \\ ~~~~ = M(A,Z) - M(A,Z-1) + (m_n - m_p)

The binding energies are

BE(^{15}\textrm{O}) = 111.95535 ~\textrm{MeV}
BE(^{15}\textrm{N}) = 115.4919 ~\textrm{MeV}

The difference of the binding energy is 3.54 MeV.


Let’s calculate the Coulomb energy based on proton charge distributed uniformly in a sphere with radiu R=1.25 A^{1/3}. For A = 15, R = 3.083 \textrm{fm}. The Coulomb energy for uniform sphere is

\displaystyle E_c = \frac{3}{5}\frac{e^2}{R} Z(Z-1), e^2 = 1.44 ~\textrm{MeV} \cdot \textrm{fm}

Thus the Coulomb energies of 15O and 15N are

E_c(^{15}\textrm{O}) = 15.69 \textrm{MeV}
E_c(^{15}\textrm{N}) =   9.81 \textrm{MeV}

The difference is 4.11 MeV, about 0.5 MeV difference than the binding energy difference!