$P\overset{?}{=}-{\varepsilon_B}(n_n,n_p)-{\varepsilon_{lepton}}(n_e,n_{\mu})+n_n{\mu}_n+n_p{\mu}_p+n_e{\mu}_e+n_{\mu}{\mu}_{\mu}$

${\varepsilon_B}(n_n,n_p)$ is given by equations 23 and 28 in Phys 554 lecture notes

${\mu_n}=\Large\frac{\partial{\varepsilon_B}(n_n,n_p)}{\partial n_n}\normalsize$

${\mu_p}=\Large\frac{\partial{\varepsilon_B}(n_n,n_p)}{\partial n_p}\normalsize$

${\mu_e}={\mu_n}-{\mu_p}=\Large\frac{\partial{\varepsilon_B}(n_n,n_p)}{\partial n_n}\normalsize-\Large\frac{\partial{\varepsilon_B}(n_n,n_p)}{\partial n_p}\normalsize\overset{?}{=}{\mu_{\mu}}$

${\varepsilon_{lepton}}(n_e,n_{\mu})\overset{?}{=}\large \frac{3}{5}\frac{p_F^{_2}{_e}}{m_e}n_e+\frac{3}{5}\frac{p_F^{_2}{_{\mu}}}{m_{\mu}}n_{\mu}\normalsize$

$n_e=n_p$

$p_F^{_2}{_e}={\mu^{_2}_e}-m^{_2}_e$

$p_F^{_2}{_{\mu}}={\mu^{_2}_{\mu}}-m^{_2}_{\mu}\overset{?}{=}{\mu^{_2}_e}-m^{_2}_{\mu}$

$n_{\mu}\overset{?}{=}\large\frac{p_F^{_3}{_{\mu}}}{3{\pi^2}}$