- #1

- 312

- 29

$$BN(N+1)+\gamma m_N m_S + b m_I m_S + \frac{c}{3}m_I m_S$$

where ##m_{I,S,N}## are the projections along the z axis (defined by the magnetic field) of the I, S and N operators (I am ignoring the ##DN^4## as that is negligible for the ##N=0,1## states we are interested in). For the ##H_z##, the diagonal terms are, given that B is along z:

$$-g_\perp\mu_Bm_S B - \frac{1}{3}(g_\parallel-g_\perp)\mu_Bm_SB- g_I\mu_N m_I B - g_{rot}\mu_Nm_N B$$

where I used from the cited literature: ##B = 6473.9588##, ##\gamma = 80.923##, ##b = 66.25## and ##c = 8.2233## (all in MHz). In terms of off-diagonal elements, there are none connecting ##N=1## to ##N=0##, as they have different parities. Within a given N manifold, the terms that matter are the ones connecting states with the same value of ##m_S##, as different values of ##m_S## are suppressed by about ##\frac{\gamma}{B}##. The only terms able to do that come from ##c(I\cdot n)(S \cdot n)## and are given by ##c\frac{\sqrt{2}}{10}m_S## and they are included in the plot below. All the other terms shouldn't matter as they are too small and I think I included all the relevant term. But I can't seem to reproduce their plots. Did I miss any term or miss-calculated something? Any insight would be really appreciated. Thank you!