  We introduce an improved model that links the frequency shift of the
$^{133}\text{Cs}$ hyperfine Zeeman transitions $\vert F = 3, m_F>
\longleftrightarrow \vert F = 4, m_F >$ to the Lorentz-violating Standard-Model
Extension (SME) coefficients of the proton and neutron. The new model uses
Lorentz transformations developed to second order in boost and additionally
takes the nuclear structure into account, beyond the simple Schmidt model used
previously in SME analyses, thereby providing access to both proton and neutron
SME coefficients including the isotropic coefficient $\tilde{c}_{TT}$. Using
this new model in a second analysis of the data delivered by the FO2 dual Cs/Rb
fountain at Paris Observatory and previously analysed in
arXiv:hep-ph/0601024v1, we improve by up to 12 orders of magnitude the present
maximum sensitivities (see arXiv:0801.0287v9) on the $\tilde{c}_{Q}$,
$\tilde{c}_{TJ}$ and $\tilde{c}_{TT}$ coefficients for the neutron and on the
$\tilde{c}_{TT}$ coefficient for the proton, reaching respectively $10^{-20}$,
$10^{-17}$, $10^{-13}$ and $10^{-15}$ GeV.
