Solution (source code)

= Solution

Take the <energy> of an isolated, field-free gas atom as zero, and let $E_b>0$ be the field-independent <binding energy> at one <adsorption site>. The two adsorbed <spin> energies are
$$
\boxed{\varepsilon_\pm=-E_b\pm\mu_{\rm B}B.}
$$
Here $\mu_{\rm B}$ is the <Bohr magneton>. The lower state is stabilized by increasing $|B|$; the assignment of the two signs to names for the <spin> projections is a convention.