= Perpendicular neutron recoil and phonon absorption
{title2=$\hbar\omega=\hbar^2Q^2/(2m_n)$}
Define transfer gained by the <neutron> as $\mathbf Q=\mathbf k_f-\mathbf k_i$. If it is perpendicular to $\mathbf k_i$, expansion of the free-neutron <kinetic energy> gives $E_f-E_i=\hbar^2Q^2/(2m_n)$. Absorbing one <phonon> requires this positive <energy> to equal $\hbar\omega$. A periodic <phonon> branch may therefore intersect a nonperiodic recoil parabola in an extended-zone representation. The sign of $\mathbf Q$ is opposite to the common sample-transfer convention and must be declared.
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