For any lattice temperature T<or approximately=10³K and different charge states Z of the centre the authors describe the dependences of non-radiative multiphonon carrier capture coefficients C^Z(T; E) on the carrier energy E by products of the familiar Sommerfeld factors s^Z(E) with corresponding energy-loss factors C⁰(T; E). As the carrier energy E is increased these 'neutral parts' C⁰(T; E) of capture coefficients decrease or increase (exponentially) in the alternative regimes of small and large lattice relaxation. Their maximum enhancements C_max⁰/C⁰(0;0), which can be produced in the latter regime, at low lattice temperatures, are shown to be approximately exp(S(1+ gamma ln gamma - gamma )) (approaching e^S in the gamma to 0 limit) where S represents the Huang-Rhys factor and gamma the ratio between thermal depth and lattice relaxation energy. For values of S of the order of 10 this 'enhanced hot-carrier capture due to large lattice relaxation' effect can thus amount to several orders of magnitude and should hence be of considerable importance for interpretations of corresponding hot-carrier capture data.