Energy loss tables

In previous versions of GEANT (up to version 3.13) the energy lost by a charged particle travelling through matter was calculated by the formula:

The quantity $dE/dx$ was calculated and tabulated for $e\pm$ , $\mu \pm$ and protons and the value for a particle of a given energy $E$₀ was calculated interpolating linearly the tables:

$.\; \{dEdx\}|$E=E0	$=$	$.\; \{dEdx\}|$E=Ei+ {E0-EiEi+1-Ei}( . {dEdx}|E=Ei+1-. {dEdx}|E=Ei) .3cm
	$=$	$GEKRT1x.\; \{dEdx\}|$E=Ei+GEKRATx. {dEdx}|E=Ei+1&sp;(Ei< E0≤Ei+1)

These formula work of course on the assumption that the error is negligible. But the error on the linear approximation is $O(2E/x\; \hspace{1em}E\; )$ which is far from negligible at low energy. In this way the energy loss at low energies was constantly underestimated and the particles could travel too far before stopping.