  A systematic study of the $R_e$-$T_m$ relation ($R_e$ = track radius, $T_m$ =
melting temperature) in insulators reveals new features of track formation. A
quantitative relationship is demonstrated between $R_e$ values measured in
various solids when $\langle s_e\rangle$=constant ($\langle s_e\rangle$ =
atomic stopping power). This effect is the consequence of a
composition-independent, identical maximum temperature distribution $\Delta
T(r,0)$, which is induced in various insulators in a narrow cylindrical volume
close to the tracks. The uniformity ceases gradually at larger distances.
$\Delta T(r,0)$ has a Gaussian shape, with a constant width w=4.5 nm, is
independent of materials parameters and it can be determined experimentally by
the measurement of Re in various insulators when $\langle s_e\rangle$=constant.
The consequences of the experimental $\Delta T(r,0)$ distribution are
discussed.
