The main part of the line energy of dislocations in solids can be desc
ribed by elastic continuum theory (linear, nonlinear and nonlocal), Th
ere remains, however, a core part which must be treated atomistically.
Based on dimensional arguments it is shown that independent of the in
teratomic potential and independent of the core configuration there ex
ists a unique correlation between the elastic energy and the atomic mi
sfit energy. This results from the fact that the displacements are cou
pled to the asymptotic field of a singular dislocation.