A new method is proposed for calculating the displacements due to an edge or screw dislocation in a crystal. The dislocation is represented by a perturbation in the phonon state of a perfect crystal and the treatment is carried out by the use of second quantization. The results agree with the classical ones at large distances from the dislocation core but show a quite different structure in the neighbourhood of the core which eliminates the singularities in the former theory.

An edge type dislocation in a simple cubic lattice is studied with the inclusion of a new double row of forces confined to the core. Particular emphasis is given to the distortion in the neighbourhood of the dislocation line. The theory is baaed on a new formula which gives the lattice distortion arising from the introduction into the crystal of E point force, the discrete structure of the medium being taken into consideration. The resulting displacements are linear functions of some matrices whose values are tabulated for the core atoms. A t greater distances from the dislocation line the present solutions are substantially the same as the classical ones.L'analyse d'une dislocation de type coin dens un rbeau cubique simple -btude qui a bt.4 abordb ailleurs [l] -est maintenant complbthe en prenant en consideration une double rang& de forces localisbs dam le noyau et en mettant tout particulit?rement en bvidence la distorsion aux alentours de la ligne de dislocation. Cette thhrie appuie Bur une nouvelle formule donnant la distorsion du rbeau A la suite de I'introduction d'une force ponctuelle, en prenant dament en considbration la structure discrhte du milieu. Les dbplacements qui en rbultent sont des fonctions linhires de matrices dont les valeurs sont calculbs pour les atomes appartenant au noyau. A des distances plus grandes de la ligne de dislocation nos solutions sont substantiellement lea mdmes que celles classiques.