Through the expansion into multiples, the concept of "multiple moment" has been reached. Examples of times of multiples are given. From these, the "quadruple moment tensor" was defined. From the classical distribution of loads ρ (r-> ') and the Taylor series potential expansion, where one of the terms of the expansion shows the quadruple moment, the classical Hamiltonian was constructed in terms of quadruple. The quantum expression HQ for H Q was obtained by replacing the classic charge density ρ (r ') by the operator ρ p , which describes the actual situation in a non - continuous load distribution. Using the technology of the Clebsh-Gordan coefficients and the irreducible tensors, the matrix elements of Ĥ Q. The relation obtained o a case where a strong field is applied on an atom is applied, and a particular relation is obtained for the calculation of the energetic levels of the quadrupole interaction. An application for an atom or ground state ion 2 S 1/2 , and nuclear spin 3/2 in a strong magnetic field, obtaining the opening of levels for the quadrupolar interaction. The quadrupolar interaction was examined in the Mössbauer effect for different examples.
