The knowledge of the nuclear matrix elements for the neutrinoless double beta decay is fundamental for neutrino physics. In this paper, an innovative technique to extract information on the nuclear matrix elements by measuring the cross section of a double charge exchange nuclear reaction is proposed. The basic point is that the initial and final state wave functions in the two processes are the same and the transition operators are similar. The double charge exchange cross sections can be factorized in a nuclear structure term containing the matrix elements and a nuclear reaction factor. First pioneering experimental results for the 40 Ca( 18 O, 18 Ne) 40 Ar reaction at 270 MeV incident energy show that such cross section factorization reasonably holds for the crucial 0 +  0 + transition to 40 Ar gs , at least at very forward angles.

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Giant resonances are collective excitation modes for many-body systems of fermions governed by a mean field, such as the atomic nuclei. The microscopic origin of such modes is the coherence among elementary particle-hole excitations, where a particle is promoted from an occupied state below the Fermi level (hole) to an empty one above the Fermi level (particle). The same coherence is also predicted for the particle–particle and the hole–hole excitations, because of the basic quantum symmetry between particles and holes. In nuclear physics, the giant modes have been widely reported for the particle–hole sector but, despite several attempts, there is no precedent in the particle–particle and hole–hole ones, thus making questionable the aforementioned symmetry assumption. Here we provide experimental indications of the Giant Pairing Vibration, which is the leading particle–particle giant mode. An immediate implication of it is the validation of the particle–hole symmetry.