Limits on the low - energy antinucleon annihilations from the Heisenberg principle

Here a short synthesis is presented of the work, developed in the last two years by the Brescia Collaboration, on the phenomenology of antinucleon-nucleon and antinucleon-nucleus annihilation at small momenta (below 300 MeV/c in the laboratory), with special stress on the role of general principles. Our work[1] in the last two years was mainly devoted to the study of the strong shadowing characterizing ¯ p annihilations onlight nuclei. The nuclear shadowing is evident in the fact that the ¯ pp total annihilation cross sections are larger than the corresponding ¯ pD and ¯ p 4 He ones for ¯ p momenta in the laboratory k < 70 MeV/c[2]. In previous works we used the word " inversion ". A related phenomenon was studied in antiprotonic atoms[3–6] and also pionic atoms[7]. Since " shadowing " can be defined as the amount of departure from the Impulse Approximation, to quantify its real presence we need first to produce an impulse approximation estimation of the measured nuclear data. Not to overrate the shadowing effects, two more points must be taken into account: (1) a correct estimation of Coulomb enhancement effects, and (2) center of mass effects. When data are represented with respect to the center of mass momentum[1], the shadowing effect is smaller, although apparently all the available nuclear annihilation cross sections become quite similar at k cm << 100 MeV/c. To fully understand the relevance of this similarity, we remind that at low energies Coulomb effects are expected to be quite strong and enhance ¯ p 4 He annihilation rates about twice with respect to ¯ pp ones. This traditional estimate of Coulomb effects[8] is based on the approximation of pointlike particles. Within an optical potential framework we recalculated these Coulomb corrections, taking into account the finite size of the ¯ p and nuclear charge distributions. One of the results[1] was that the advantage of the Helium charge with respect to the Hydrogen case was not that large, in the laboratory frame.