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Consideration is given to the relative intensities of muon-poor extensive air showers observed at mountain altitudes and at sea level. It is shown that the available results to date do not support the earlier hypothesis that primary gamma rays are responsible, and instead, a process involving charged primary cosmic rays is indicated.

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An antisymmetrized second-order microscopic calculation of the imaginary optical potential for "Ca(n,n) is made using random-phase approximation transition densities to the intermediate excited states. An optical Green's function is used for the intermediate projectile propagator. Both inelastic and (n,p) charge exchange intermediate states of the nucleus are included and a finite range effective projectile-target nucleon interaction is used. The local approximation to the calculated imaginary optical potential is surface peaked but at a smaller radius than most of the phenomenological potentials, and the depth is somewhat smaller. Collectivity and intermediate charge-exchange states are shown to play an important role.NUCLEAR REACTIONS (n, n) scattering, calculation of optical potential; E = 30 MeV. culation of the optical potential using a phenomenological effective interaction of 6-function type, the random-phase approximation (RPA) vectors of Gillet-Sanderson' for the intermediate target states, and a free-particle propagator for the intermediate projectile. Similar in approach are 179

A new derivation of the reciprocity theorem is given. The general invariance property of the Hamiltonian which leads to symmetry of the Green's function for a quantum mechanical system is exhibited. It is found that reciprocity does not necessarily imply Hermiticity of the Hamiltonian, so that the ``complex optical model potential,'' for example, satisfies the reciprocity relations. The concept of reciprocity is then generalized to include a somewhat wider class of symmetry properties. Some properties of antiunitary transformations are discussed.

All available B(E2) values in the mass region 8&Z, N &20 relevant to the isovector electric quadrupole operator are compared to the theoretical B(E2) values based on Chung-Wildenthal Ods/&-1s&/) Od3/2 shell-model wave functions with harmonic oscillator radial wave functions, and some selected cases are compared with local and energy dependent Woods-Saxon potential wave functions. The empirical effective charges deduced from these comparisons are insensitive to differences in mass, state, and dominant single-nucleon orbit. The value for the effective charge parameter e~-e"extracted in the harmonic oscillator approximation is consistent with 1.0e. The values extracted with local and energydependent Woods-Saxon potentials, which are more meaningfully related to the underlying structure of the isovector polarizability, are consistent with 0.7e and 0.6e, respectively. Some inadequacies in the experimental data and theoretical models are discussed and improvements are suggested. NUCLEAR STRUCTURE 17&3 &39 nuclei: comparison of experimental E2 isovector matrix elements with shell-model predictions; extraction of the isovector effective charge; full basis Ods/&-1s&/2 Od3/f shell-model wave functions; Chung-Wildenthal Hamiltonians.

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