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To systematically describe evaporation spectra for light and heavy compound nuclei over a large range of excitation energies, it was necessary to consider three ingredients in the statistical model. First, transmission coefficients or barrier penetration factors for charged-particle emission are typically taken from global fits to elastic-scattering data. However, such transmission coefficients do not reproduce the barrier region of evaporation spectra and reproduction of the data requires a distributions of Coulomb barriers. This is possibly associated with large fluctuations in the compound-nucleus shape or density profile. Second, for heavy nuclei, an excitation-energy dependent level-density parameter is required to describe the slope of the exponential tails of these spectra. The level-density parameter was reduced at larger temperatures, consistent with the expected fadeout of long-range correlation, but the strong A dependence of this effect is unexpected. Last, to describe the angular-momentum dependence of the level density in light nuclei at large spins, the macroscopic rotational energy of the nucleus has to be reduced from the values predicted with the finite-range liquid-drop model.