Abstract
In the present paper it is described an analysis procedure suited for experiments where cross-sections strongly varying with energy are measured using beams having large energy dispersion. These cross-sections are typically the sub-barrier fusion excitation function of reactions induced by radioactive beams. The large beam energy dispersion, typical of these experiments, can lead to ambiguities in the association of the effective beam energy to the reaction product yields and consequently to an error in the determination of the excitation function. As a test case, the approach is applied to the experiments 6 Li+120 Sn and 7 Li+119 Sn measured in the energy range 14 MeV ≤ Ec.m. ≤28 MeV. The complete fusion cross sections are deduced from activation measurements using the stacked target technique. The results of these experiments, that employ the two weakly-bound stable Li isotopes, show that the complete fusion cross sections above the barrier are suppressed of about 70% and 85% with respect to the Universal Fusion Function, used as a standard reference, in the 6 Li and 7 Li induced reactions respectively. Moreover, the excitation functions of the two systems at energies below the barrier, do not show significant differences, despite the two systems have different n -transfer Qvalue .
Highlights
The mean cross-section, σmean, of a given reaction process, is experimentally deduced by using the equation: σmean = Y Nt0 · NB (1)where Nt0 is the number of atoms per unit area of the target, and NB the number of beam particles passing through the target
This paper highlights the problem associated with the extraction of the correct excitation function in the case where cross-sections strongly varying with energy, with beams having large energy dispersion, are measured
These experiments are typically the sub-barrier fusion excitation function measurements with radioactive beams, where it is necessary to maximise the experimental yields due to the low intensity of the beams combined with the small cross-sections involved
Summary
The mean cross-section, σmean, of a given reaction process, is experimentally deduced by using the equation: σmean. If one has to derive an excitation function, the problem is how to relate these measured mean cross-sections to effective beam energies It is assumed σmean = σ(E) where Eis the energy in the centre of the target, as calculated by energy-loss programs. The probability distribution function w(t) of a given target can be determined experimentally using the residual energy spectra of α-particles emitted from a 241Am source passing through the target, and SRIM simulations. As can be seen from the figures, the iteration process will give the correct excitation function (red symbols overlap with the full line) This is true only if the correct beam energy distributions inside the targets are used. No mention is made in [7]
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