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Mapping Below-Barrier Breakup Probabilities to Above-Barrier Complete Fusion Suppression

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Zeptosecond Dynamics of Transfer‐Triggered Breakup

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Abstract

Breakup functions for below-barrier reactions of \(^{9}\mathrm{Be}\) with \(^{27}\mathrm{Al}\), \(^{28}\mathrm{Si}\), \(^{144}\mathrm{Sm}\), \(^{168}\mathrm{Er}\), \(^{186}\mathrm{W}\), \(^{196}\mathrm{Pt}\), \(^{208}\mathrm{Pb}\) and \(^{209}\mathrm{Bi}\) and \(^{7}\mathrm{Li}\) with \(^{27}\mathrm{Al}\), \(^{28}\mathrm{Si}\), and \(^{58}\mathrm{Ni}\) were extracted using the methods described in the previous chapter. Separate breakup functions for each transfer process in each beam-target combination will be presented and systematic trends will be investigated. These below-barrier breakup functions will be used as input to Kookaburra and M-Platypus to predict the contribution of breakup to above-barrier complete fusion suppression.

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Notes

  1. 1.

    Kookaburra and M-Platypus take breakup functions for different resonances \(\rho _\ell (E_\mathrm {p}^*)\) (Eq. 2.18) as input. Breakup functions for particular resonances are not necessarily the same as those found by gating on particular narrow peaks. As seen in Fig. 2.5a, b, distributions containing narrow resonances have a “tail” of probability extending to high \(E_\mathrm {p}^*\). By producing breakup functions based on a gate on a narrow resonance, and assigning it to the whole excitation distribution containing the narrow resonance, contributions from the high \(E_\mathrm {p}^*\) tail of that resonance are assigned to the broad resonances. This results in a slightly lower breakup strength for the narrow resonance and a slightly higher breakup strength for the broad resonance. However, given that the high \(E_\mathrm {p}^*\) tail of events is weakly populated compared to the peak this is a fair approximation.

  2. 2.

    For reactions of \(^{9}\)Be with \(^{144}\)Sm to \(^{209}\)Bi targets, a useful parameterisation of \(R_\mathrm {B}\) is \(R_\mathrm {B} = 1.44(A_T^{1/3}+A_P^{1/3})\), which reproduces the SPP calculation of \(R_\mathrm {B}\) to within 0.1 fm.

  3. 3.

    The errors in \(F_\mathrm {ICF}\) arise from the statistical error in the least squares fit to the breakup probabilities. The input breakup probability when calculating \(F_\mathrm {ICF}\) was varied by \(\pm 1\) sigma in both slope parameter and strength parameter, and the resulting \(F_\mathrm {ICF}\) calculated. The asymmetry in the error bars therefore arise from a nonlinear response of Kookaburra to variation in the breakup function. The model sensitivities of Kookaburra must be investigated further.

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  1. Department of Nuclear Physics, Research School of Physics and Engineering, Australian National University, Canberra, ACT, Australia

    Kaitlin Jennifer Cook

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Cook, K.J. (2018). Mapping Below-Barrier Breakup Probabilities to Above-Barrier Complete Fusion Suppression. In: Zeptosecond Dynamics of Transfer‐Triggered Breakup. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-96017-3_7

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