Additive empirical parametrization and microscopic study of deuteron breakup

Comparative assessment of the total breakup proton-emission cross sections measured for 56 MeV deuteron interaction with target nuclei from ${}^{12}\mathrm{C}$ to ${}^{209}\mathrm{Bi}$, with an empirical parametrization and recently calculated microscopic neutron-removal cross sections was done at the same time with similar data measured at 15, 25.5, 70, and 80 MeV. Comparable mass dependencies of the elastic-breakup (EB) cross sections provided by the empirical parametrization and the microscopic results have been also found at the deuteron energy of 56 MeV, while the assessment of absolute-values variance up to a factor of two was not possible because of the lack of EB measurements at energies higher than 25.5 MeV. While the similarities represent an additional validation of the microscopic calculations, the cross-section difference should be considered within the objectives of further measurements.

Figure 1

Comparison of experimental [7, 8, 9, 10] total breakup proton-emission (solid symbols) and elastic-breakup (open circles) fractions, and the corresponding parametrizations [22] (solid and dash-dotted curves, respectively) as well as the normalized EB fractions (dotted) for deuterons incident on nuclei from ${}^{27}\mathrm{Al}$ (a) to ${}^{232}\mathrm{Th}$ (i) at energies up to 80 MeV.

Figure 2

Comparison of the mass dependence of the measured [7, 8, 9, 10] total BU proton-emission cross sections (a)–(d) and fractions (e)–(h) with the predictions of the microscopic theory for neutron removal cross sections [19] (asterisks) and of the empirical parametrization (crosses), connected by dashed lines for eye guiding, for target nuclei from ${}^{12}\mathrm{C}$ up to ${}^{209}\mathrm{Bi}$, at the incident energies of 15, 25.5, 56, 70, and 80 MeV.

Figure 3

Total-reaction (thick solid curves), direct interactions (DI, thin-solid curve), BU (dashed curves), stripping $(d,p)$ (dash-dot-dotted curves) and $(d,n)$ (dash-dotted curves), and pick-up $(d,t)$ (dotted curves) and $(d,\alpha )$ (short-dotted curves) reaction cross sections for deuterons on ${}^{27}\mathrm{Al}, {}^{54}\mathrm{Fe}, {}^{58}\mathrm{Ni}, {}^{64}\mathrm{Ni}, {}^{93}\mathrm{Nb}$, and ${}^{238}\mathrm{U}$ [3, 4, 5, 24] (see text).

Figure 4

Comparison of the mass dependence of the EB cross sections (a) and fractions (b) predicted by the microscopic theory [19] (asterisks) and empirical parametrization (crosses), connected by dashed lines for eye guiding, for deuterons incident on target nuclei from ${}^{12}\mathrm{C}$ up to ${}^{232}\mathrm{Th}$, at energy of 56 MeV, as well as of (c) the excitation functions of the EB cross sections measured for deuterons on ${}^{62}\mathrm{Ni}$ [10], and the microscopic [19] and phenomenological predictions for ${}^{58,62}\mathrm{Ni}$ target nuclei (see text).