Microscopic description of production cross sections including deexcitation effects

Background: At the forefront of the nuclear science, production of new neutron-rich isotopes is continuously pursued at accelerator laboratories all over the world. To explore the currently unknown territories in the nuclear chart far away from the stability, reliable theoretical predictions are inevitable.

Purpose: To provide a reliable prediction of production cross sections taking into account secondary deexcitation processes, both particle evaporation and fission, a new method called TDHF+GEMINI is proposed, which combines the microscopic time-dependent Hartree-Fock (TDHF) theory with a sophisticated statistical compound-nucleus deexcitation model, GEMINI++.

Methods: Low-energy heavy ion reactions are described based on three-dimensional Skyrme-TDHF calculations. Using the particle-number projection method, production probabilities, total angular momenta, and excitation energies of primary reaction products are extracted from the TDHF wave function after collision. Production cross sections for secondary reaction products are evaluated employing GEMINI++. Results are compared with available experimental data and widely used grazing calculations.

Results: The method is applied to describe cross sections for multinucleon transfer processes in ${}^{40}\mathrm{Ca}+{}^{124}\mathrm{Sn}$ ($E_{\mathrm{c}.\mathrm{m}.}\simeq 128.54\mathrm{MeV}$), ${}^{48}\mathrm{Ca}+{}^{124}\mathrm{Sn}$ ($E_{\mathrm{c}.\mathrm{m}.}\simeq 125.44\mathrm{MeV}$), ${}^{40}\mathrm{Ca}+{}^{208}\mathrm{Pb}$ ($E_{\mathrm{c}.\mathrm{m}.}\simeq 208.84\mathrm{MeV}$), ${}^{58}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ ($E_{\mathrm{c}.\mathrm{m}.}\simeq 256.79\mathrm{MeV}$), ${}^{64}\mathrm{Ni}+{}^{238}\mathrm{U}$ ($E_{\mathrm{c}.\mathrm{m}.}\simeq 307.35\mathrm{MeV}$), and ${}^{136}\mathrm{Xe}+{}^{198}\mathrm{Pt}$ ($E_{\mathrm{c}.\mathrm{m}.}\simeq 644.98\mathrm{MeV}$) reactions at energies close to the Coulomb barrier. It is shown that the inclusion of secondary deexcitation processes, which are dominated by neutron evaporation in the present systems, substantially improves agreement with the experimental data. The magnitude of the evaporation effects is very similar to the one observed in grazing calculations. TDHF+GEMINI provides better description of the absolute value of the cross sections for channels involving transfer of more than one proton, compared to the grazing results. However, there remain discrepancies between the measurements and the calculated cross sections, indicating a limit of the theoretical framework that works with a single mean-field potential. Possible causes of the discrepancies are discussed.

Conclusions: To perfectly reproduce experimental cross sections for multinucleon transfer processes, one should go beyond the standard self-consistent mean-field description. Nevertheless, the proposed method will provide valuable information to optimize production mechanisms of new neutron-rich nuclei through its microscopic, nonempirical predictions.

Figure 1

Production cross sections for lighter fragments in the ${}^{40}\mathrm{Ca}+{}^{124}\mathrm{Sn}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}\simeq 128.54\mathrm{MeV}$. Each panel shows cross sections for different proton-transfer channels. The horizontal axis is the neutron number of the fragments. Red filled circles denote the experimental data [74]. Red filled areas represent TDHF results for primary reaction products. Cross sections for secondary reaction products obtained with TDHF+GEMINI are shown by blue solid lines. For comparison, grazing results [82] are also shown by green shaded histograms.

Figure 2

Same as Fig. 1, but for the ${}^{48}\mathrm{Ca}+{}^{124}\mathrm{Sn}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}\simeq 125.44\mathrm{MeV}$. The experimental data were reported in Ref. [75].

Figure 3

Same as Figs. 1 and 2, but for the ${}^{40}\mathrm{Ca}+{}^{208}\mathrm{Pb}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}\simeq 208.84\mathrm{MeV}$. The data for $E_{\mathrm{c}.\mathrm{m}.}\simeq 197.10\mathrm{MeV}$ were also analyzed, getting very similar results (not shown). The experimental data were reported in Ref. [76].

Figure 4

Same as Figs. 1, 2, 3, but for the ${}^{58}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}\simeq 256.79\mathrm{MeV}$. The experimental data were reported in Ref. [77].

Figure 5

Same as Fig. 1 for the ${}^{40}\mathrm{Ca}+{}^{124}\mathrm{Sn}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}\simeq 128.54\mathrm{MeV}$, but cross sections by TDHF+GEMINI with a simpler treatment of $E^{*}$ and $J$ (see text for details) are shown by blue shaded histograms, instead of grazing results.

Figure 6

Same as Fig. 5, but for the ${}^{48}\mathrm{Ca}+{}^{124}\mathrm{Sn}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}\simeq 125.44\mathrm{MeV}$.

Figure 7

Same as Figs. 5 and 6, but for the ${}^{40}\mathrm{Ca}+{}^{208}\mathrm{Pb}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}\simeq 208.84\mathrm{MeV}$.

Figure 8

Same as Figs. 5, 6, 7, but for the ${}^{58}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}\simeq 256.79\mathrm{MeV}$.

Figure 9

Production cross sections for lighter fragments in the ${}^{64}\mathrm{Ni}+{}^{238}\mathrm{U}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}\simeq 307.35\mathrm{MeV}$. Each panel shows cross sections for different proton-transfer channels. The horizontal axis is the mass number of the fragments. Cross sections associated with side collisions are shown (see text). Cross sections for secondary products evaluated by TDHF+GEMINI (with ${\overline{E}}_{N,Z}^{*}$ and $\overline{J}$ as in Figs. 5, 6, 7, 8) are shown by blue solid lines. The experimental data were reported in Ref. [78]. grazing results [82] are also shown by green shaded histograms, for comparison.

Figure 10

Same as Fig. 9, but for the ${}^{136}\mathrm{Xe}+{}^{198}\mathrm{Pt}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}\simeq 644.98\mathrm{MeV}$. The experimental data and the grazing results were taken from Ref. [79] (see [99] for a comment on this point).