Predicting the production of neutron-rich heavy nuclei in multinucleon transfer reactions using a semi-classical model including evaporation and fission competition, GRAZING-F

Background: Multinucleon transfer reactions have recently attracted attention as a possible path to the synthesis of new neutron-rich heavy nuclei.

Purpose: We study transfer reactions involving massive nuclei with the intention of understanding if the semi-classical model GRAZING coupled to an evaporation and fission competition model can satisfactorily reproduce experimental data on transfer reactions in which fission plays a role.

Methods: We have taken the computer code grazing and have added fission competition to it (grazing-f) using our current understanding of ${\Gamma }_n/{\Gamma }_f$, fission barriers, and level densities.

Results: The code grazing-f seems to satisfactorily reproduce experimental data for $+1p,+2p$, and $+3p$ transfers but has limitations in reproducing measurements of larger above-target and below-target transfers. Nonetheless, we use grazing-f to estimate production rates of neutron-rich $N=126$ nuclei, actinides, and transactinides.

Conclusions: The grazing code, with appropriate modifications to account for fission decay as well as neutron emission by excited primary fragments, does not predict large cross sections for multinucleon transfer reactions leading to neutron-rich transactinide nuclei but predicts opportunities to produce new neutron-rich actinide isotopes.

Figure 1

Excitation energy distributions predicted by grazing in the reaction ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$ at $E_{\mathrm{c}.\mathrm{m}.}=423,450,526,617$ MeV for the partial wave leading to the highest cross section for producing primary product ${}_{78}{}^{204}\mathrm{Pt}{}_{126}$. The partial wave $L$ is given in the panels.

Figure 2

Panel (a) shows a comparison between simulations of the primary yields of $Z=98$ products in the ${}^{238}\mathrm{U}+{}^{248}\mathrm{Cm}$ reaction with grazing by constructing a weighted cross section (solid line) and a single simulation at the midtarget energy (dashed line.) The effective target thickness is $4.8$ mg/${\mathrm{cm}}^2$ and the weighted simulation is made by assuming a stack of ten identical target slices. Panel (b) shows the deviation.

Figure 3

Cross sections of surviving nuclei in the reaction ${}^{238}\mathrm{U}+{}^{248}\mathrm{Cm}$ at entering projectile energy $E_{\mathrm{lab}}=1760$ MeV. Experimental data from Ref. [37] are shown as solid symbols and the predicted cross sections (grazing-f) as solid lines. The measurement of ${}^{251}\mathrm{Bk}$ is a lower limit which is indicated with an arrow. Dotted lines show the predicted yields of primary products. Dashed lines shows the Langevin simulations in Ref. [10].

Figure 4

Predicted transfer (grazing) and transfer-fission cross sections (grazing-f) as a function of midslice energy in the ${}^{238}\mathrm{U}+{}^{238}\mathrm{U}$ reaction at entering energy $E_{\mathrm{lab}}=2059$ MeV.

Figure 5

Cross sections of surviving nuclei in the reaction ${}^{238}\mathrm{U}+{}^{238}\mathrm{U}$ at $E_{\mathrm{lab}}=1628,1785,2059$ MeV. Experimental data from Ref. [37] are shown as solid symbols and predicted cross sections (grazing-f) as solid lines. Dotted lines show the predicted yield of primary products. Dashed lines shows the Langevin simulations in Ref. [10].

Figure 6

Predicted (grazing-f) cross sections of surviving nuclei with $Z=92$ to 94 in the ${}^{238}\mathrm{U}+{}^{238}\mathrm{U}$ reaction at entering energy $E_{\mathrm{lab}}=2059$ MeV. Unknown isotopes are shown as open circles.

Figure 7

Predicted (grazing-f) cross sections of surviving nuclei in the reaction ${}^{129}\mathrm{Xe}+{}^{248}\mathrm{Cm}$ at $E_{\mathrm{lab}}=780$ MeV, ${}^{132}\mathrm{Xe}+{}^{248}\mathrm{Cm}$ at $E_{\mathrm{lab}}=805$ MeV, and ${}^{136}\mathrm{Xe}+{}^{248}\mathrm{Cm}$ at $E_{\mathrm{lab}}=769$ MeV (solid lines) compared to experimental data [6, 8] (solid symbols). Predicted primary product yields are shown as dotted lines.

Figure 8

Predicted (grazing-f) cross sections of surviving nuclei in the reaction ${}^{136}\mathrm{Xe}+{}^{249}\mathrm{Cf}$ at $E_{\mathrm{lab}}=749,813,877$ MeV (solid lines) compared to experimental data [9] (solid symbols).

Figure 9

Predicted (grazing-f) cross sections of surviving nuclei in the reaction ${}^{136}\mathrm{Xe}+{}^{244}\mathrm{Pu}$ at $E_{\mathrm{lab}}=826$ MeV (solid lines) compared to experimental data [7] (solid symbols). Predicted primary product yields are shown as dotted lines.

Figure 10

Predicted (grazing-f) cross sections of surviving nuclei in the reaction ${}^{86}\mathrm{Kr}+{}^{248}\mathrm{Cm}$ at $E_{\mathrm{lab}}=435,457,520$ MeV (solid lines) compared to experimental data [6] (solid symbols). Predicted primary product yields are shown as dotted lines.

Figure 11

Cross sections of surviving nuclei in the reaction ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$ at $E_{\mathrm{c}.\mathrm{m}.}=423,450,526,617$ MeV. The simulations (grazing-f) are shown as solid lines. Unknown isotopes are shown as open circles and unknown isotopes with $N=126$ are shown as solid circles.

Figure 12

Cross sections of surviving nuclei in the reaction ${}^{144}\mathrm{Xe}+{}^{248}\mathrm{Cm}$ at $E_{\mathrm{lab}}=800$ MeV. The predictions (grazing-f) are shown as solid lines. Unknown isotopes are shown as open circles. Predicted primary product yields are shown as dotted lines.

Figure 13

Cross sections of surviving nuclei in the reaction ${}^{129,132,136,144}\mathrm{Xe}+{}^{248}\mathrm{Cm}$ at $E_{\mathrm{c}.\mathrm{m}.}/V_{\text{int}}=1.05$. The predictions (grazing-f) are shown as solid lines. Unknown isotopes are shown as open circles.

Figure 14

Predicted (grazing-f) cross sections of surviving nuclei in the reaction ${}^{86,94}\mathrm{Kr}+{}^{248}\mathrm{Cm}$ at $E_{\mathrm{c}.\mathrm{m}.}/V_C=1.45$. The predictions (grazing-f) are shown as solid lines. Unknown isotopes are shown as open circles.

Figure 15

Cross sections of surviving nuclei in the reaction ${}^{238}\mathrm{U}+{}^{249}\mathrm{Bk}$ at $E_{\mathrm{c}.\mathrm{m}.}/V_C=1.05$ and $1.45$. The predictions (grazing-f) are shown as solid lines. Unknown isotopes are shown as open circles.