Interaction of ${}^{11}$Li with ${}^{208}$Pb

Background: ${}^{11}$Li is one of the most studied halo nuclei. The fusion of ${}^{11}$Li with ${}^{208}$Pb is the subject of a number of theoretical studies with widely differing predictions, ranging over four orders of magnitude, for the fusion excitation function.

Purpose: The purpose was to measure the excitation function for the ${}^{11}$Li $+$ ${}^{208}$Pb reaction.

Methods: A stacked foil and degrader assembly of ${}^{208}$Pb targets was irradiated with a ${}^{11}$Li beam producing center-of-target beam energies from above-barrier to near-barrier energies (40–29 MeV). The intensity of the ${}^{11}$Li beam (chopped) was 1250 particles/s and the beam on-target time was 34 h. The $\alpha$ decay of the stopped evaporation residues (EVRs) was detected in an $\alpha$-detector array at each beam energy in the beam-off period (the beam was on for $\le$5 ns and then off for 170 ns).

Results: The observed nuclidic yields of ${}^{212/215}$At and ${}^{214}$At are consistent with being produced in the complete fusion of ${}^{11}$Li with ${}^{208}$Pb. The observed yields of ${}^{213}$At appear to be the result of the breakup of ${}^{11}$Li into ${}^9\text{Li}+2n$, with the ${}^9$Li fusing with ${}^{208}$Pb. The magnitudes of the total fusion cross sections are substantially less than most theoretical predictions.

Conclusions: It is possible to measure the EVR production cross sections resulting from the interaction of ${}^{11}$Li with ${}^{208}$Pb using current-generation radioactive beam facilities. Both complete fusion and breakup fusion processes occur in the interaction of ${}^{11}$Li with ${}^{208}$Pb. An important breakup process leads to the fusion of the ${}^9$Li fragment with ${}^{208}$Pb.

Figure 1

Various theoretical predictions for the ${}^{11}$Li + ${}^{208}$Pb fusion excitation function, after Refs. [1, 2]. See text for a detailed discussion.

Figure 2

Comparison of measured nuclidic yields (data points) from the ${}^9$Li + ${}^{208}$Pb reaction with predictions of Refs. [32, 33, 34] (lines).

Figure 3

Comparison of the measured fusion excitation function [31] for the ${}^9$Li + ${}^{208}$Pb reaction with the predictions of coupled channels calculations and with Ref. [4].

Figure 4

Schematic diagram of the experimental apparatus.

Figure 5

Photographs of cubical scattering chamber array showing (a) overall view, (b) the target and detectors, and (c) the detectors only.

Figure 6

A typical $\alpha$ spectrum.

Figure 7

Comparison of EVR measurements for the ${}^7$Li + ${}^{209}$Bi reaction.

Figure 8

Comparison of predictions of Refs. [32, 33, 34] (lines) for the ${}^{11}$Li + ${}^{208}$Pb reaction.

Figure 9

Comparison of predictions of Refs. [32, 33, 34] (lines) for complete fusion in the ${}^{11}$Li + ${}^{208}$Pb reaction with the measured data.

Figure 10

Comparison of measured nuclidic yields (data points) from the ${}^9$Li + ${}^{208}$Pb reaction with the shifted yields from the ${}^{11}$Li + ${}^{208}$Pb reaction.

Figure 11

Comparison of various theoretical predictions for the ${}^{11}$Li + ${}^{208}$Pb fusion excitation function, after Refs. [1, 2], with our data.

Figure 12

Comparison of coupled-channels calculations and data for the total interaction cross sections for ${}^{9,11}$Li with ${}^{208}$Pb.

Figure 13

Comparison of the “reduced” fusion excitation functions for the ${}^6$Li + ${}^{208}$Pb [12], ${}^7$Li + ${}^{208}$Pb [10], ${}^8$Li + ${}^{208}$Pb [13], the ${}^9$Li + ${}^{208}$Pb reactions [31] and the ${}^{11}$Li + ${}^{208}$Pb reaction (this work).