Angular distributions of transfer reaction $^{208}$Pb($^{7}$Li,$^{6}$He)$^{209}$Bi
were measured at $E_{\mathrm{lab}}$($^7$Li) = 21.2, 24.3, 25.67, 28.55, 32.55, 37.55 and 42.55 MeV.
By fitting the experimental data with the theoretical frameworks
of Distorted Wave Born Approximation (DWBA), the optical
model parameters of halo nuclear system $^{6}$He + $^{209}$Bi were extracted.
The breakup threshold anomaly (BTA) was observed clearly in
the imaginary potential, and a further decreasing trend in the deep sub-barrier region
was observed for the first time in a halo system.
Furthermore, the dispersion relation is found of
no use to describe the connection between the real and imaginary parts.