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Quasiparticle scattering rate in a strongly polarised Fermi mixture

We analyse the scattering rate of an impurity atom in a Fermi sea as a function of momentum and temperature in the BCS-BEC crossover. The cross section is calculated using a microscopic multichannel theory for the Feshbach resonance scattering, including finite range and medium effects. We show that pair correlations significantly increase the cross section for strong interactions close to the unitarity regime. These pair correlations give rise to a molecule pole of the cross section at negative energy on the BEC side of the resonance, which smoothly evolves into a resonance at positive scattering energy with a non-zero imaginary part on the BCS side. The resonance is the analogue of superfluid pairing for the corresponding population balanced system. Using Fermi liquid theory, we then show that the low temperature scattering rate of the impurity atom is significantly increased due to these pair correlations for low momenta. We demonstrate that finite range and mass imbalance effects are significant for the experimentally relevant $^6$Li-$^{40}$K mixture, and we finally discuss how the scattering rate can be measured using radio-frequency spectroscopy and Bose-Fermi mixtures.