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In this investigation, we examine how the precision of energy spectra andscattering phase shifts, extracted in lattice QCD, depend upon the degree ofdistillation type smearing. We use the variational method to extract energyspectra for the isospin-1, $J^{PC}=1^{--}$ channel and use the L\"{u}schermethod to compute scattering amplitudes, relevant for the $\rho$ resonance, in$\pi\pi$ elastic scattering. Optimised interpolating operators for a singleground state pion are constructed and these are used to construct two pionoperators. Calculations are performed on an anisotropic lattice with a pionmass of $m_\pi=236$ MeV. We provide a comprehensive comparison of energyspectra and scattering phase shifts across distillation spaces of varying rank.

Utilising optimised operators and distillation to extract scattering phase shifts