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A theoretical investigation is conducted on the s- and p-wave elastic scatterings of positronium by a lithium ion Li+ with the scattering energy below 1.41 eV, corresponding to the threshold of the e+-Li channel. The confined variational method is applied to serve as the theoretical framework for this study. To accurately account for correlations between involved particles, explicitly correlated Gaussians are employed as basis functions, which are optimized through a hybrid approach combining stochastic variational and energy-gradient-based methods. Additionally, a straightforward yet effective algorithm is developed for the automatic adjustment of confining potentials. The s-wave zero-energy pickoff annihilation parameter 1Zeff,0 is accurately determined to be 0.126 ± 0.002, which yields an enhancement factor of 1.88 compared with the value 0.067 obtained using the fixed-core stochastic variational method [Phys. Rev. A 65, 034709 (2002)]. Finally, a broad p-wave resonance structure is predicted at the incident energy of approximately 0.27 eV, with the annihilation parameter 1Zeff,1 at the resonance center estimated to be around 0.034. 

The confined variational method is used to study the elastic scattering of the positron from the ground-state helium with the scattering energy in the range from 0.05 eV to 11.02 eV. Describing the correlation effect with explicitly correlated Gaussians, we obtain accurate phase shifts, S-wave scattering length, elastic scattering cross sections, and annihilation parameters for different incident momenta. Specifically, by a least-squares fit of the data to the effective-range theory, we determine the room temperature annihilation parameter Zeff = 3.955, which is in perfect agreement with the measured result of 3.94 ± 0.02 [J. Phys. B 8, 1734 (1975)].