Searching for $^4\overline{L}i$ by momentum correlation function of $\overline{p}-^3\overline{H}e$

The observed heaviest anti-nucleus so far is $^4\overline{H}e$ which is found in relativistic heavy ion collider in 2011. The yield of $^4\overline{L}i$ is four times bigger than that of $^4\overline{H}e$ according to the thermal model. From previous scattering experiment, we know that the $^4Li$ has a very short life time about $1.197\times10^{-22}s$. It decays into $^3{H}e$ and ${p}$. In experiment, the correlation function of $\overline{p}-^3\overline{H}e$ will offer us a method to observe $^4\overline{L}i$ by CPT symmetry. In this paper, we use the blast-wave model and Lednicky-Lyuboshitz analytical model to obtain a prediction of the correlation function of $\overline{p}-{}^3\overline{H}e$ with/without $^4\overline{L}i$ decay in Au + Au collisions at $\sqrt{S_{NN}}$ = 200 GeV. The correlation function with $^4\overline{L}i$ decay is found to exhibit a peak at $k^* \approx$ 0.073GeV/$c$. The results offer a guide for the experimental search for $^4\overline{L}i$ in relativistic heavy ion collision.