Production of $^4{\rm Li}$ and $p\!-\!^3{\rm He}$ correlation function in relativistic heavy-ion collisions

The thermal and coalescence models both describe well yields of light nuclei produced in relativistic heavy-ion collisions at LHC. We propose to measure the yield of $^4{\rm Li}$ and compare it to that of $^4{\rm He}$ to falsify one of the models. Since the masses of $^4{\rm He}$ and $^4{\rm Li}$ are almost equal, the yield of $^4{\rm Li}$ is about 5 times bigger than that of $^4{\rm He}$ in the thermal model because of different numbers of spin states of the two nuclides. Their internal structures are, however, very different: the alpha particle is well bound and compact while $^4{\rm Li}$ is weakly bound and loose. Consequently, the ratio of yields of $^4{\rm Li}$ to $^4{\rm He}$ is significantly smaller in the coalescence model and it strongly depends on the collision centrality. Since the nuclide $^4{\rm Li}$ is unstable and it decays into $^3{\rm He}$ and $p$, the yield of $^4{\rm Li}$ can be experimentally obtained through a measurement of the $p\!-\!^3{\rm He}$ correlation function. The function carries information not only about the yield of $^4{\rm Li}$ but also about the source of $^3{\rm He}$ and allows one to determine through a source-size measurement whether of $^3{\rm He}$ is directly emitted from the fireball or it is formed afterwards. We compute the correlation function taking into account the $s-$wave scattering and Coulomb repulsion together with the resonance interaction responsible for the $^4{\rm Li}$ nuclide. We discuss how to infer information about an origin of $^3{\rm He}$ from the correlation function, and finally a method to obtain the yield of $^4{\rm Li}$ is proposed.