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

Abstract

AbstractThe 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 $$^4\mathrm{Li}$$ 4 Li and compare it to that of $$^4\mathrm{He}$$ 4 He to falsify one of the models. Since the masses of $$^4\mathrm{He}$$ 4 He and $$^4\mathrm{Li}$$ 4 Li are almost equal, the yield of $$^4\mathrm{Li}$$ 4 Li is about 5 times bigger than that of $$^4\mathrm{He}$$ 4 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 $$^4\mathrm{Li}$$ 4 Li is weakly bound and loose. Consequently, the ratio of yields of $$^4\mathrm{Li}$$ 4 Li to $$^4\mathrm{He}$$ 4 He is significantly smaller in the coalescence model and it strongly depends on the collision centrality. Since the nuclide $$^4\mathrm{Li}$$ 4 Li is unstable and it decays into $$^3\mathrm{He}$$ 3 He and p, the yield of $$^4\mathrm{Li}$$ 4 Li can be experimentally obtained through a measurement of the $$p\!-\!^3\mathrm{He}$$ p - 3 He correlation function. The function carries information not only about the yield of $$^4\mathrm{Li}$$ 4 Li but also about the source of $$^3\mathrm{He}$$ 3 He and allows one to determine through a source-size measurement whether of $$^3\mathrm{He}$$ 3 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 $$^4\mathrm{Li}$$ 4 Li nuclide. We discuss how to infer information about an origin of $$^3\mathrm{He}$$ 3 He from the correlation function, and finally a method to obtain the yield of $$^4\mathrm{Li}$$ 4 Li is proposed.