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

Abstract

Abstract 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 $$^4\mathrm{Li}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>Li</mml:mi> </mml:mrow> </mml:math> and compare it to that of $$^4\mathrm{He}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>He</mml:mi> </mml:mrow> </mml:math> to falsify one of the models. Since the masses of $$^4\mathrm{He}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>He</mml:mi> </mml:mrow> </mml:math> and $$^4\mathrm{Li}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>Li</mml:mi> </mml:mrow> </mml:math> are almost equal, the yield of $$^4\mathrm{Li}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>Li</mml:mi> </mml:mrow> </mml:math> is about 5 times bigger than that of $$^4\mathrm{He}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>He</mml:mi> </mml:mrow> </mml:math> 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 $$^4\mathrm{Li}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>Li</mml:mi> </mml:mrow> </mml:math> is weakly bound and loose. Consequently, the ratio of yields of $$^4\mathrm{Li}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>Li</mml:mi> </mml:mrow> </mml:math> to $$^4\mathrm{He}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>He</mml:mi> </mml:mrow> </mml:math> is significantly smaller in the coalescence model and it strongly depends on the collision centrality. Since the nuclide $$^4\mathrm{Li}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>Li</mml:mi> </mml:mrow> </mml:math> is unstable and it decays into $$^3\mathrm{He}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msup> <mml:mi>He</mml:mi> </mml:mrow> </mml:math> and p , the yield of $$^4\mathrm{Li}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>Li</mml:mi> </mml:mrow> </mml:math> can be experimentally obtained through a measurement of the $$p\!-\!^3\mathrm{He}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mspace/> <mml:mo>-</mml:mo> <mml:msup> <mml:mspace/> <mml:mn>3</mml:mn> </mml:msup> <mml:mi>He</mml:mi> </mml:mrow> </mml:math> correlation function. The function carries information not only about the yield of $$^4\mathrm{Li}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>Li</mml:mi> </mml:mrow> </mml:math> but also about the source of $$^3\mathrm{He}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msup> <mml:mi>He</mml:mi> </mml:mrow> </mml:math> and allows one to determine through a source-size measurement whether of $$^3\mathrm{He}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msup> <mml:mi>He</mml:mi> </mml:mrow> </mml:math> 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 $$^4\mathrm{Li}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>Li</mml:mi> </mml:mrow> </mml:math> nuclide. We discuss how to infer information about an origin of $$^3\mathrm{He}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msup> <mml:mi>He</mml:mi> </mml:mrow> </mml:math> from the correlation function, and finally a method to obtain the yield of $$^4\mathrm{Li}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>4</mml:mn> </mml:msup> <mml:mi>Li</mml:mi> </mml:mrow> </mml:math> is proposed.

Topics & Concepts