| Summary: | We analyze the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>p</mi><mi>T</mi></msub></semantics></math></inline-formula> spectra of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>π</mi><mo>±</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>K</mi><mo>±</mo></msup></semantics></math></inline-formula>, <i>p</i>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>p</mi><mo>¯</mo></mover></semantics></math></inline-formula> produced in different centralities’ Au-Au collisions at different collision energies from 7.7 to 62.4 GeV using a two-component Erlang distribution in the framework of a multi-source thermal model. The fitting results are consistent with the experimental data, and the yield ratios of negative to positive particles are obtained from the normalization constants. Based on the yield ratios, the chemical potentials of light hadrons (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula>, <i>K</i>, and <i>p</i>) and quarks (<i>u</i>, <i>d</i>, and <i>s</i>) are extracted. This study shows that only the yield ratios of <i>p</i> decrease with the increase in centrality. The logarithms of these yield ratios in the same centrality show obvious linear dependence on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt></mrow></semantics></math></inline-formula>. The extracted chemical potentials (the absolute magnitude for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula>) of light hadrons and quarks decrease with the increase in energy. The curves of chemical potential vs. energy for all centralities derived from the linear fits of the logarithms of the yield ratio as a function of energy have their maximum (the absolute magnitude for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula>) at the same energy of 3.526 GeV, which is possibly the critical energy of phase transition from a liquid-like hadron state to a gas-like quark state in the collision system.
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