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<p>We simulated proton collective flows in Au + Au collisions at a beam energy of 1.23<i>A</i> GeV using the isospin-dependent quantum molecular dynamics model. We applied the event-plane method to calculate the first- to fourth-order flow coefficients in different <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(v_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>v</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> classes, studying the correlations among them. Nearly all event classes satisfy the scaling relation <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(v_3\propto v_{1}v_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>v</mi> <mn>3</mn> </msub> <mo>∝</mo> <msub> <mi>v</mi> <mn>1</mn> </msub> <msub> <mi>v</mi> <mn>2</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>. Quadrangular flow <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(v_4\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>v</mi> <mn>4</mn> </msub> </math></EquationSource> </InlineEquation> also approximately follows the scaling relation <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(v_4 = 0.5 v_2^2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>v</mi> <mn>4</mn> </msub> <mo>=</mo> <mn>0.5</mn> <msubsup> <mi>v</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </math></EquationSource> </InlineEquation>. Additionally, we calculated the Pearson correlation coefficients between the first to fourth harmonic flows for protons, thereby quantifying the inter-harmonic correlations. The Pearson linear correlation coefficient <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(corr(v_{n},\varepsilon _{n})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mi>o</mi> <mi>r</mi> <mi>r</mi> <mo stretchy="false">(</mo> <msub> <mi>v</mi> <mi>n</mi> </msub> <mo>,</mo> <msub> <mi>ε</mi> <mi>n</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> between each flow harmonic and the corresponding eccentricity under different centralities is also examined.</p>

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Correlations among proton collective flows in Au + Au collisions at Ebeam = 1.23A GeV within the isospin-dependent quantum molecular dynamics model

  • 期刊论文

  • 发表日期：

    2026年7月23日

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  • Ling-Meng Fang,
  • Yu-Gang Ma,
  • Song Zhang

摘要

We simulated proton collective flows in Au + Au collisions at a beam energy of 1.23A GeV using the isospin-dependent quantum molecular dynamics model. We applied the event-plane method to calculate the first- to fourth-order flow coefficients in different \(v_2\) v 2 classes, studying the correlations among them. Nearly all event classes satisfy the scaling relation \(v_3\propto v_{1}v_{2}\) v 3 ∝ v 1 v 2 . Quadrangular flow \(v_4\) v 4 also approximately follows the scaling relation \(v_4 = 0.5 v_2^2\) v 4 = 0.5 v 2 2 . Additionally, we calculated the Pearson correlation coefficients between the first to fourth harmonic flows for protons, thereby quantifying the inter-harmonic correlations. The Pearson linear correlation coefficient \(corr(v_{n},\varepsilon _{n})\) c o r r ( v n , ε n ) between each flow harmonic and the corresponding eccentricity under different centralities is also examined.