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<p>The response function of a many-fermion system, defined via the particle density fluctuations, diverges at very small momentum transfer <i>q</i>. This divergence leads to an unphysical behavior for the response function. We resolve this by introducing a correction term based on time-reversal symmetry. The modified response function is symmetric, well-behaved at low <i>q</i>, and simplifies within the impulse approximation to a form expressed through the momentum distribution. We apply both the original and corrected formulations to interacting nuclear matter. The corrected response function shows improved consistency with experimental data and theoretical definitions, especially when <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(q \rightarrow 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, where the correction term has the most significant effect. Additionally, calculations of the structure factor show that the correction ensures conformity with quantum-fluid sum rules at low momentum transfer, while its effect is negligible for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(q \ge 3~\textrm{fm}^{-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>≥</mo> <mn>3</mn> <mspace width="3.33333pt" /> <msup> <mtext>fm</mtext> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Correction to the response of many-fermion systems and its impulse approximation

  • 期刊论文

  • 发表日期：

    2026年2月10日

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  • Yahya Younesizadeh,
  • Younes Younesizadeh,
  • Shahab Zorriasatein

摘要

The response function of a many-fermion system, defined via the particle density fluctuations, diverges at very small momentum transfer q. This divergence leads to an unphysical behavior for the response function. We resolve this by introducing a correction term based on time-reversal symmetry. The modified response function is symmetric, well-behaved at low q, and simplifies within the impulse approximation to a form expressed through the momentum distribution. We apply both the original and corrected formulations to interacting nuclear matter. The corrected response function shows improved consistency with experimental data and theoretical definitions, especially when \(q \rightarrow 0\) q → 0 , where the correction term has the most significant effect. Additionally, calculations of the structure factor show that the correction ensures conformity with quantum-fluid sum rules at low momentum transfer, while its effect is negligible for \(q \ge 3~\textrm{fm}^{-1}\) q ≥ 3 fm - 1 .