超流核上的低能s波中子散射中的两个幺正极限
Two unitary limits in low-energy $s$-wave neutron scattering on superfluid nuclei
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中文总结 AI 辅助
本研究通过解析方法结合哈特利-福克-博戈留波夫框架与方势阱模型，揭示超流核低能s波中子散射中存在两个由对关联产生的幺正极限，明确了有效程展开的适用范围及共振极点的关键作用。
中文摘要 AI 辅助
弱束缚超流核中的低能s波散射强烈受到对关联的影响。本工作中，我们在坐标空间哈特利-福克-博戈留波夫（Hartree-Fock-Bogoliubov）框架内，利用示意方势阱模型对低能s波准粒子散射开展解析研究，统一推导了相移、弹性散射截面、散射长度及有效程的解析表达式。我们证明对关联会产生两个不同的幺正极限，其特征为散射长度发散：一个对应类粒子幺正极限，即使没有对关联也存在，且可由有效程展开很好描述；另一个是对关联诱导的类空穴幺正极限，与准粒子共振相关，导致有效程展开失效。这些结果明确了有效程展开的适用范围，凸显了共振极点在描述超流核低能s波准粒子散射中的关键作用。
英文摘要
Low-energy $s$-wave scattering in weakly bound superfluid nuclei is strongly influenced by pairing correlations. In this work, we present an analytical study of low-energy $s$-wave quasiparticle scattering within the coordinate space Hartree-Fock-Bogoliubov framework using a schematic square-well model. Analytical expressions for the phase shift, elastic cross section, scattering length, and effective range are derived in a unified manner. We demonstrate that pairing correlations give rise to two distinct unitary limits, characterized by the divergence of the scattering length. One corresponds to the particle-like unitary limit, which persists even without pairing and is well described by the effective range expansion. The other is a pairing-induced hole-like unitary limit associated with quasiparticle resonances, leading to a breakdown of the effective range expansion. These results clarify the validity of the effective range expansion and highlight the essential role of resonance poles in describing low-energy $s$-wave quasiparticle scattering in superfluid nuclei.
