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arXiv 2302.08331quant-phcond-mat.quant-gas
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低能散射参数:任意angular momentum有效射程和散射长度的理论推导

Low-energy scattering parameters: A theoretical derivation of the effective range and scattering length for arbitrary angular momentum

Jordi Pera, Jordi Boronat

摘要:

低能散射研究中最重要的参数是横波和纵波散射长度以及横波有效射程。我们解决了散射问题,并找到了两个有用的公式的散射长度和有效范围的任何角动量,只要维格纳阈值定律成立。使用该形式主义,我们得到了一组有用的公式的角动量散射参数的四种不同的模型势:硬球,软球,球阱,以及势垒势。分析了接近于费什巴赫共振的散射参数的行为。我们的推导可以作为学习散射理论的实践活动。

英文摘要:

The most important parameters in the study of low-energy scattering are the s-wave and p-wave scattering lengths and the s-wave effective range. We solve the scattering problem and find two useful formulas for the scattering length and the effective range for any angular momentum, as long as the Wigner threshold law holds. Using that formalism, we obtain a set of useful formulas for the angular-momentum scattering parameters of four different model potentials: hard-sphere, soft-sphere, spherical well, and well-barrier potentials. The behavior of the scattering parameters close to Feshbach resonances is also analyzed. Our derivations can be useful as hands-on activities for learning scattering theory.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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