非整数几何中的两体连续态
Two-body continuum states in non-integer geometry
摘要：
研究了两个短程相互作用粒子在形变外振子场中的波函数、相移和相应的弹性截面。为此，我们使用等效的$d$ -方法采用非整数维$d$。使用方阱势，我们推导出散射长度和相移的解析表达式。特别是，我们考虑的尺寸，$d_E$，为无限的散射长度，其中Efimov效应发生通过添加第三个粒子。我们明确给出了$d$和普通三维空间中等效的连续波函数，并证明了两种方法中相移是相同的。因此，$d$方法可以用来获得低能量的两体弹性截面在一个外场。
英文摘要：
Wave functions, phase shifts and corresponding elastic cross sections are investigated for two short-range interacting particles in a deformed external oscillator field. For this we use the equivalent $d$-method employing a non-integer dimension $d$. Using a square-well potential, we derive analytic expressions for scattering lengths and phase shifts. In particular, we consider the dimension, $d_E$, for infinite scattering length, where the Efimov effect occurs by addition of a third particle. We give explicitly the equivalent continuum wave functions in $d$ and ordinary three dimensional (3D) space, and show that the phase shifts are the same in both methods. Consequently the $d$-method can be used to obtain low-energy two-body elastic cross sections in an external field.
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