论文标题
非整数几何形状中的两体连续态
Two-body continuum states in non-integer geometry
论文作者
论文摘要
研究了两个短距离相互作用的粒子在变形的外部振荡器场中的两个短距离相互作用的粒子，研究了波函数，相移和相应的弹性横截面。为此，我们使用同等的$ d $ -METHOD，使用非整数尺寸$ d $。使用方孔电势，我们得出用于散射长度和相移的分析表达式。特别是，我们考虑了无限散射长度的尺寸，即$ d_e $，其中通过添加第三个粒子发生Efimov效应。我们在$ d $和普通的三维（3D）空间中明确给出等效的连续波函数，并证明两种方法中的相移相一样。因此，$ d $ - 方法可用于在外部场中获得低能的两体弹性横截面。
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.
