We analyze the collision of three particles with arbitrary mass ratio at zero collision energy, assuming arbitrary short-range potentials, and generalize the three-body scattering hypervolume $D$ first defined for identical bosons in 2008. We solve the three-body Schrödinger equation asymptotically when the three particles are far apart or one pair and a third particle are far apart, deriving two asymptotic expansions of the wave function, and the parameter $D$ appears at the order $1/B^4$, where $B$ is the overall size of the triangle formed by the particles. We then analyze the ground state energy of three such particles with vanishing or negligible two-body scattering lengths in a large periodic volume of side length $L$, where the three-body parameter contributes a term of the order $D/L^6$. From this result we derive some properties of a two-component Bose gas with negligible two-body scattering lengths: its energy density at zero temperature, the corresponding generalized Gross-Pitaevskii equation, the conditions for the stability of the two-component mixture against collapse or phase separation, and the decay rates of particle densities due to three-body recombination.

中文翻译：

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不等质量粒子的三体散射超体积

我们分析了三个具有任意质量比的粒子在零碰撞能量下的碰撞，假设任意短程势，并概括了三体散射超体积 $D$ 在 2008 年首次为相同的玻色子定义。当三个粒子相距很远或一对和第三个粒子相距很远时，我们渐近地求解三体薛定谔方程，推导出波函数的两个渐近展开式，以及参数 $D$ 出现在订单中 $1/{乙}^4$， 在哪里 $乙$是由粒子形成的三角形的整体大小。然后，我们分析了三个这样的粒子的基态能量，它们在边长的大周期体积中具有消失或可忽略的二体散射长度$升$，其中三体参数贡献了阶数 $D/{升}^6$. 根据这个结果，我们推导出具有可忽略的双体散射长度的双组分玻色气体的一些性质：它在零温度下的能量密度、相应的广义 Gross-Pitaevskii 方程、双组分混合物抵抗坍塌的稳定性条件或相分离，以及三体复合引起的粒子密度衰减率。