We study the three-boson bound-state mass and wave functions for ground and excited states within the three-body relativistic framework with Kamada and Glöcke boosted potentials in the limit of a zero-range interaction. We adopt a nonrelativistic short-range separable potential, with Yamaguchi and Gaussian form factors, and drive them towards the zero-range limit by letting the form factors' momentum scales go to large values while keeping the two-body binding fixed. We show that the three-boson relativistic masses and wave functions are model-independent towards the zero-range limit, and the Thomas collapse is avoided, while the nonrelativistic limit kept the Efimov effect. Furthermore, the stability in the zero-range limit is a result of the reduction of boosted potential with the increase of the virtual pair center of mass momentum within the three-boson system. Finally, we compare the present results with Light-Front and Euclidean calculations.

我们研究了三体相对论框架内基态和激发态的三玻色子束缚态质量和波函数，其中 Kamada 和 Glocke 增强了零距离相互作用极限的势。我们采用具有 Yamaguchi 和 Gaussian 形状因子的非相对论短程可分离势，并通过让形状因子的动量尺度达到大值同时保持二体绑定固定，将它们推向零范围极限。我们表明，三玻色子相对论质量和波函数在零范围极限附近与模型无关，并且避免了 Thomas 坍缩，而非相对论极限保持了 Efimov 效应。此外，零范围极限的稳定性是随着三玻色子系统中虚拟质心对动量的增加而增加的势能降低的结果。最后，我们将当前结果与 Light-Front 和 Euclidean 计算进行比较。