We address the question of constraints on the $$\varLambda n$$ amplitude as a result of observing a $$\varLambda nn$$ resonance above the $$\varLambda nn$$ three-body threshold. To examine this question, we will first demonstrate that by starting with a $$\varLambda n$$ interaction based upon the experimental $$\varLambda p$$ data and then scaling the $$\varLambda n$$ potential by $$\approx 8\%$$ one can generate a $$\varLambda nn$$ resonance, and with a sufficiently large scaling one can generate a $$\varLambda nn$$ bound state. This is achieved using the three-body Faddeev equations with rank one separable potentials for all pairwise interactions. The use of separable potentials is motivated by two factors: (i) the Faddeev equations reduce to a set of one dimensional integral equations that can be analytically continued into the complex energy plane where resonances reside. (ii) The $$\varLambda n$$ amplitude can be defined in terms of the effective range parameters. As a result we can explore the question: What constraint can be placed on the $$\varLambda n$$ effective range parameters by the $$\varLambda nn$$ resonance parameters?

中文翻译：

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$$\varLambda nn$$ Λ nn 共振能约束$$\varLambda n$$ Λ n 振幅吗？

我们通过观察 $$\varLambda nn$$ 三体阈值上方的 $$\varLambda nn$$ 共振来解决 $$\varLambda n$$ 振幅的约束问题。为了研究这个问题，我们将首先证明，从基于实验性 $$\varLambda p$$ 数据的 $$\varLambda n$$ 交互开始，然后通过 $$\ 缩放 $$\varLambda n$$ 潜力大约 8\%$$ 可以生成 $$\varLambda nn$$ 共振，并且具有足够大的缩放比例可以生成 $$\varLambda nn$$ 绑定状态。这是使用三体 Faddeev 方程实现的，其中所有成对相互作用具有一级可分离势。可分离势的使用受到两个因素的推动：(i) Faddeev 方程简化为一组一维积分方程，这些方程可以解析地延续到共振所在的复能平面。(ii) $$\varLambda n$$ 振幅可以根据有效范围参数来定义。因此，我们可以探讨以下问题：$$\varLambda nn$$ 共振参数可以对 $$\varLambda n$$ 有效范围参数施加什么约束？