Employing the covariant baryon chiral perturbation theory, we calculate the leading and next-to-leading order two-pion exchange (TPE) contributions to $NN$ interactions up to order $O(p^3)$. We compare the so-obtained $NN$ phase shifts of $2\leq L\leq 6$ and mixing angles of $2\leq J\leq6$ with those obtained in the non-relativistic baryon chiral perturbation theory, which allows us to check the relativistic corrections to the middle-range part of $NN$ interactions. We show that the contributions of relativistic TPE are more moderate than those of the non-relativistic TPE. The relativistic corrections play an important role in F-waves especially the $^3\text{F}_2$ partial wave. Moreover, the relativistic results seem to converge faster than the non-relativistic results in almost all the partial waves studied in the present work, consistent with the studies performed in the one-baryon sector.

中文翻译：

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协变重子手性微扰理论中核子-核子相互作用的双介子交换贡献

使用协变重子手性扰动理论，我们计算了前导和次前导双离子交换 (TPE) 对 $NN$ 相互作用的贡献，直到 $O(p^3)$ 阶。我们将如此获得的 $2\leq L\leq 6$ 的 $NN$ 相移和 $2\leq J\leq6$ 的混合角与在非相对论重子手征扰动理论中获得的相移进行比较，这使我们能够检查对 $NN$ 相互作用的中间部分的相对论修正。我们表明相对论 TPE 的贡献比非相对论 TPE 的贡献更温和。相对论修正在 F 波中起着重要作用，尤其是 $^3\text{F}_2$ 分波。此外，在目前工作中研究的几乎所有部分波中，相对论结果似乎比非相对论结果收敛得更快，