We make variational estimates for the binding energies of ²H, ³H, ⁴He, ¹⁶O, ⁴⁰Ca, showing their running with the Similarity Renormalization Group (SRG) cutoff towards the infrared region and show the generalized Tjon lines that emerge from the calculations. We infer the SRG evolution of the three-body contributions for the ³H and ⁴He binding energies by computing the two-body contributions with a variational approach assuming that four-body forces are negligible. At any given SRG cutoff, the three-body contributions may then be inferred as being the experimental value minus the two-body contributions. The off-shell/on-shell transition at a critical SRG cutoff ${\lambda }_c$ drives the behavior of all binding energies and this scale is the turning point of the generalized Tjon lines. Also, at ${\lambda }_c$ the ratios between three-body and two-body contributions to the binding energies, $B_{{\lambda }_c}\left(3\right)∕B_{{\lambda }_c}\left(2\right)$, are the same in both ³H and ⁴He systems and equal to $1∕4$, so that $B_{{\lambda }_c}\left(2\right)=4B_{{\lambda }_c}\left(3\right)$. All calculations are carried out with the Idaho–Salamanca N3LO potential, which is evolved with the SRG up to the infrared fixed point ($\lambda \to 0$) in all S, P, D, F and G partial-wave channels in order to compute the variational binding energies at several SRG cutoff scales.

我们对² H，³ H，⁴ He，¹⁶ O，⁴⁰ Ca的结合能进行了变分估计，显示了它们以相似重整化组（SRG）截止向红外区域的运行，并显示了从Thon线出现的广义Tjon线计算。我们推断出³ H和⁴的三体贡献的SRG演化他假设四体力可忽略不计，通过变分方法计算两体贡献来束缚能量。在任何给定的SRG截止值处，然后可以将三体贡献推断为实验值减去两体贡献。临界SRG截止时的脱壳/脱壳过渡${\lambda }_C$驱动所有结合能的行为，该尺度是广义Tjon线的转折点。另外，在${\lambda }_C$ 三体和两体对结合能的贡献率， ${乙}_{{\lambda }_C}（3）∕{乙}_{{\lambda }_C}（\mathrm{2个}）$，在³ H和⁴ He系统中都相同，等于$\mathrm{1个}∕4$， 以便 ${乙}_{{\lambda }_C}（\mathrm{2个}）=4{乙}_{{\lambda }_C}（3）$。所有计算均使用爱达荷州-萨拉曼卡N3LO电势进行，该电势随SRG演化到红外固定点（$\lambda \to 0$）在所有S，P，D，F和G子波通道中，以计算几个SRG截止尺度下的变化结合能。