A new Δh method for finding the asymptotic normalization coefficient (ANC) was recently proposed by the author (2021). It was shown that the denominator of the re-normalized scattering amplitude ${\tilde{f}}_l$ includes the factor $d_l(E)={\mathrm{\Delta }}_l(E)+h_{\mathrm{r}}(E)-h(\eta )$, where ${\mathrm{\Delta }}_l(E)$ is the nuclear interaction part of the effective-range function (ERF) and $\mathrm{\Delta }h(E)=h_{\mathrm{r}}(E)-h(\eta )$ is the difference of the related Coulomb terms. Here $h_{\mathrm{r}}(E)=\mathrm{Re}h(\eta )$ for $E>0$, $\eta =1/a_{\mathrm{B}}k$ is the Sommerfeld parameter, $a_{\mathrm{B}}$ is the Bohr radius. The equation $d_l(E)=0$ determines the ${\tilde{f}}_l$ poles at $E=-\epsilon$ (ε is a binding energy). In the present paper to calculate $\mathrm{\Delta }h(-\epsilon )$ the function $h_{\mathrm{r}}(E)$ is analytically continued to $E<0$. For this the series of $h_{\mathrm{r}}(E)$ in powers of ${(a_{\mathrm{B}}k)}^2$ which converges if ${(a_{\mathrm{B}}k)}^2<1$ should be used. It is found that the first dominant term ${(a_{\mathrm{B}}k)}^2/12$ of the asymptotic series h_as(E) is the same for $h_{\mathrm{r}}$(E) and h(η) (at $E<0$ for h(η)) when E→0. The subtraction of this dominant term from both $h_{\mathrm{r}}$(E) and h(η) simplifies the Δh(−ε) calculation. Here the Δh method applies to the ground and first excited S-wave bound states of ¹⁶O (¹⁶O${\leftrightarrow }^4$He${+}^{12}$C) which meet the condition $|a_{\mathrm{B}}k{|}^2<1$. For ¹⁶O the standard ERF method does not work due to the large product Z₁Z₂ of the ⁴He and ¹²C charges. For the P− and D- wave ¹⁶O states the binding energies ε are so small that the approximate Δ method, when $d_l(E)\approx {\mathrm{\Delta }}_l(E)$, is valid. ANCs for the ground and first excited P-wave bound states of ⁷Be (⁷Be${\leftrightarrow }^3$He${+}^4$He) are also calculated by polynomial fitting the sum ${\mathrm{\Delta }}_l(E)+h_{\mathrm{r}}(E)$ up to $E^2$ in an analogy with the ERF method. The results for Δh and EFR methods are close to each other. For this system $a_{\mathrm{B}}\kappa >1$ and the Δh method has no advantages over the standard ERF method. The Δh method opens up a new direction for systems with large Z₁Z₂ values when the ERF method no longer works.

作者（2021）最近提出了一种新的 Δh 方法，用于寻找渐近归一化系数（ANC）。结果表明，重新归一化的散射幅度的分母${\stackrel{～}{F}}_{升}$ 包括因素 $d_{升}(乙)={\mathrm{\Delta }}_{升}(乙)+H_{\mathrm{r}}(乙)-H(\eta )$， 在哪里 ${\mathrm{\Delta }}_{升}(乙)$ 是有效射程函数 (ERF) 的核相互作用部分，并且 $\mathrm{\Delta }H(乙)=H_{\mathrm{r}}(乙)-H(\eta )$是相关库仑项的差值。这里$H_{\mathrm{r}}(乙)=\mathrm{关于}H(\eta )$ 为了 $乙>0$, $\eta =1/{\mathrm{一种}}_{\mathrm{乙}}克$ 是索末菲参数， ${\mathrm{一种}}_{\mathrm{乙}}$是玻尔半径。等式$d_{升}(乙)=0$ 决定了 ${\stackrel{～}{F}}_{升}$ 极点在 $乙=-\epsilon$（ε是结合能）。在本文中计算$\mathrm{\Delta }H(-\epsilon )$ 功能 $H_{\mathrm{r}}(乙)$ 继续分析 $乙<0$. 为此系列$H_{\mathrm{r}}(乙)$ 在权力的 ${({\mathrm{一种}}_{\mathrm{乙}}克)}^2$ 如果收敛 ${({\mathrm{一种}}_{\mathrm{乙}}克)}^2<1$应该使用。发现第一个显性项${({\mathrm{一种}}_{\mathrm{乙}}克)}^2/12$的渐近级数h_作为( E ) 是相同的$H_{\mathrm{r}}$( E ) 和h ( η ) (在$乙<0$对于h ( η )) 当E →0 时。从两者中减去这个主导项$H_{\mathrm{r}}$( E ) 和h ( η ) 简化了 Δ h (- ε ) 计算。这里所述的Δh方法适用于地面和第一激发小号-wave的束缚态¹⁶ O（¹⁶ ö${\leftrightarrow }^4$他${+}^{12}$C) 满足条件 $|{\mathrm{一种}}_{\mathrm{乙}}克{|}^2<1$. 对于¹⁶ O，由于⁴ He 和¹² C 电荷的大乘积 Z ₁ Z ₂，标准 ERF 方法不起作用。对于P - 和D - 波¹⁶ O 态，结合能ε非常小以至于近似 Δ 方法，当$d_{升}(乙)\approx {\mathrm{\Delta }}_{升}(乙)$， 已验证。用于接地和第一激发ANCS P的-wave束缚态⁷成为（⁷铍${\leftrightarrow }^3$他${+}^4$He) 也通过多项式拟合计算得出 ${\mathrm{\Delta }}_{升}(乙)+H_{\mathrm{r}}(乙)$ 取决于 ${乙}^2$类似于 ERF 方法。Δh 和 EFR 方法的结果彼此接近。对于这个系统${\mathrm{一种}}_{\mathrm{乙}}\kappa >1$Δh 方法与标准 ERF 方法相比没有优势。当 ERF 方法不再适用时，Δh 方法为具有较大 Z ₁ Z ₂值的系统开辟了新的方向。