Asymptotic characteristics of decay channels of states of light nuclei in the ab initio approach

A new convenient method for accurate theoretical calculations of quantities of traditional theory of nuclear reactions such as widths of resonances (including subthreshold), and asymptotic normalization coefficients is proposed. This provides a step towards the development of a new alternative technique for an ab initio description of light nuclei spectroscopic data. As an illustration of this method, the computational results for all relevant two-body decay channels of all known and some theoretically predicted states of ${}^7\mathrm{Li}$ nucleus are shown. Well proven on a large amount of data, the Daejeon16 potential was used in the calculations. The greatest part of the results turn out to be in a good agreement with the experimental data contained in spectroscopic tables.

Figure 1

CFFs ${\mathrm{\Phi }}_l\left(\rho \right)$ for $7/2_1^{-}$ state of ${}^7\mathrm{Li}$ nucleus for ${}^4\mathrm{He}+{}^3\mathrm{H}$ decay channel computed using $N_{\mathrm{tot}}^{\max }=15$ and different values of cutoff parameter $N_{cl}^{\max }$: 0 – solid line, 2 – dashed line, 4 – dashed-dotted line.

Figure 2

Asymptotic regular (dashed line) and irregular (solid line) solutions for $7/2_1^{-}$ state of ${}^7\mathrm{Li}$ nucleus for ${}^4\mathrm{He}+{}^3\mathrm{H}$ channel.

Figure 3

Logarithmic derivatives of CFF ${\mathrm{\Phi }}_l\left(r\right)$ (solid line) and irregular asymptotic solution $G_l\left(\rho \right)$ (dashed line) for $7/2_1^{-}$ state of ${}^7\mathrm{Li}$ nucleus for ${}^4\mathrm{He}+{}^3\mathrm{H}$ channel.

Figure 4

Asymptotic normalization coefficient (${\mathrm{fm}}^{-1/2}$) in the region of matching point for the $3/2^{-}$ (solid line) and $1/2^{-}$ (dashed line) states. Triangles indicate positions of the matching point.

Figure 5

The ratio of the CFF and the irregular Coulomb function ${\mathrm{\Phi }}_l\left(r\right)/G_l(\eta ,kr)$ in the region of the matching point for the $7/2_1^{-}$ (solid line), $5/2_1^{-}$ (dashed line), and $5/2_2^{-}$ (dashed-dotted line) states and the ratio of the CFF ${\mathrm{\Phi }}_l\left(r\right)$ and ${\left[G_l^2(\eta ,kr)+F_l^2(\eta ,kr)\right]}^{1/2}$ (dotted line) for high-excited $7/2_2^{-}$ state. Triangles indicate positions of the matching point.