High-precision ${}^{144}\mathrm{Sm}(\alpha ,\alpha ){}^{144}\mathrm{Sm}$ scattering at low energies and the rate of the ${}^{144}\mathrm{Sm}(\alpha ,\gamma ){}^{148}\mathrm{Gd}$ reaction

Background: The $\alpha$-nucleus optical potential plays a crucial role in the calculation of $\alpha$-induced reaction cross sections at low energies in the statistical model which are the basis for the reliable prediction of astrophysical reaction rates.

Purpose: The present study attempts to constrain the $\alpha$-nucleus potential for ${}^{144}\mathrm{Sm}$ $+$ $\alpha$ by the analysis of angular distributions of ${}^{144}\mathrm{Sm}(\alpha ,\alpha ){}^{144}\mathrm{Sm}$ elastic scattering.

Methods: Between ${20}^{\circ }$ and ${175}^{\circ }$ complete elastic $\alpha$ scattering angular distributions were measured on the ${}^{144}\mathrm{Sm}$ $p$ isotope with high precision at $E_{\mathrm{lab}}$ = 16.13 MeV, at $E_{\mathrm{lab}}$ = 18.07 MeV, and at $E_{\mathrm{lab}}$ = 19.87 MeV.

Results: The angular distributions at 18 and at 20 MeV allow a determination of the parameters of the $\alpha$-nucleus potential with small uncertainties, whereas the 16 MeV data cannot constrain well these parameters. A prediction of the ${}^{144}\mathrm{Sm}(\alpha ,\gamma ){}^{148}\mathrm{Gd}$ cross section at very low energies from the present fits overestimates the experimental data from literature.

Conclusions: The tension between the relatively high cross sections from the analysis of elastic ($\alpha ,\alpha$) scattering at $16–20$ MeV and the low cross sections of the ($\alpha ,\gamma$) data at deep sub-Coulomb energies around 10 MeV requires further study. The energy gap between the ($\alpha ,\alpha$) and ($\alpha ,\gamma$) data can be best filled by new ($\alpha ,n$) data.

Figure 1

Schematic view of the scattering chamber with monitor detectors (M1 and M2, mounted in the wall of the chamber at fixed $\pm$ ${15}^{\circ }$ angles) and detectors (D1–D7 on the two turntables) used to measure the yield of the elastically scattered $\alpha$ particles. For details, see text.

Figure 2

Typical spectra at $E_{\alpha }$ = 16.13 MeV, ${\vartheta }_{\mathrm{lab}}$ = ${40}^{\circ }$ (a) and at $E_{\alpha }$ = 19.87 MeV, ${\vartheta }_{\mathrm{lab}}$ = ${140}^{\circ }$ (b). The peak from elastic ${}^{144}\mathrm{Sm}\text{−}\alpha$ scattering is well resolved from both elastic and inelastic events (the energies of the excited states are indicated in parenthesis). Note the logarithmic scale of all spectra.

Figure 3

Relative yield of ${}^{12}\mathrm{C}$ recoil nuclei in coincidence with elastically scattered $\alpha$ particles. A Gaussian fit to the experimental data is also shown. The shaded area represents the angular uncertainty.

Figure 4

Angular distribution of ${}^{144}\mathrm{Sm}(\alpha ,\alpha ){}^{144}\mathrm{Sm}$ elastic scattering at $E_{\alpha }$ = 16.13 MeV (normalized to Rutherford cross section). For further discussion see text.

Figure 5

Angular distribution of ${}^{144}\mathrm{Sm}(\alpha ,\alpha ){}^{144}\mathrm{Sm}$ elastic scattering at $E_{\alpha }$ = 18.07 MeV (normalized to Rutherford cross section). For further discussion see text.

Figure 6

Angular distribution of ${}^{144}\mathrm{Sm}(\alpha ,\alpha ){}^{144}\mathrm{Sm}$ elastic scattering at $E_{\alpha }$ = 19.87 MeV (normalized to Rutherford cross section). For further discussion see text.

Figure 7

Total reaction cross section ${\sigma }_{\mathrm{reac}}$ (shown as astrophysical $S$ factor) from the Atomki-V2 potential (full black line) and from the real parts of the fits at 16 MeV (violet dash-dotted), 18 MeV (orange long-dashed), and 20 MeV (green dotted). The total cross sections from the present analysis of elastic $(\alpha ,\alpha )$ scattering are shown by thick black circles (see also Table 1). In addition, ${\sigma }_{\mathrm{reac}}$ from the Atomki-V2 potential is decomposed into the $(\alpha ,\gamma )$ (red dotted) and $(\alpha ,n)$ (blue short-dashed) cross sections. The arrows indicate the classical Gamow windows for typical temperatures of the $p$ process. For further discussion see text.

Figure 8

Total real potential $V\left(r\right)=V_C\left(r\right)+\lambda ·V_F(r/w)$ of the global Atomki-V2 potential [28] as a reference and the fits at 16, 18, and 20 MeV. The inset shows the effective barrier which is higher for the fit with $w<1.0$ at 16 MeV and lower for the fits with $w>1.0$ at 18 and 20 MeV. The dashed black box indicates the range of the inset with $7.5\le r\le 12.5$ fm and $0\le V\left(r\right)\le 20$ MeV [i.e., the barrier region with repulsive $V\left(r\right)>0$.

Figure 9

Total reaction cross section ${\sigma }_{\mathrm{reac}}$ (shown as astrophysical $S$ factor) from the Atomki-V2 potential (full black line) and from various other global $\alpha$-OMPs from literature: McFadden and Satchler [40], Avrigeanu et al. [41], and Demetriou et al. [42]. The arrows indicate the classical Gamow windows for typical temperatures of the $p$ process; the vertical arrow indicates the $(\alpha ,n)$ threshold. For further discussion see text.