New measurement of the ${}^{144}\mathrm{Sm}(\alpha ,\gamma ){}^{148}\mathrm{Gd}$ reaction rate for the $\gamma$ process

Background: Most of the heavier $p$ isotopes are believed to be produced in the $\gamma$ process whose reaction path crucially depends on the proton and $\alpha$-particle penetrability at sub-Coulomb energies. Both nuclei of the samarium $p$-process chronometer, ${}^{146}\mathrm{Sm}$ and ${}^{144}\mathrm{Sm}$, are produced in the $\gamma$ process, and their initial abundance ratio is very sensitive to the $(\gamma ,n)$ and $(\gamma ,\alpha )$ branching ratio on ${}^{148}\mathrm{Gd}$. The ${}^{148}\mathrm{Gd}(\gamma ,\alpha ){}^{144}\mathrm{Sm}$ reaction rate was measured roughly 20 years ago by means of the activation technique and its surprising results triggered adjustments to the global low-energy $\alpha +\text{nucleus}$ optical-model potentials (OMPs).

Purpose: We want to take advantage of modern $\alpha$-particle spectroscopy techniques in order to constrain the controversial previous results on the ${}^{148}\mathrm{Gd}(\gamma ,\alpha ){}^{144}\mathrm{Sm}$ reaction rate.

Method: The ${}^{148}\mathrm{Gd}(\gamma ,\alpha ){}^{144}\mathrm{Sm}$ reaction rate has been determined by measuring the cross section of the reverse reaction ${}^{144}\mathrm{Sm}(\alpha ,\gamma ){}^{148}\mathrm{Gd}$, applying the activation technique to the $\alpha$ decay of ${}^{148}\mathrm{Gd}$. Targets have been irradiated at the cyclotron of the Physikalisch-Technische Bundesanstalt in Braunschweig, Germany. The $\alpha$-particle spectroscopy has been carried out with a state-of-the-art low-background ionization chamber of the Technische Universität Dresden, Germany.

Results: Cross sections for the ${}^{144}\mathrm{Sm}(\alpha ,\gamma ){}^{148}\mathrm{Gd}$ reaction have been measured between 10.66 and 12.66 MeV with much higher precision than in the previous measurement. The results agree with earlier results within their uncertainties. The statistical-model analysis has been carried out using the talys code on the basis of the latest parametrizations of $\alpha$-OMPs. The best reproductions of the experimental results within the statistical model have been used to calculate the reaction rates.

Conclusion: The values presented here suggest a steeper increase in the astrophysical $S$ factor towards lower center-of-mass energies. Different parametrizations of the $\alpha$-OMP were able to describe the experimental values sufficiently. Further measurements at energies below 11.0 MeV are suggested.

Figure 1

The relevant section of the nuclear chart. While ${}^{144}\mathrm{Sm}$ is produced via the $(\gamma ,\alpha )$ reaction on ${}^{148}\mathrm{Gd}, {}^{146}\mathrm{Sm}$ is the product of the decay chain starting at ${}^{146}\mathrm{Gd}$. The latter one is mainly produced via a series of $(\gamma ,n)$ reactions on stable gadolinium isotopes. After the activation, the nucleus ${}^{148}\mathrm{Gd}$ decays with a half-life of 71.10(12) yr [29] via $\alpha$ decay directly to the ground state of ${}^{144}\mathrm{Sm}$, leaving no $\gamma$-ray fingerprint. See text for details.

Figure 2

Top: Rutherford backscattering spectra for the different samples. Same shades represent same distance from the center of the sample. Bottom: Measured sample compositions as a function of the position on the targets. See text for details.

Figure 3

$\alpha$-particle spectra for all samples, irradiated with $\alpha$-particle energies of $E_{\alpha }=$ 13.0 to 11.0 MeV. The data are shown as crosses with their respective uncertainty bands. The solid lines show the result of the fraction fitting method for each sample. See text for details.

Figure 4

Measured cross section as a function of effective center-of-mass energy compared to the work of Somorjai et al. [31]. See text for details.

Figure 5

Measured cross section compared to statistical model calculations. ${\chi }^2$ values for the different models have been calculated for three different subsets of the experimental data, which are listed in Table 7. See text for details.

Figure 6

Visualization of the results of the hyperparameter optimization in comparison to the experimental values. See text for details.

Figure 7

The ratio of the $(\gamma ,n)$ and $(\gamma ,\alpha )$ reactions rates plotted together with the reaction rate from the Reaclib library [71]. The blue-shaded area represents a factor 10 uncertainty in the Reaclib predictions. The orange-shaded band represents the area of predictions from the best iterations of the hyperparameter optimization. The dashed line represents a ratio of one, indicating equality between the $(\gamma ,n)$ and $(\gamma ,\alpha )$ reaction rates. Hence, everything above the dashed line favors the production of ${}^{146}\mathrm{Sm}$ over ${}^{144}\mathrm{Sm}$. See text for details.