Determination of $^{170,172}$Yb($α,n$)$^{173,175}$Hf reaction cross sections in a stacked-target experiment

TL;DR

This work measures $^{170,172}$Yb($ alpha,n$)$^{173,175}$Hf cross sections using a novel stacked-target activation setup to probe the $ alpha$-nucleus optical-model potential relevant to the astrophysical p-process. Geant4-based energy-loss simulations determine interaction energies in each target layer and Mn benchmarks validate the energy determination, while background subtraction enhances sensitivity by about a factor of four. The measured cross sections agree well with TALYS-1.95 predictions across multiple $ alpha$-OMP choices, and cross-section ratios within the Yb chain are reliably reproduced, providing constraints on the evolution of the $ alpha$-OMP with neutron-to-proton ratio. These results improve input for astrophysical reaction networks and highlight the need for data on $^{174,176}$Yb to complete the chain, with in-beam experiments required for the stable products.

Abstract

The ytterbium isotopic chain offers multiple stable isotopes on which cross sections can be measured and insights into the evolution of the $α$ optical-model potential with the neutron-to-proton ratio can be gained. It also includes the $p$ nucleus $^{168}$Yb, the abundance of which is significantly impacted by the $^{164,166}$Yb($α,γ$) reactions. In order to study the $^{170,172}$Yb($α,n$)$^{173,175}$Hf reaction cross sections and compare them with $^{168}$Yb($α,n$)$^{171}$Hf cross sections, that have already been measured, the activation method was used. During irradiation the targets were arranged in stacks of four to reduce the required irradiation time. The average interaction energy inside each ytterbium layer was determined via Geant4 simulations. A manganese layer was used to verify the simulations by comparing the measured $^{55}$Mn($α,(2)n$)$^{57,58}$Co reaction cross sections to previous results. For irradiation the 10 MV FN tandem accelerator located at the University of Cologne was used and the activation measurement was performed utilizing the Cologne Clover Counting setup. For the $^{170}$Yb($α,n$) reaction seven cross sections at center-of-mass energies between 12.7 and 16.5 MeV were measured. For the $^{172}$Yb($α,n$) reaction six cross sections for center-of-mass energies of 13.1 to 16.5 MeV could be determined with an additional upper limit at E$_{c.m.}$ = 12.3 MeV. Comparisons to theoretical models show that state-of-the-art $α$-optical model potentials are able to reproduce the measured cross sections very well. The ratios of ($α, n$) reaction cross sections in the ytterbium isotopic chain can be accurately reproduced as well.

Figures (6)

• Figure 1: Sensitivity of theoretical cross sections for the $^{164,166,170,172}$Yb($\alpha,n$)$^{167,169,173,175}$Hf reactions to the $\alpha$-, $\gamma$-, proton- and neutron-widths. The sensitivities were taken from Ref. Rauscher.
• Figure 2: Water cooled target chamber designed to accommodate a stack of four targets. Above the chamber the target composition and the arrangement of targets in a stack are illustrated.
• Figure 3: Normalization of a background spectrum to a spectrum obtained from a $^{172}$Yb target. The original spectrum was obtained at an energy of E$_{c.m.}$ = 13.9 MeV and the background spectrum at an energy of E$_{c.m.}$ = 12.0 MeV. The inset shows the background subtraction resulting from it.
• Figure 4: Relative deviations between reaction yields determined from the spectra of all eight detector crystals and all observed $\gamma$-ray lines. Which $\gamma$-ray line was used is coded in colors and symbol shapes. The lower x-axis shows the number of the detector crystal used, where number 9 corresponds to the average of all individual detector crystals (light blue) and number 10 to the yield determined from the sum spectra (black). Whether the reaction yield was determined from original or background corrected spectra is marked by open or closed symbols. Yields determined from background corrected sum spectra were used as reference values. The upper x-axis displays the interaction energy at which the reaction yields were measured with vertical lines separating individual targets.
• Figure 5: Reaction cross sections determined for the $^{55}$Mn($\alpha,(2)n$)$^{57,58}$Co reference reactions (top panels) and the $^{170,172}$Yb($\alpha,n$)$^{173,175}$Hf reactions of interest (bottom panels). For the reference reactions previous results as well as theoretical values taken from the Tendl-2019 database are shown tanakaIwataXianguanRizviSinghLevkovskiTimsSudarTENDL-2019. Which kind of target was used to obtain the reaction cross sections is indicated by the labels $^{170}$Yb and $^{172}$Yb. More information on the analysis of the reference reactions will be published in a forthcoming paper. For the Yb reactions theoretical calculations performed using the Talys1.95 code are shown talys1.9. These calculations utilized various $\alpha$-OMPs introduced in Refs. aomp-mcfaddenaomp-demetriouaomp-koningBTM. Three $\alpha$-OMPs by Demetriou $\textit{et al.}$ are shown. The first of these uses an imaginary part consisting of a volume term only. The second adds a surface term to the imaginary part and the third one relates the imaginary part consisting of a volume and a surface term to the real part via a disperion relation. Theoretical values taken from the Tendl-2019 database are shown as well.