Stellar $s$-process neutron capture cross sections on ${}^{78,80,84,86}\mathrm{Kr}$ determined via activation, atom trap trace analysis, and decay counting

We present a detailed account of neutron capture experiments of astrophysical relevance on ${}^{78,80,84,86}\mathrm{Kr}(n,\gamma )$ reactions at the border between weak and main $s$ process. The experiments were performed with quasi-Maxwellian neutrons from the Liquid-Lithium Target (LiLiT) and the mA-proton beam at 1.93 MeV (2–3 kW) of the Soreq Applied Research Accelerator Facility (SARAF). The setup yields high-intensity $\approx 40$ keV quasi-Maxwellian neutrons (3–5 $\times {10}^{10} n$/s) closely reproducing the conditions of $s$-process stellar nucleosynthesis. A sample of 100 mg of atmospheric, pre-nuclear-age Kr gas contained in a Ti spherical shell was activated in the LiLiT neutron field. The abundances of long-lived Kr isotopes (${}^{81,85g}\mathrm{Kr}$) were measured by atom counting via atom trap trace analysis (ATTA) at Argonne National Laboratory and low-level counting (LLC) at University of Bern. This work is the first measurement of a nuclear cross section using atom counting via ATTA. The activities of short-lived Kr isotopes (${}^{79,85m,87}\mathrm{Kr}$) were measured by $\gamma$-decay counting with a high-purity germanium detector. Maxwellian-averaged cross sections for $s$-process thermal energies are extracted. By comparison to reference values, our nucleosynthesis network calculations show that the experimental cross sections have a strong impact on calculated abundances of krypton and neighboring nuclides, in some cases improving agreement between theory and observations.

Figure 1

The $s$-process path in the krypton region (thick arrows indicate the primary $s$-process flow, shaded lines indicate weaker captures). Green (solid horizontal arrows) mark the neutron capture reactions studied in this work by activation, while blue (diagonal) arrows identify $\beta$ decays. A zoom of the branching at ${}^{85}\mathrm{Kr}$, including $\beta$ decays and internal transitions, is highlighted.

Figure 2

(a) The 18 mm wide, 1.5 mm thick lithium film, as photographed through the vacuum chamber view port, flows on the concave back wall of the lithium nozzle. A tantalum plate used for beam positioning can be seen near the upper left corner of the lithium nozzle. When extracted, the plate clears the beam path. (b) Drawing of the nozzle and open duct. The holes in the sides of the nozzle “ears” are used for inserting thermocouple wires for temperature readings.

Figure 3

(a) Diagram of the Liquid-Lithium Target (LiLiT) and activation target assembly. The ($\approx 1.5$ mA, $\approx 9$ mm full width) proton beam (open red arrow) impinges on the free-surface lithium film (blue) (see [24] for details). The Kr-filled sphere (see text) and Au foil are positioned in the outgoing neutron cone (green dotted lines) in a vacuum chamber separated from the LiLiT chamber. The retractable shaft (at left) is used to load and unload rapidly the target assembly. (b) Photograph of the Kr gas sphere mounted in an aluminum circular frame on the center line of the chamber. A 0.5 mm thick pure Al plate (displaced for clarity to the bottom of the figure to unveil the sphere) supports the Au monitor and a thin (parasitic) ${\mathrm{ZrO}}_2$ target, covering the Kr-filled sphere. (c) Ti sphere (see [33] for details) used to contain the pressurized Kr gas for irradiation and the sphere holder for irradiation at SARAF-LiLiT.

Figure 4

(b) An auto-radiographic scan of the 13 mm diameter gold foil from the Kr irradiation above neutron production threshold. Colors indicate activity, decreasing from red to blue. (a) Profiles of a vertical (X) and horizontal (Y) slice of the scan. A vertical offset in neutron distribution (4.8(2) mm) is observed attributed to vertical steering of the proton beam. This offset is taken into account in the simulations.

Figure 5

(a) Part of the ${}^8\mathrm{Be}$ energy level scheme. The two high energy $\gamma$'s at 14.6 and 17.6 MeV are shown in red. See [23] for more details. (b) Spectrum of the ${}^{196}\mathrm{Au}$ decay from the ${}^{197}\mathrm{Au}(\gamma ,n){}^{196}\mathrm{Au}$ reaction in a Au monitor foil for the under threshold run (irradiation $B$). (c) Zoom in on the relevant photopeaks in the spectrum.

Figure 6

Simulated neutron spectrum (black histogram) impinging on the Kr, $\frac{d{n}_{\mathrm{sim}}}{d{E}_n}$. Also shown is a fit to Maxwell-Boltzmann (MB) distribution (red curve) $E_n{e}^{-\frac{E_n}{kT}}$ at 42.5 keV in the range of 0–120 keV.

Figure 7

Setup of the sphere placed in the lead brick with the stainless steel “stem” shielded by the lead and the Ti sphere, centered at 5 cm from the thin Be window on the face of the HPGe detector.

Figure 8

$\gamma$-ray spectrum obtained by counting sphere #43 activity for 1872 s, starting 9007 s after end of irradiation $A$ with an unshielded HPGe detector. The photopeaks from the decay of the activated $\mathrm{Kr}(n,\gamma )$ isotopes are labeled in keV.

Figure 9

$\gamma$-ray spectrum obtained by counting sphere #59 activity for 7208 s, starting 2844 s after end of irradiation $B$ with a shielded HPGe detector. The photopeaks from the decay of the activated $\mathrm{Kr}(\gamma ,n)$ isotopes are labeled in keV.

Figure 10

Decay curves of ${}^{79,85m,87}\mathrm{Kr}$. The half-lives obtained from exponential fits of the curves (see text) are in good agreement with the adopted values in the literature (labeled in the figure).

Figure 11

The number of ${}^{85m}\mathrm{Kr}$ decaying via ${\beta }^{-}$ calculated from the $\gamma$ photopeak at 151.2 keV [75.2(5)% intensity], and via IT calculated from the $\gamma$ photopeak at 304.9 keV [14.0(3)% intensity]. The measured ratio is 0.188(9) in good agreement with the intensity ratio 0.186(4) in [49] (see Table 2).

Figure 12

Typical spectrum of the trap capture rate of ${}^{81,83,85}\mathrm{Kr}$ versus laser frequency shift (relative to a reference transition in stable ${}^{84}\mathrm{Kr}$) measured for an atmospheric Kr sample (${}^{81}\mathrm{Kr}/\text{Kr}=9.3\times {10}^{-13}$ [39]). Figure adapted from [52], see text.

Figure 13

(a) Schematic of the ATTA atomic beamline. Atoms (dotted line) travel from left to right, starting at the radio-frequency discharge source, passing through laser-induced collimation and Zeeman slowing stages, and ending in the MOT where they are imaged by a CCD camera. (b) Integrated CCD camera signal (divided by 1000) over a region of interest during the ${}^{81}\mathrm{Kr}$ trapping cycles over the course of measuring the Kr gas sample (irradiation $B$) displayed vs time. Zero-, one- and two-${}^{81}\mathrm{Kr}$ atom trapping events are observed.

Figure 14

Sample (upper histogram) and background (lower) $\beta$ spectra for measurement 1. Only a fraction of the particle decay energy (687 keV) is released within the counter before they reach its wall. Events with energies greater than 33 keV are recorded as saturated events in the last MCA channels and are included in the ${}^{85}\mathrm{Kr}$ activity analysis.

Figure 15

514 keV photopeak next to the 511 keV photopeak for the irradiation above neutron production threshold. This region in the spectrum was fitted to two Gaussians and a linear background. The amount of ${}^{85g}\mathrm{Kr}$ produced during the irradiation was determined from this fit (see Table 5).

Figure 16

Comparison of the ${\mathrm{MACS}}_{\exp }$(30 keV) measured in this work (red squares) with previously measured MACS. Black (blue) open dots correspond to time-of-flight (activation) experiments.

Figure 17

Astrophysical reaction rates for ($n,\gamma$) reactions on Kr isotopes calculated with the MACS values of Table 12.

Figure 18

Ratios between the yields obtained with cross sections measured in this work and those calculated with reference cross sections ref A (low-mass star) and ref B (massive star): (a) nuclides are grouped by atomic number; (b) selected nuclides whose yields differ by more than 5%. See text for details.