Neutron capture cross section of 83 Kr

The neutron capture cross section of 83 Kr has been measured via the time-of-ﬂight technique between 25 meV and 500 keV. The experiment used the DANCE array at the Los Alamos National Laboratory. Maxwellian Averaged Cross Sections have been derived for a range of stellar temperatures and are found to be in good agreement with previous data. The impact of the new cross sections on stellar nucleosynthesis has been investigated.


Introduction
Nearly all elements heavier than iron are produced in a neutron induced process. The two major processes are the r process (rapid) and the s process (slow) which differ mainly by neutron density and duration. While the range for neutron density during the s process is 10 8 < n n cm −3 ≤ 10 12 with exposure times upto thousands of years, the neutron density during the r process is 10 20 < n n cm −3 ≤ 10 22 lasting only for a few seconds [1,2]. Only a few isotopes on the proton-rich side of the valley of stability get significant contributions from other processes like the γ -process [3][4][5].
About 50% of the elements beyond strontium are produced during the main component of the s-process, which takes place in thermally pulsing Red Giant stars (TP-AGB). These stars have left the main sequence after finishing hydrogen core burning. They are about 50-100 times bigger and cooler than our sun while their masses are between 3 and 9 solar masses [6]. In the classical picture, the s-process starts with an iron seed exposed to free neutrons. Since the neutron densities are low, an unstable isotope produced by a series of neutron capture reactions will almost always β-decay back to its stable isobar before capturing another neutron. Thus, the a e-mail: reifarth@physik.uni-frankfurt.de (corresponding author) s-process builds up the elements following the neutron-rich side of the nuclear valley of stability until it terminates in the lead-bismuth region. In the more advanced stellar picture, the seed is more than just iron, but also other elements from previous phases or original composition of the star [7].
If the neutron capture rate is comparable to the β-decay rate a so called branching points exists. This means the sprocess path can follow two distinct ways. The branching ratio is hereby depended on the temperature of the star [8,9].
In this paper we report on measurments of the neutron capture cross sections of 83 Kr near the branching point 85 Kr [10]. The experiment was performed at Los Alamos Neutron Science Center (LANSCE) using the 4π BaF 2 Detector for Advanced Neutron Capture Experiments (DANCE) [11]. This allowed using Q-value and multiplicity cuts to discriminate between respective Kr isotope and background events.

83 Kr sample
Preparation of suitable samples provided a particular challenge. As krypton is a noble gas it exhibits a low freezeout temperature (120 K at standard pressure), which complicated the filling process of the utilized high pressure stainless steel spheres with a diameter of 10 mm and 0.2 mm wall thickness, see Fig. 1. Further details can be found here [12]. Enriched 83 Kr with a purity of 99.933% was used [13]. The total amount of gas in the sphere was 26.12 ± 0.01 mg at a pressure of 13.79 bar. For the use at DANCE a new target holder had to be designed that held the gas sphere at an angle of 61 degrees so only the gas filled spherical top part was inside the neutron beam. The overall length of this target holder design is 66.4 mm and therefore about 18.7 mm longer compared to the standard holder that is usually used at DANCE. During the designing special attention was given to the centering of the gas sphere in the detector.

Experiment
The experiment to determine the neutron capture cross section for 83 Kr was performed at Lujan Neutron Scattering Center at LANL [14]. The facility provides white neutron pulses with a repetition rate of 20 Hz. The neutrons are produced via a spallation reaction triggered by a proton beam impinging a tungsten block with a current of about 100 µA [15,16]. To measure an energy depended cross section the time of flight method was employed, which uses the neutron flight time between production at the spallation target and the (n,γ )-reaction in the detector [17]. With a flight path of 20.28 m it is possible to determine the neutron energy of a reaction.

Dance
The main instrument to determine the (n,γ ) cross section was DANCE. A calorimetric detector composed of 162 elements, whereas two are left out for the beam pipe. The remaining 160 BaF 2 detectors cover a solid angle of 3.5π [18]. This allows the detection of the γ -rays of a cascade following a neutron capture event with very high efficiency. A high detection efficiency allows the discrimination of cneutron captures on different substances within a sample based on the sum of all γ -rays detected, which is close to the reaction Q-value. The detector segmentation was used to further differentiate between capture events on the sample and events caused by scattered neutrons by using the number of responding detectors of an event. Neighboring detectors which have fired were assumed to be a single cluster of detectors and the number of such clusters is referred to as the cluster multiplicity (Mcl) [19]. This which was used in the analysis of the Kr data. The detector sphere formed by the BaF 2 crytals has an inner radius of r i = 10.5 cm and an outer radius of r o = 16.5 cm. Inside this sphere, a 6 LiH sphere was placed to significantly suppress events caused by scattered neutrons [19].
The scintallator material BaF 2 contains an intrinsic and unavoidable Ra contamination from the productions process. The subsequent decay of Ra produces signals from the emitted α-particles. These signals can be distinguished from the γ -radiation by taking advantage of the two decay components of BaF 2 with τ fast = 0.6 ns− 0.8 ns and τ slow = 630 ns where the α-particles almost exclusively excite the slow component. By examining both components a data cut can be employed to remove the signals originating from α-particles (see [18] for details). 83 Kr was irradiated for about 3 h in total. To reduce pileup in the large resonances, the target mass was reduced to 26.12±0.01 mg. Further reduction was not sensible, because of the to resulting poor signal to background ratio. Most of the background originated from neutron interactions with the stainless steel sphere. Instead, the proton current reaching the spallation target was reduced to about 40 µA for 1 h. For the rest of the time allocated to the 83 Kr measurement, the full current was used to achieve good statistics in the regions between resonances. A second measurement with an identical empty target sphere and holder was performed to account for background from the detector and the sample.

Neutron monitor calibration
The characteristic neutron spectrum, (E), with the neutron energy E, from the spallation source at LANSCE had to be unfolded from the data to extract the capture cross section, σ (E). The general correlation is given by: σ (E)· (E) = C, with C the detected counts in the energy bin at E. For this purpose a 6 Li beam monitor (BM) was used, which was placed down-stream of the sample, outside the DANCE array. It detects the neutrons via 6 Li(n,α). To correct for the difference in flux a factor k BM was introduced so the flux at the sample is given by: To determine k BM an additional measurement using an Au foil with a thickness of 5000 Å was performed: Here Au denotes the detector efficiency which was determined with GEANT3 simulations (see Sect. 4.4).
At a neutron energy of 4.89 eV 197 Au(n,γ ) has a large resonance of 2.74 10 4 b. The measured data were fitted to the evaluated ENDF/B-VII.1 cross section [20]. k BM can then be used for all following Kr measurements.

Scatter correction
To correct for effects of scattering and absorption in the sample Monte Carlo simulations were performed using the evaluated capture and elastic scatter cross sections. Further parameter were the target geometry and the target density. For every energy step 10 6 neutrons were simulated and their path through the sample tracked and compared to an unscattered neutron. In case of low statistics the number of neutrons was increased in certain energy steps to reduce the uncertainty below 0.1%.

Energy calibration
Energy calibration was achieved using the intrinsic alpha activity of the detector material (see Sect. 3.1). For this method to work the alpha lines of Ra and Po, which is part of Ra decay chain, were initially calibrated with a 88 Y γ -source and verified with the same source at the end of the experiment. For every run the energy was then corrected with this γ -calibrated alpha spectrum.

Efficiency
To determine the correct detector efficiency for specific cuts to Mcl and deposited energy in the detector (E sum ) the detector response had to be simulated. For this work GEANT3 [21] simulations were chosen as they were successfully performed before and exhibited good agreement with former measurements [22,23]. First, γ -cascades were created using the tool DICEBOX [24], with these the efficiency could be simulated in GEANT3 using the complete DANCE setup.

DICEBOX
In DICEBOX a level structure is simulated above a critical energy E crit below which all levels with energy, spin and parity are known from measurements. To do this a Monte Carlo approach was chosen which uses, dependent on the simulated nucleus, different models for level density and photon strength functions to create the level structure of the excited nucleus. As it is uncertain which or if a physical model fully describes an excited nucleus, several models were employed. For E1 photon strength functions the Generalized Lorentzian Model [25] was used. For M1 a spinflip resonance plus low-energy enhancement given by the form DMG · ex p(−E g /E tr ) and the single-particle model in which the M1 photon strength function is a constant has been used. The single-particle model in which the E2 photon strength function is a constant was chosen for E2. For each set of models 15 realizations with 5 · 10 5 cascades were simulated whereas a realization is the creation of a nucleus with newly created level structure above E crit .

GEANT3
The γ -cascades obtained from DICEBOX were then implemented in the GEANT3-simulation of the DANCE array. The simulation included 160 BaF 2 crystals and the following specifications: • A spherical crystal mounting made of aluminum.
• A PVC crystal wrapping of about 0.7 mm.
• The photo multiplier tubes glued to the crystals. • A 6 LiH sphere with an inner radius of 10.5 cm and an outer radius of 16.5 cm.
• Two detectors that were mounted but not giving signals.
• The simulations uses the same energy threshold of 150 keV as the data analysis.
84 Kr contains a long lived level at 3.24 MeV with a half life of 1.83 µs [26] that occured about 2% of the time. This time is much longer than the coincidence window of 10 ns used for the measurement. To account for this level the cascade from DICEBOX was split and it is expected that in this case only a part of Q-value energy will be deposited in the detector.
The measured E sum spectra show very good agreement with the simulations in the resonances at 229 eV, 314 eV and 513 eV. However at the resonace at 28 eV simulations show larger discrepancies. The measured data show a shift to lower energies of the Q-value peak that cannot be reproduced with the simulations (see Fig. 3). In this energy range larger systematic uncertainties had to be taken into account.
The efficiency to detect a 83 Kr(n,γ ) event was calculated to 0.160 ± 0.004 if the same cuts on deposited energy and cluster multiplicity are applied as for the experimental data (see next section).

Cuts
The two dimensional spectrum measured with DANCE is shown in Fig. 4. These include a cut on the cluster mulciplicity Mcl. For 83 Kr an analysis of the Mcl distribution showed only a small amount of events with Mcl = 1 or Mcl = 2. As these contain overproportionally many events from scattered neutrons as well, they were not used for further analysis. The spectrum showed further events with Q-values other than the main Kr constituents. In the case of 83 Kr(n,γ ), with a Q-value of 10.52 MeV [20], this is mainly from the target sphere and holder as well as from the most common Ba isotopes 134 < A < 138. The high Q-value of 83 Kr(n,γ ) allowed for a energy cut E sum = 9.5-11 MeV removing almost all beam-related background events.

83 Kr cross section
To account for the high count rates in the resonances at 28 eV and 229 eV the sample was measured twice (see Sect. 3.2). The 40 µA measurement reduced pile-up in those resonances while the second 100 µA measurement collected enough statistics in the in regions between the resonances. Both measurements were then combined using Eq. 3.
(3)  [27] where N b,x is the number of events per energy bin and N p,x is the number of protons hitting the spallation target in the respective measurement. Furthermore the sample background from the steel sphere was subtracted from the spectrum by normalizing the measurement of the empty sphere to the 83 Kr spectrum. Here a strong 585 eV resonance from the steel sphere was chosen, that is also clearly visible in the 83 Kr measurement. Figure 5 shows the normalized spectra. The resulting spectrum in combination with the neutron scatter correction (Sect. 4.2), the efficiency (Sect. 4.4) and the neutron flux correction (Sect. 4.1) allowed for the calculation of the energy dependent neutron capture cross section using Eq. 4.
With i the respective energy bin, C x,i the events in either the 83 Kr or the background spectrum, σ BM,i the cross section of the neutron monitor, f sc, 83 Kr,i the scatter correction factor, N p the number of protons and 83 Kr the 83 Kr efficiency. The number of atoms was calculated using Eq. 5.
Here m83 Kr is the weight of the sphere with and m sphere without 83 Kr. M83 Kr is the molar mass and N A Avogadro constant. The resulting cross section is show in Fig. 6.

MACS
For the calculation of the astrophysically relevant MACS for 83 Kr Eq. 6 was used. Where i/ j is the respective energy bin, E i /E j the corresponding energy in the middle of that bin and E i / E j the bin width. As a result of the large uncertainties at an energy E n > 10 5 eV, the evaluated cross section was used for this energy region. With a correction factor k MACS from Eq. 7. Fig. 8 Ratio of the abundances of the nucleosynthesis products calculated with NETZ Fig. 9 Comparison of the NETZ simulations with Kr s-process abundances form SiC grains. Data from [32,33] MACS83 Kr = 4 π The MACS at different energies from 5 to 100 keV in comparison to the KADoNIS v0.3 values are shown in Table  1 and Fig. 7.

NETZ
To examine the impact of the 83 Kr neutron capture cross sections measured in this work, sensitivity studies with the tool NETZ [23,28,29] were performed. NETZ simulates a reaction network depending on neutron density, temperature, and electron density, where several neutron induced reaction channels are taken into account, as well as αand β-decays. The ratio of this work with KADoNIS v0.3 is shown in Fig.  8.
These simulations are the basis for a comparison of sprocess abundances gained from SiC grains. Such grains develop in the outer regions of AGB stars when the outer envelope is rich in carbon due to convection [30]. An analysis for different Kr isotopes was done by Pignatari et al. [31]. Figure 9 shows a comparison with the NETZ simulations. For that purpose, the absolute abundances from NETZ were normalized to the abundance of 82 Kr which is a s-only isotope. In accordance to Pignatari the data was again normalized to the solar abundance. A good agreement for 83 Kr and 84 Kr can be observed. For 86 Kr the difference is much larger with a factor of 2-8.

Summary
The neutron capture cross section of 83 Kr was measured at the DANCE setup at the Los Alamos National laboratory. The new data is in good agreement with data from the KADoNIS v0.3 database. The impact of the cross section measured in this work was analysed using the NETZ code. These results were additionally compared with presolar grain distribution from Pignatari et al.