Accelerator mass spectrometry measurements of the C13 ( n , gamma ) C-14 and N14 ( n , p ) C-14 cross sections

Accelerator mass spectrometry measurements of the 13C(n,γ )14C and N(n, p)14C cross sections A. Wallner,1,* M. Bichler,2 K. Buczak,3 I. Dillmann,4,† F. Käppeler,4 A. Karakas,5 C. Lederer,3,‡ M. Lugaro,6 K. Mair,3 A. Mengoni,7 G. Schätzel,3 P. Steier,3 and H. P. Trautvetter8 1Department of Nuclear Physics, Research School of Physics and Engineering, The Australian National University, 2601, Canberra, Australia and VERA Laboratory, University of Vienna, A-1090 Vienna, Austria 2Atominstitut, Vienna University of Technology, A-1020 Vienna, Austria 3VERA Laboratory, University of Vienna, A-1090 Vienna, Austria 4Karlsruhe Institute of Technology (KIT), Campus North, Institute of Nuclear Physics, PO Box 3640, D-76021 Karlsruhe, Germany 5School of Astronomy & Astrophysics, Mt. Stromlo Observatory, Australian National University, Canberra, Australia 6Konkoly Observatory, Hungarian Academy of Sciences, Hungary 7CERN, CH-1211 Geneva 23, Switzerland 8Ruhr University Bochum, D-44801 Bochum, Germany (Received 1 November 2015; published 11 April 2016)


I. INTRODUCTION
Half of the elemental abundances of the heavy elements are built by the slow neutron capture process (s process). As only moderate neutron densities are reached during stellar evolution, neutron capture rates are of the order of several months to years, much lower than typical β decay rates, thus restricting the s-process reaction path essentially to a sequence of (n,γ ) reactions and β − decays along the stability valley. Accordingly, neutron cross sections are the key nuclear physics input for any quantitative s-process model. Stellar s-process scenarios are related to the He burning phases in massive stars and in thermally pulsing low-mass asymptotic giant branch (AGB) stars. Of special interest in the context of this work is the so-called main s component associated with AGB stars, where the 13 C(α,n) reaction constitutes the dominant neutron source, whereas the weak s process * anton.wallner@anu.edu.au † Present address: TRIUMF, Vancouver BC, Canada. ‡ Present address: University of Edinburgh, UK. in massive stars is driven by the 22 Ne(α,n) source. Because of their lower neutron to seed ratio massive stars contribute mostly to the mass region from Fe to Sr, whereas AGB stars are mainly responsible for the s abundances between Zr and the Pb/Bi region. Important differences refer also to the respective temperature regimes, which are determining the burning conditions and the strength of neutron densities and neutron exposures (for more details, see [1,2] and references therein).

A. Main s process and the 13 C pocket in AGB stars
When AGB stars reach their final evolutionary stage, the core consists of inert C and O, and the stellar energy is now produced by the alternating activation of long H burning and comparably short He burning phases. This situation is sketched in Fig. 1. The high-energy release during the short He shell burning periods gives rise to thermal instabilities with strong convection and mixing. The temperature at the bottom of these He shell flashes rises to up to ∼250 MK (T 8 ∼ 2.5), sufficient for neutron production via 22 Ne(α,n) reactions. Although peak neutron densities around 10 10 cm −3 are reached in this way, the He shell flashes contribute only about 5% to the total neutron budget in AGBs. After each thermal instability the convective envelope can sink deep into the He-rich intershell, dredging up to the stellar surface the products of He burning (such as 12 C) and of the s process. During the subsequent long phases of H burning the larger part of the neutron exposure is produced via 13 C(α,n) reactions in the so-called " 13 C pocket" when a certain amount of H may mix from the envelope into the He intershell at the deepest extent of each dredge-up episode. The 13 C pocket consists of a thin layer as shown in Fig. 1 that forms after an He shell flash, when a certain amount of H is mixed from the envelope into the He intershell. These protons are captured by the 12 C admixture in the intershell leading to the reaction sequence 12 C(p,γ ) 13 N(β + ) 13 C. The exact way the 13 C pocket is formed is complicated and still affected by persistent uncertainties as summarized in [1]. For practical reasons, a parametrized form was initiated by Gallino et al. [3] that was essentially guided by the observed s abundances. Only recently, there have been attempts to describe the formation of the 13 C pocket on the basis of realistic stellar physics [4][5][6].

B. New study of 13 C(n,γ ) and 14 N(n, p) via activation and atom counting of the product 14 C
An important aspect of the 13 C pocket comes from the simultaneous formation of 14 N via 13 C(p,γ ) 14 N reactions. Note that both 13 C and 14 N are of primary origin, i.e., produced by the star itself independent of the initial metallicity. 14 N represents a significant neutron poison because of its large (n,p) cross section. So far, this reaction as well as the 13 C(n,γ ) reaction are poorly known. Therefore, activation studies were performed using well-defined neutron fields and subsequent accelerator mass spectrometry (AMS) for sensitive cross section measurements for the 13 C(n,γ ) channel, targeting discrepancies at kT = 25 keV between the two existing experiments [7,8] and theoretical work [9]. We also provide first experimental results at higher energies as well as improve the information on the 14 N(n,p) reaction.
In the astrophysically relevant keV neutron energy range, the (n,γ ) cross sections of the light elements are usually of the order of some 10-100 μbarn, about 100-1000 times smaller than in the s-process domain between Fe and the Pb/Bi region. Nevertheless, they may constitute significant neutron poisons because a small capture cross section can be compensated by a very high abundance as in case of the 13 C and 14 N content of the pocket. While 12 C(n,γ ) 13 C reactions are also competing for neutrons, the produced 13 C will then act as a target for the 13 C(α,n) 16 O reaction so that the neutrons consumed by capture on 12 C are recycled, and thus recovered for the sprocess budget [10]. On the contrary, the 13 C(n,γ ) reaction hampers the production of neutrons not only in the manner of a usual poison, because the captured neutrons are lost for the s process, but also because primary 13 C target nuclei are transformed into long-lived 14 C.
The second reaction studied, 14 N(n,p) 14 C, has a considerably higher cross section of ∼2 mb at keV energies because of the larger phase space in the exit channel. 14 N has an additional poisoning effect weakening the neutron source: The protons produced in the 14 N(n,p) reactions remove 13 C via (p,γ ) reactions as in the CNO cycle. As a consequence, the constituents 14 N, 13 C, neutrons, and protons, form a reaction cycle with the end product being again 14 N. As such, this reaction represents the most important neutron poison in s-process nucleosynthesis.
An overview of the main reactions concerning neutron production and neutron poisons in the 13 C pocket is given in Fig. 2.
We investigated both reactions in the energy range around kT = 25 keV (simulating a Maxwell-Boltzmann distribution) and at two higher energies around E n = 125 and 180 keV. These studies were complemented by measurements at thermal neutron energies for constraining the s-wave direct capture (DC) component of the cross section, which decreases with 1/v n and is still important at keV energies in both cases. In the experiment, the irradiations with thermal and keV neutrons were performed at the TRIGA research reactor of the Atominstitut (ATI) in Vienna and at the 3.7 MV Van de Graaff (VdG) accelerator of the Karlsruhe Institute of Technology, respectively. After neutron activation the irradiated samples were subsequently analyzed at the AMS facility VERA. In this approach the produced 14 C atoms in the sample are directly counted rather than measuring the associated γ radiation or the protons emitted during the irradiation.
The present status of both reactions is summarized in Sec. II. Section III describes the sample material used. The 045803-2 neutron irradiations and the AMS measurements are described in Secs. IV and V, followed by the data analysis and the results, which are presented in Sec. VI. The final Maxwellian averaged cross sections (MACS) are calculated in Sec. VII and compared with the values derived from evaluated cross sections and with the KADoNiS compilation [11,12]. The impact of the new MACS results on the s process in thermally pulsing low-mass asymptotic giant branch (AGB) stars is discussed in Sec. VIII.

II. EXISTING DATA
A. 13 C(n,γ ) 14 C The cross section of this reaction is determined by the interplay of sand p-wave DC contributions with the tail of a pronounced capture resonance at E n = 143 keV. Experimental data in the keV region are scarce for this reaction. First results by Raman et al. [7] were consolidated by Shima et al. [8], providing values for E n = 25.1, 40, and 61.1 keV (see also Fig. 7). At higher energies the cross section is dominated by a resonance at E n = 143 keV, of which only the neutron width is known so far. Possible interference effects with the p-wave DC component could therefore affect the cross section at astrophysical energies as well. Calculations by Herndl et al. [9] suggest that the reaction rate is essentially determined by the 143-keV resonance at temperatures above T 8 ∼ 3, whereas the sand p-wave DC contributions are dominating below. Nevertheless, the predicted energy dependence in [9] is in conflict with the experimental data around 30 keV. This discrepancy and the uncertain capture strength of the 143-keV resonance motivated the present work to extend the investigated energy range beyond the astrophysically important region to include the two data points at and slightly above the 143-keV resonance. B. 14 N(n, p) 14 C Much more work exists for 14 N(n,p) 14 C in the keV energy range [13][14][15][16], The measurements by Koehler and O'Brien [14] support a 1/v energy dependence almost up to 100 keV. Above that energy the cross section is determined by the tails of two resonances at 493 and 655 keV. Between 10 and 200 keV most experimental data are in good agreement, except for the values by Brehm et al. [13], which are approximately two to three times lower (see also Fig. 6). This difference would have stringent consequences for the role of 14 N as a neutron poison as well as for the production of 19 F, which depends on the amount of protons emitted in the 14 N(n,p) reactions. While the 19 F abundance is not much affected by the 10% uncertainty of most experimental cross sections, this becomes a critical issue if one includes the data of Brehm et al. [17,18]. There are also large discrepancies between the evaluated 14 N(n,p) cross sections in the JEFF-3.1, ENDF/B-VII, JENDL, and BROND libraries, especially above about 50 keV.
Accordingly, the present measurements on 14 N were performed at the same neutron energies as for 13 C, in particular with respect to the discrepancies between existing experimental data and evaluated cross sections.  14 C/ 13 C ratios and the corresponding production cross section for 14 C measured by irradiation of enriched 13 C-graphite samples with thermal neutrons.

III. SAMPLES
With natural carbon (∼99% 12 C, ∼1% 13 C) it is difficult to reach a significant 14 C signal above the present background levels achievable in AMS. Therefore, the 13 C(n,γ ) reaction was studied with samples of 13 C-enriched graphite (98% 13 C) from AMT Ltd., Israel.
A general complication in measurements of the 13 C(n,γ ) cross sections is that even spurious contents of 14 N in the sample material also produce significant amounts of 14 C via the 14 N(n,p) reaction, owing to its much higher cross section as illustrated in Table IV.
In view of this problem, the 14 N content of the 13 C-enriched graphite was characterized by two different methods: Because the cross section ratio σ np /σ nγ is highest at thermal energies (Table IV) and because the thermal cross sections of both reactions are well known, the parasitic 14 C production through the 14 N(n,p) channel could be studied with high sensitivity. The results of the thermal irradiations of 13 C-enriched graphite are summarized in Table I. From the measured effective thermal cross section, σ prod [the sum of 14 C production from 13 C(n,γ ) and 14 N(n,p)], the intrinsic 14 N content in the graphite samples was then determined using the thermal cross section values for 13 C(n,γ ) and 14 N(n,p) as outlined in Sec. VI B 2.
The samples for studying the 14 N(n,p) 14 C reaction were prepared from uracil (C 4 H 4 N 2 O 2 ). Owing to the low 13 C(n,γ ) cross section and to the low 13 C abundance any parasitic 14 C production from neutron capture on 13 C was negligible (less than 0.35%).

IV. NEUTRON ACTIVATIONS AT keV ENERGIES
At the Karlsruhe VdG accelerator neutrons in the keV energy range were produced via the 7 Li(p,n) 7 Be reaction by protons impinging on a Li target. Selecting the proton energy at 1912 keV, 31 keV above the reaction threshold, generates a broad neutron spectrum in a forward cone according to kinematics and energy loss in the Li target. The corresponding setup at the Karlsuhe VdG accelerator is sketched in Fig. 3, illustrating the incoming proton beam, the conical neutron field emerging from the Li target, and the irradiated sample sandwich in close geometry to the neutron source. As the angle-integrated spectrum represents a good approximation of the true stellar neutron spectrum for a thermal energy of kT = 25 keV (Fig. 4), measurements in this quasi-Maxwell-Boltzmann (q-MB) spectrum are yielding MACS values for an effective thermal energy of kT = 25 keV with very little corrections [20,21].
The Li targets were produced by evaporation onto 1-mm thick windows of Faraday cups mounted at the end of the proton beam line. In the evaporation process, the thickness of the Li layers was determined with a calibrated oscillating quartz monitor.
For the 13 C(n,γ ) 14 C activations, samples were prepared from 13 C-enriched graphite powder. The powder was enclosed in small Al containers 6 mm in diameter. Gold foils served as monitors for the neutron fluence determination [21] and were attached to the 13 C sample to form a stack of 197 Au -13 C-197 Au. The uracil powder was pressed into pellets and similarly sandwiched between Au foils for the 14 N(n,p) studies.
In addition to the quasistellar neutron spectrum for kT = 25 keV produced at E p = 1912 keV, spectra with an energy spread of ±30 keV and mean energies of ∼125 and ∼180 keV were produced with the 7 Li(p,n) reaction at higher FIG. 4. Experimental neutron energy distributions used in the 14 N measurement. Apart from minor differences, the same spectra were applied in the 13 C runs (see Table II). proton energies of 1960 and 2000 keV. With typical proton beam intensities of 100 μA, a fluence of ∼10 15 neutrons per cm 2 could be obtained within five to seven days of activation (Table II). The neutron spectra obtained in this way have been calculated by means of the PINO code [22] (for details and individual data on the experimental neutron energy distributions, see Supplemental Material [23]).
The neutron spectra used in the irradiations are shown in Fig. 4. Although the 13 C and 14 N sandwich samples were irradiated simultaneously, the corresponding neutron spectra differ slightly because of small differences in their distance from the Li targets during the irradiations.
The main parameters for the Karlsruhe neutron activations are summarized in Table II. The applied neutron fluence for the  Table VI).

045803-4
various samples was determined from the induced activities of the gold monitor foils, using the 197 Au(n,γ ) cross section as a reference. The adopted gold reference cross section was taken from the new version KADONIS V1.0 [24]. Between kT = 5 and 50 keV it was derived by the weighted average of recent measurements at GELINA [25] and n TOF [26,27] and between kT = 60−100 keV by the average of the evaluated cross sections from the data libraries JEFF-3.2, JENDL-4.0, ENDF/B-VII.1 [28][29][30]. This choice is in perfect agreement with a new activation measurement by the group in Sevilla [31]. The energy-differential gold cross section was folded with the neutron spectra used in these measurements. Note the effective values listed in column five of Table II are reflecting a change of 5.3% in the gold reference cross section compared to the values previously used in similar activation experiments.

V. ACCELERATOR MASS SPECTROMETRY
A. The VERA facility AMS was introduced to laboratory experiments in nuclear astrophysics already in 1980 by Paul et al. [32] with a first study of the 25 Mg(p,n) 26 Al reaction. In particular, the past few years have seen an increasing number of nuclear astrophysics measurements with the AMS technique for charged particle and neutron induced reactions (see, e.g., [33][34][35][36][37][38][39][40][41]).
Contrary to other mass spectrometric techniques AMS has the great advantage that it does not suffer from molecular interference effects, because molecules are completely destroyed in the gas stripper of the tandem accelerator. This method allows one even to separate specific atomic isobars, which can differ in their abundance ratios by many orders of magnitude. Therefore, AMS offers a highly sensitive and complementary tool for cross-section measurements of nuclear reactions leading to radioactive nuclides, independent of their half-lives or decay patterns. The list of reaction products of interest for astrophysics includes radioisotopes over the entire mass range, e.g., 10 Be, 14 C, 26 Al, 36 Cl, 41 Ca, 55,60 Fe, 59,63 Ni, 68 Ge, 79 Se, 129 I, 182 Hf, 202 Pb g , 210 Bi m , and a number of actinide isotopes including 244 Pu.
The present AMS measurements have been performed at the Vienna Environmental Research Accelerator (VERA) which represents a state-of-the-art AMS facility based on a 3-MV tandem [42,43]. A schematic view of the VERA facility is shown in Fig. 5 including the detection devices for recording the stable 12,13 C and the low-intensity 14 C ions.

B. AMS measurements
Both reactions under study are producing 14 C. Measurements of 14 C are commonly performed in most AMS laboratories, especially for 14 C dating. However, the samples from the neutron activations differ from routine measurements, because of the 10 000 times higher isotope ratio 13 C/ 12 C in the 13 C-enriched samples compared to natural material, where the 13 C abundance is only about 1%. Possible systematic uncertainties arising from the high enrichment have been studied with reference samples made from the original 13 C graphite that were activated at thermal energies. In this way, FIG. 5. Schematic layout of the AMS facility VERA. Negative ions ( 12,13,14 C − ) were extracted from the ion source and after lowenergy mass analysis injected into the tandem accelerator. After gas stripping in the terminal and further acceleration, ions with charge 3 + and an energy of 12 MeV were selected with the analyzing magnet. The stable 12 C and 13 C ions were counted as current with Faraday cups, whereas the low-intensity 14 C fraction in the beam was subjected to further background suppression by the electrostatic analyzer and were eventually recorded with one of the energy detectors (A, B or C). mass fractionation effects, which could lead to a systematic offset of the measured isotope ratio for such enriched materials, were excluded. These test runs were also used to study whether the highly enriched 13 C sample gave rise to an enhanced AMS background compared to measurements on natural graphite (which is assumed to be 14 C-free). It could be demonstrated that the amount of 14 C produced in the activations at keV neutron energies was high enough that this background did not jeopardize the final uncertainties [38,43,44].
The 13 C-enriched material used in this work was amorphous graphite powder. Prior to neutron irradiations the 14 C content of this material was determined with AMS. When the standard 14 C setup with particle detector A (Fig. 5) was used for analyzing the 13 C graphite and the uracil samples, it turned out that the 13 C-enriched graphite gave slightly enhanced 14 C count rates. The excess was interpreted as some leaky 13 C beam reaching the particle detector. Because these signals were indistinguishable from true 14 C events, two different particle detection systems further downstream were used instead, comprising an additional magnetic deflector and a multianode ionization chamber (detector B in Fig. 5) as well as a time-of-flight-detector (detector C). This enhanced setup gave stable isotope ratios 14 C/ 13 C = (1 ± 0.2) × 10 −14 for nonirradiated 13 C graphite (see Fig. 2 in [38]), corresponding to 48%, 11%, and 21% of the additional 14 C produced in the neutron irradiations at kT =25, 128, and 182 keV, respectively. Therefore, a series of nonirradiated blank samples  was measured in all beam times together with the irradiated samples to monitor the stability of the blank isotope ratios. The 14 C content in the blank samples contributed between 2% and 10% to the final uncertainties.
After the neutron irradiations the 13 C-enriched material was homogenized and a few mg were mixed with pure Ag powder as a binder and pressed into Al sample holders. A sample wheel with a capacity of 40 samples was then loaded into the sputter ion source of the AMS system.
Because of the low 14 C content in the 13 C-enriched samples, it was important to avoid contamination with natural carbon (with a 14 C/ 12 C ratio ∼10 −12 ). Therefore, the stable carbon atom ratio 13 C/ 12 C was measured together with the 14 C/ 13 C ratio to monitor any such contamination. During the AMS runs the 13 C/ 12 C ratios were usually ranging between 10 and 70, thus any significant contamination with natural carbon could be excluded.
The 14 C content of unprocessed uracil was measured to (1.8 ± 1.0) × 10 −14 , in agreement with the value measured with processed (graphitized) samples, which yielded 14 C/ 12 C ratios of (1.4 ± 0.5) × 10 −14 . The irradiations of the uracil samples at Karlsruhe with keV neutrons generated isotope ratios 14 C/ 12 C of ∼3-7×10 −13 , much higher than the background contributions from the 14 C content of unprocessed uracil, the background in the AMS runs of ∼10 −15 , and a potential contamination with natural carbon during sample processing.
However, potential 14 C losses in the (n,p) reaction from outgassing of the reaction product 14 C could not be excluded a priori, because 14 C could potentially be released from the uracil matrix via recoil, subsequently forming gaseous 14 CO or 14 CO 2 . Uracil samples were irradiated at the TRIGA reactor in a thermal spectrum with an epithermal to thermal flux ratio of 1.3% [45] to study whether some of the freshly produced 14 C could be lost into the gas phase by conversion into 14 CO or 14 CO 2 .
The samples for these irradiations were prepared in different ways, by pressing uracil into pellets and by using the original powder in closed quartz ampoules. The latter form had the advantage that any gaseous 14 C could be extracted from the ampoules by separating it in a first step of the standard 14 C graphitization. After irradiation, AMS measurements were performed on unprocessed uracil, i.e., powder directly pressed into the AMS sample holders, as well as on uracil fully processed into graphite powder. The results demonstrated that outgassing of freshly produced 14 C from the uracil matrix was 2.5% and compatible with 14 C production from 14 N in residual air in the quartz ampoules.
The AMS measurements were carried out with sub-mg pieces, taken randomly from the powderized uracil pellet. Although the pellets were thoroughly mixed after the irradiation, such small pieces were probably still not fully homogenized. Because of the close irradiation geometry of the pellet with respect to the neutron-producing Li target (pellet 6 mm in diameter, distance to target 2.57 mm), differences in the neutron flux of up to 30% might, in fact, be possible. This was reflected in the various runs, where differences up to 20% were found between the individual AMS samples of the same pellet. Therefore, between 11 and 14 sputter samples were measured from each pellet to balance the individual scatter. As the averaged isotope ratios did not show significant differences between unprocessed and processed sputter samples, it could be demonstrated that the final uncertainty was affected by 3%.
All samples ( 13 C graphite and uracil) were sputtered with a Cs beam and negative ions extracted from the ion source. An automated measurement procedure alternatively switched between the three different carbon isotopes ( 12,13,14 C) five times per second. The ion currents of the stable 12 C and 13 C were measured for milliseconds using Faraday cups at both, the low-energy side (before entering the accelerator, as 12,13 C − ) and at the high-energy side (mass and charge selected ions after the analyzing magnet, as 12,13 C 3+ ). The reaction product 14 C 3+ was counted with the particle detection system for 95% of the sputtering time. Typical measuring times per such a run were about 200 s. Then another sample (unknown, blank or standard) was measured with the same setup. Typically, 5 to 10 runs were performed on each sample per measurement series, each series consisting of typically five sputter samples per neutron energy.
Overall, more than 200 AMS samples were measured in 6 and 10 beam times dedicated to the 13 C-enriched graphite and uracil samples, respectively. All measured isotope ratios were normalized to the principal modern radiocarbon standard oxalic acid I (NIST SRM 4990 B, also termed HOX-I) and oxalic acid II (HOX-II; NIST SRM 4990 C) [46,47]. This extensive body of data served to verify the reproducibility of the results and to reduce systematic backgrounds from the low isotope ratios in the irradiated samples. Statistical uncertainties were practically negligible in the final data.

A. Neutron fluence
The neutron fluence applied during the irradiations is determined from the induced activity in the gold monitor foils, which was measured with a well-calibrated HPGe detector. The number of counts C in the characteristic 411.8-keV line in the γ -ray spectrum recorded during the measuring time t m [20] is related to the number of activated nuclei A at the end of irradiation by where γ denotes the detector efficiency, I γ the intensity per decay, and t w the waiting time between irradiation and activity measurement. The factor K γ describes the γ -ray self-absorption in the sample, which is for the very thin gold disks in very good approximation [48], where μ is the γ -ray self-absorption [49] and x the sample thickness.
The number of activated nuclei A can also be expressed by the neutron fluence tot = t a 0 (t)dt, the spectrum averaged capture cross section σ , and the sample thickness N in 045803-6 atoms/cm 2 as The fluence was determined from the activities of the Au monitor foils by folding the experimental neutron energy distributions (Ratynski and Käppeler distribution for 25 keV, and the simulated distributions around 125 and 180 keV) with the cross-section data for the 197 Au(n,γ ) reaction.
The factor f b in Eq. (3) corrects for the fraction of activated nuclei that decayed already during irradiation. By this correction nonuniformities in the neutron flux from the decreasing performance of the Li targets as well as fluctuations in the beam intensity were properly taken into account. This correction is small or negligible for activation products with half-lives much longer than the irradiation time t a , but fluctuations in the neutron flux had to be considered for the gold activities, where the half-life of t 1/2 = 2.62 d is shorter than the irradiation time. In the expression, (t) is the time dependence of the neutron intensity recorded throughout the irradiation with the 6 Li glass monitor and λ the decay rate of the product nucleus 198 Au.
The main uncertainties in the fluence determination are from the gold reference cross section and the γ efficiency of the HPGe detector. The spectrum-averaged (n,γ ) cross sections of 197 Au (Table II) are affected by uncertainties of 1.5%-2%. The γ efficiency was repeatedly measured with a set of calibrated sources and was known with an uncertainty of ±2.0%. All other uncertainties were very small and contribute less than 0.5% to the total 3% uncertainty of the neutron fluence.

14 N(n, p) 14 C
The experimental cross sections can simply be calculated from the following equation: where 14 C/ 14 N denotes the isotope ratio measured via AMS, and tot the neutron fluence discussed before. Note the particular advantage of the AMS method, i.e., that the cross section is determined by the measured isotope ratio only, completely independent of the sample mass and the decay properties of the product nucleus. In fact, the measured isotope ratio for the 14 N(n,p) 14 C reaction is 14 C/ 12 C, because 12 C is directly correlated with the number of 14 N atoms via the stoichiometry of the uracil compound C 4 H 4 N 2 O 2 where 12 C/ 14 N=1.98 (99% 12 C, 1% 13 C).
The measured 14 C/ 12 C isotope ratios are listed in Table III together with the resulting spectrum averaged cross sections. Compared to typical experimental backgrounds in 14 C-AMS measurements ( 14 C/ 12 C ∼3 × 10 −16 for unprocessed and ∼10 −15 for processed samples), it is obvious that machine backgrounds are not a critical issue for the uncertainty budget. The systematic uncertainties are summarized in Table VI.
The new spectrum-averaged cross-section data for 14 N(n,p) (full squares) are plotted in Figure 6 together with previous experimental data and with the JEFF-3.2 evaluation [50]. At 25 keV there is perfect agreement with the work of Sanami et al. [16]. Up to about 100 keV all data are well consistent with a 1/v shape of the cross section. The only exception are the values of Brehm et al. [13], which should be rejected in further evaluations.
A best-fit cross section was obtained via following the prescription of the JEFF 3.2 evaluation [50], where the first term corresponds to the 1/v extrapolation of the thermal cross section (1860 ± 30 mb [19]) and the second term considers the tails of the resonances at 493 keV and above. The best-fit cross section (solid line in Fig. 6) was obtained by adopting the well-confirmed 1/v trend below about 25 keV, the resonance contribution was modified to match our data points at 123 and 178 keV. This implies that the strength of the resonance at E n = 493 keV reported in [51] had to be reduced by a factor of 3.3, resulting in significantly lower cross sections than in JEFF-3.2. Folded with the neutron energy spectra of this work, all experimental results are well reproduced by the best-fit cross section as indicated by open boxes in Fig. 6. The width of the boxes corresponds to the full width at half maximum (FWHM) of the respective neutron spectra.

13 C(n,γ ) 14 C
In the analysis of the 13 C(n,γ ) cross section the measured 14 C/ 13 C ratios had to be corrected for parasitic 14 C production via 14 N(n,p) from a nitrogen contamination of FIG. 6. The 14 N(n,p) 14 C cross section between 1 and 400 keV. The plot shows a comparison of the present results (full squares) with existing experimental data [13][14][15][16] and with the evaluated cross section in the JEFF-3.2 library [50]. In general, there is very good agreement with existing data except for the values of Brehm et al. [13]. The solid line represents a best-fit cross section, yielding average values (FWHM indicated by open boxes) in good agreement with the experimental results.
the enriched 13 C material. (Interestingly, the 14 N content in natural graphite was below the detection limit of <0.01%). The total number of produced 14 C atoms is where σ 13C and σ 14N denote the 13 C(n,γ ) and 14 N(n,p) cross sections and N 13C and N 14N are the number of 13 C and 14 N atoms in the sample, respectively. With The thermal cross section of 13 C(n,γ ) 14 C is 1.37 ± 0.04 mb [19]. This means that (9.1 ± 0.6) mb out of the measured σ prod = 10.5 mb (Table I) are from 14 N(n,p) reactions in the sample. From the measured σ prod and the thermal cross-section ratio (Table IV) one finds an isotope ratio of 14 N / 13 C = 0.0049 ± 0.0004, in full agreement with the direct AMS result of 0.005 ± 0.001.
Eventually, the 13 C(n,γ ) cross section can be expressed as The correction for the amount of 14 C from the 14 N contamination of the 13 C-enriched samples was determined using the measured cross-section values for 14 N(n,p) described above. At kT = 25 keV, the parasitic 14 N(n,p) component was even larger than 14 C generated from the 13 C(n,γ ) reaction and it contributed about 43% to the final uncertainty. At the higher neutron energies of 128 and 182 keV the corrections were only 3.2 and 4.5%, respectively.
The measured 14 C/ 13 C isotope ratios and the resulting cross sections for the 13 C(n,γ ) 14 C reaction are listed in Table V and the related systematic uncertainties are summarized in Table VI.
The present results for the 13 C(n,γ ) 14 C cross section are plotted in Fig. 7 together with previous experimental results [7,8], and with the evaluated data from the JEFF-3.2 library [28]. A best fit to the present data (solid line) was obtained following the prescription of Herndl et al. [9], that considered the effect of the direct radiative capture (DRC) channel in detail. To reproduce the data points at 128 and 182 keV it was particularly important that also the p-and d-wave DRC components were considered including a constructive interference between the p-wave part and the 152.4-keV resonance by this approach.
The best fit was obtained with the expression, where σ R denotes the resonant part described by the usual Breit-Wigner form with the resonance parameters taken from Ref. [19], except that the capture width was increased by 60% to γ = 0.35 eV for matching the data points at 128 and 182 keV. The s-wave DRC component σ s DRC is represented  by a 1/v extrapolation of the thermal cross section [19], and the d-wave part was adopted from the work of Herndl et al. [9]. The last term describes the interference between the p-wave DRC component and the resonant part, which changes sign at the resonance. The phase shift δ(E n ) is given by The p-wave component, which is characterized by an √ E n energy dependence, was then adjusted to best reproduce the experimental data at 128 and 182 keV.
In this way it was possible to reproduce the data points at 128 and 182 keV within the respective uncertainties, in contrast to attempts neglecting the interference term. At 25 keV, the situation remains ambiguous because the present data point is somewhat uncertain because of the large correction for the 14 N contamination of the sample. Lower than previous data [7,8], the fit matches the measured cross section well within the 1σ uncertainty as shown in Fig. 7. The importance of the p-and d-wave DRC components is illustrated by comparison of the best fit with the recent JEFF-3.2 evaluation [28], where these components had been neglected (dashed line). The evaluation is significantly underestimating the measured cross section, particularly in the astrophysically relevant region below the resonance at 152.4 keV.

VII. MAXWELLIAN AVERAGED CROSS SECTIONS
Maxwellian averaged cross sections (MACS) for kT = 5-100 keV have been calculated using the best-fit cross sections to the measured data as indicated by the solid lines in Figs. 6 and 7. The MACS values for both reactions are listed in Table VII. For the 14 N(n,p) reaction, the 1.6% uncertainty of the thermal value was adopted for the 1/v term. As the resonant part is firmly constrained by the measured cross sections at 123 and 178 keV, the 6% uncertainty of these data points was assigned to this component. Accordingly, the respective MACS uncertainties correspond to the relative contributions of the two terms in Eq. (6).
Compared to the MACS data calculated with the JEFF 3.2 evaluation of the 14 N(n,p) cross section [50], the new values are lower by 1%, 11%, and 100% at thermal energies of 10, 25, and 100 keV, respectively.
The uncertainties of the MACS calculation for the 13 C(n,γ ) reaction had to consider all terms in Eq. (10). For the resonant part σ R , an uncertainty of 9% was considered, corresponding the uncertainties of the data points at 128 and 182 keV, which are constraining the resonant part. As the s-wave DRC component was normalized via the thermal cross section, the 1% uncertainty of this value [19] was adopted for this modest contribution. To accommodate the existing experimental values below 60 keV, a conservative uncertainty of 30% was assigned to the p-wave DRC component. For the d-wave DRC component, which contributes mostly above the 152.4-keV resonance, an uncertainty of 20% was estimated for the adopted DRC calculation of Herndl et al. [9].
For thermal energies up to 20 keV the present MACS values for 13 C and the recommended values in KADONIS [12] are compatible within uncertainties. However, above kT 25 keV the new data are consistently higher because (i) the constructive interference between the 152-keV resonance and the p-wave DRC component and (ii) the effect of the previously neglected d-wave DRC contribution.
The present MACS results are compared in Fig. 8 with data obtained from the evaluated cross sections in the JEFF-3.2 library [50]. As expected from the respective cross sections in Figs. 6 and 7 the 14 N(n,p) 14  of the p-and d-wave DC components were neglected in the evaluated cross section.

VIII. IMPACT FOR s-PROCESS CALCULATIONS
We investigated the effect of the new stellar cross sections on the s process in low-mass AGB stars using stellar models of initial mass 2 M and two different metallicities: solar (Z = 0.014) and roughly 1/10th of solar (Z = 0.001). The nucleosynthesis post-processing code includes a nuclear network up to Po and is fed with the results from evolutionary sequences computed using the MONASH/MT STROMLO evolutionary code [52] in terms of temperatures, densities, convective velocities, and locations of the convective borders at each time and point in the star. Detailed information about the stellar evolutionary sequences can be found in [53] and [54]. The numerical method used in this study was described by Lugaro et al. [55].
During the post-processing we artificially included a proton profile in the He-rich intershell at the deepest extent of each dredge-up episode (as schematically illustrated in Fig. 1). The proton abundance is chosen such that it decreases exponentially from the envelope value ∼0.7 to a value of 10 −4 at a location in mass 2 × 10 −3 M below the base of the envelope. A thin region forms as a result of such mixing, which is rich in 13 C in the bottom layers and in 14 N in the top layer. We run all the tests with the same input for the stellar and the nuclear physics (mixing, rates, initial abundances, etc.), except that we modified the rates of the 13 C(n,γ ) 14 C and the 14 N(n,p) 14 C reactions to those reported here. We compare the results to those obtained using the 13 C(n,γ ) 14 C rate from the KADONIS database and the 14 N(n,p) 14 C rate from Caughlan and Fowler (1980), which are the recommended rates in the JINA reaclib database that we employ as the standard in our models. The 14 N(n,p) rate from Caughlan and Fowler [56] is roughly 20% higher than the rate reported here and close to the evaluation by Koehler and O'Brien [14].
Changing the 13 C(n,γ ) rate alone did not make any difference in the final results. Changing the 14 N(n,p) rate alone resulted in a small increase (by 15% at most in the Z=0.014 model and by 4% at most in the Z = 0.001 model) in the amount of Ba and Pb produced. This was expected as the new rate is lower than the previous, which results in a higher number of free neutrons in the 13 C pocket and a higher production of the heavier s-process elements. When we changed both rates to the new values the effect was slightly strengthened in the low-metallicity model (up to a 9% increase in Ba) because of the feedback between the two reactions.
We also experimented with a model of a 1.25 M star with Z=0.01, where the third dredge-up was calculated using overshoot (see details in [57]). In this case the 13 C pocket is artificially included as in the other models, however, because the temperature in that region only reaches up to 70 MK before the onset of the following thermal instability, the 13 C(α,n) 16 O reaction is not activated until the 13 C nuclei are ingested in the following convective region [58]. In this case the impact of the 14 N(n,p) 14 C neutron poison reaction is even more crucial because the large amount of 14 N present in the H-burning ashes is ingested at the same time. The total number of free neutrons is much lower than in the 2 M models and the production of the elements belonging to the first, rather than the second and third, s-process peak is favored. In any case, also in this model the new rates produce marginal changes (an increase of 16% in Ba).
Overall there are no major differences between the different sets of models, especially in relation to observational counterparts such as data from spectroscopic observations and meteoritic stardust grains, whose determinations have larger uncertainties than the differences found here. The present rates allow us to confirm the accuracy of the current s-process results in relation to the behavior of these two fundamental reactions.

IX. SUMMARY
Over the past decade AMS measurements have provided data for open questions in nuclear astrophysics. In the present work we exemplified this technique via measurements of the 13 C(n,γ ) and 14 N(n,p) reaction cross sections. Samples containing 13 C and 14 N were irradiated at the Karlsruhe Van de Graaff accelerator in a neutron field with the proper energy distribution for the direct determination of a Maxwellianaveraged cross section at 25-keV thermal energy, and also with broad neutron energy distributions of E n = 123 and 178 keV mean energy. After neutron activation the amount of 14 C produced was quantitatively determined by AMS. 13 C(n,γ ) 14 C and 14 N(n,p) 14 C reactions act both as neutron poisons in s-process nucleosynthesis, while 14 N(n,p) also serves as a proton donator, leading to a delayed neutron recycling. The protons released in this reaction are as well important for the production of 19 F.
The measured 13 C(n,γ ) cross section at kT = 25 keV was found to be significantly smaller than previous results. With  the data points at 128 and 182 keV neutron energy, the strength of the resonance at 143 keV could be constrained for the first time. Together with a more rigorous treatment of the direct radiative capture (DRC) channels [9], this resulted in much improved MACS data above kT = 20 keV. The 14 N(n,p) 14 C cross section was measured at similar neutron energies, in a quasistellar spectrum for kT = 25 keV and at 123 and 178 keV. Also in this case, the contributions of resonances at 493 keV and above could be constrained, yielding reduced MACS values by 1%, 11%, and 100% at kT = 10, 25, and 100 keV, respectively.
The impact of the new MACS data on the s-process abundance distribution is somewhat modest. Abundances are found to change by less than 20% for different sets of models, smaller than the intrinsic uncertainties of observational counterparts such as data from spectroscopic observations and meteoritic stardust grains. Accordingly, the present rates allow us to confirm the accuracy of the current s-process results.