Measurement of the stellar $^{58}$Ni$(n,\gamma)^{59}$Ni cross section with AMS

TL;DR

This study measures the neutron capture cross section of $^{58}$Ni to produce $^{59}$Ni using activation and AMS techniques, providing more accurate data relevant for astrophysics and nuclear science.

Contribution

The paper presents the first measurement of the $^{58}$Ni$(n, ext{γ})^{59}$Ni cross section using combined activation and AMS, resolving previous discrepancies and improving data accuracy.

Findings

Measured Maxwellian-averaged cross section at 30 keV: 30.4 mbarn

Results are consistent with recent TOF measurements within uncertainties

Resolved discrepancies between older TOF data and previous values

Abstract

The $^{58}$Ni$(n,\gamma)^{59}$Ni cross section was measured with a combination of the activation technique and accelerator mass spectrometry (AMS). The neutron activations were performed at the Karlsruhe 3.7 MV Van de Graaff accelerator using the quasi-stellar neutron spectrum at $kT=25$ keV produced by the $^7$Li($p,n$)$^7$Be reaction. The subsequent AMS measurements were carried out at the 14 MV tandem accelerator of the Maier-Leibnitz-Laboratory in Garching using the Gas-filled Analyzing Magnet System (GAMS). Three individual samples were measured, yielding a Maxwellian-averaged cross section at $kT=30$ keV of $\langle\sigma\rangle_{30\text{keV}}$= 30.4 (23)$^{syst}$(9)$^{stat}$ mbarn. This value is slightly lower than two recently published measurements using the time-of-flight (TOF) method, but agrees within the uncertainties. Our new results also resolve the large discrepancy between older TOF measurements and our previous value.

Tables

Table 1. Table 1: Isotopic Berglund and Wieser ( 2011 ) and solar abundances (based on meteorites and relative to A Si subscript 𝐴 Si A_{\rm{Si}} = 10 6 ) Anders and Grevesse ( 1989 ) of the stable Ni isotopes.

Isotope	Isotopic abundance [%]	Solar abundance
58Ni	68.077 (19)	3.36$\times$104
60Ni	26.223 (15)	1.29$\times$104
61Ni	1.140 (1)	5.62$\times$102
62Ni	3.635 (4)	1.79$\times$103
64Ni	0.926 (2)	4.57$\times$102
${\Sigma }_{\mathrm{Ni}}$	100	4.93$\times$104

Table 2. Table 2: Summary of the sample and activation parameters. " ​ t a ​ c ​ t ​ " " subscript 𝑡 𝑎 𝑐 𝑡 " "t_{act}" is the irradiation time and ” Φ t ​ o ​ t subscript Φ 𝑡 𝑜 𝑡 \Phi_{tot} ” the total neutron exposure. ’Diameter’ refers to the diameter of the irradiated pellet.

Sample	N(58Ni)	Diameter	$t_{act}$	${\Phi }_{tot}$
	($\times {10}^{20}$atoms)	(mm)	(d)	($\times$1014 n)
ni-1	1.652	8	6.0	8.73
ni-2	1.649	8	6.0	8.50
ni-3	5.307	6	5.0	9.23

Table 3. Table 3: New recommended MACS of 197 Au(n, γ 𝛾 \gamma ) 198 Au from KADoNiS v1.0 Dillmann and Plag ( 2016b ) in comparison with the previously recommended values Bao  et al. ( 2000 ); Dillmann  et al. ( 2009a ) . The values given in brackets are the respective uncertainties.

197Au(n,$\gamma$)198Au
$kT$	${⟨\sigma ⟩}_{30keV}$ (mbarn)	${⟨\sigma ⟩}_{30keV}$ (mbarn)	Ratio
(keV)	KADoNiS v1.0	KADoNiS v0.3	$\frac{v1.0}{v0.3}$
5	2109 (20)	2050	1.029
8	1487 (13)	-	-
10	1257 (10)	1208	1.041
15	944 (10)	904	1.044
20	782 (9)	746	1.048
25	683 (8)	648	1.054
30	613 (7)	582 (9)	1.053
40	523 (6)	496	1.054
50	463 (5)	442	1.048
60	425 (5)	406	1.047
80	370 (4)	356	1.039
100	332 (4)	312	1.064

Table 4. Table 4: Uncertainties from the activation and AMS measurement, separated as systematical and statistical contributions. Statistical contributions include regular statistical uncertainties (e.g. particle counting) and originally systematic contributions with a random effect due to repetition (e.g. sample position during irradiation).

	Activation measurement
Source of uncertainty	Systematic (%)	Statistical (%)
197Au cross section	1.4	–
Detector efficiency	2.0	–
Abundance 58Ni	0.03	–
$\gamma$-ray intensity 198Au	0.13	–
Sample position unc.	–	1.5
Sample mass 197Au	–	0.3
Counting statistics 198Au	–	0.25
Total activation	3.6	1.5
	AMS measurement
Source of uncertainty	Systematic (%)	Statistical (%)
AMS standard	4.1	–
58Ni current111Per individual reading (twice per data run).	–	13
Beam transmission	–	10
Counting statistics222Taken as $\sqrt{N}/N$ per data run with $N$ events.	–	(5-20)
59Co background333Only included for sample ni-1.	–	10 / - / -
Total AMS 444Per data run, without counting statistics.,555Total statistical error for samples ni-1/ ni-2 / ni-3.	4.1	13.5/ 3.4/ 5.5
Total act. + AMS 555Total statistical error for samples ni-1/ ni-2 / ni-3.	7.7	13.6/ 3.8/ 5.7

Table 5. Table 5: Overview of the results from the AMS measurements and the deduced experimental cross sections ⟨ σ ⟩ e ​ x ​ p subscript delimited-⟨⟩ 𝜎 𝑒 𝑥 𝑝 \langle\sigma\rangle_{exp} weighted with the statistical uncertainties from the activation and the AMS measurement. The isotope ratio is measured as N Ni 59 subscript 𝑁 superscript Ni 59 N_{{}^{59}\text{Ni}} / N Ni 60 subscript 𝑁 superscript Ni 60 N_{{}^{60}\text{Ni}} and transformed into N Ni 59 subscript 𝑁 superscript Ni 59 N_{{}^{59}\text{Ni}} / N Ni 58 subscript 𝑁 superscript Ni 58 N_{{}^{58}\text{Ni}} and N Ni 59 subscript 𝑁 superscript Ni 59 N_{{}^{59}\text{Ni}} / N Ni subscript 𝑁 Ni N_{\text{Ni}} using the corresponding isotopic abundances (see Table  1 ). For discussion of the uncertainties, see Sec.  III.5 .

Sample	AMS data runs	$N_{{}_{}{}^{59}\text{Ni}}$/$N_{\text{Ni}}$	$N_{{}_{}{}^{59}\text{Ni}}$/$N_{{}_{}{}^{58}\text{Ni}}$	${⟨\sigma ⟩}_{exp}$	Systematic	Statistical
				(mbarn)	(mbarn)	(mbarn)
ni-1	3	1.80$\times$10-11	2.65$\times$10-11	30.4	2.3	4.1
ni-2	20	1.68$\times$10-11	2.47$\times$10-11	29.0	2.2	1.1
ni-3	10	2.02$\times$10-11	2.97$\times$10-11	32.2	2.5	1.8
Weighted average				29.9	2.3	0.9

Table 6. Table 6: Spectrum-averaged cross sections ⟨ σ ⟩ e ​ v ​ a ​ l subscript delimited-⟨⟩ 𝜎 𝑒 𝑣 𝑎 𝑙 \langle\sigma\rangle_{eval} from different evaluated libraries and the respective normalization factor F n ​ o ​ r ​ m subscript 𝐹 𝑛 𝑜 𝑟 𝑚 F_{norm} = ⟨ σ ⟩ e ​ x ​ p subscript delimited-⟨⟩ 𝜎 𝑒 𝑥 𝑝 \langle\sigma\rangle_{exp} / ⟨ σ ⟩ e ​ v ​ a ​ l subscript delimited-⟨⟩ 𝜎 𝑒 𝑣 𝑎 𝑙 \langle\sigma\rangle_{eval} .

Database	${⟨\sigma ⟩}_{eval}$ (mbarn)	$F_{norm}$
ENDF/B-VII.1 Chadwick et al. (2011)	33.3	0.90
JEFF-3.2 Koning (2014)	38.6	0.77
JENDL-4.0 Shibata et al. (2011)	38.7	0.77

Table 7. Table 7: Maxwellian averaged cross sections ⟨ σ ⟩ k ​ T subscript delimited-⟨⟩ 𝜎 𝑘 𝑇 \langle\sigma\rangle_{kT} (in mbarn) for 58 Ni calculated with the energy dependency of ENDF/B-VII.1 (”This work”). The following two columns show the values from the two TOF measurements Guber  et al. ( 2010 ); Zugec  et al. ( 2014 ) , and the last column gives the new recommended MACS from the new KADoNiS v1.0 database Dillmann and Plag ( 2016a ) based on these two TOF measurements.

$kT$	${⟨\sigma ⟩}_{kT}$ [mbarn]
[keV]	ENDF/B-VII.1 Chadwick et al. (2011)	This work	n_TOF Zugec et al. (2014)	ORELA Guber et al. (2010)	KADoNiS v1.0
5	38.7 (45)	34.7	41.3 (23)syst(6)stat	39.0 (21)	40.0 (22)
10	48.1 (48)	43.2	50.1 (28)syst(7)stat	48.4 (22)	49.0 (22)
15	44.7 (43)	40.1	45.9 (25)syst(7)stat	44.9 (20)	45.3 (20)
20	40.3 (39)	36.2	41.0 (22)syst(6)stat	40.5 (18)	40.7 (18)
25	36.7 (35)	32.9	37.2 (20)syst(6)stat	36.9 (16)	37.0 (16)
30	33.9 (33)	30.4 (23)syst(9)stat	34.2 (18)syst(6)stat	34.0 (15)	34.1 (15)
40	29.8 (29)	26.7	30.3 (15)syst(5)stat	29.9 (13)	30.1 (15)
50	26.9 (26)	24.2	27.7 (14)syst(4)stat	27.1 (12)	27.3 (12)
60	24.8 (24)	22.2	25.8 (13)syst(3)stat	24.9 (11)	25.3 (11)
80	21.7 (21)	19.5	23.2 (11)syst(3)stat	21.8 (9)	22.3 (10)
100	19.5 (18)	17.5	21.3 (10)syst(2)stat	19.6 (8)	20.3 (9)

Table 8. Table 8: Comparison of Maxwellian averaged cross sections at k ​ T 𝑘 𝑇 kT =30 keV from previous experiments, evaluated libraries, compilations, and theoretical predictions. The values in brackets are the respective experimental uncertainties. Theoretical values are given without error bars.

Reference	${⟨\sigma ⟩}_{30keV}$	Ratio to
	[mbarn]	this work
Experimental data
This work	30.4 (23)syst(9)stat	1.00(7)
n_TOF (2014) Zugec et al. (2014)	34.2(18)syst(6)stat	1.13(6)
ORELA new eval. (2010) Guber et al. (2010)	34.0 (15)	1.12(5)
ORELA (1993) Perey et al. (1993)	40.2 (60)	1.32(20)
Karlsruhe (1984) Wisshak et al. (1984)	38.0 (25)	1.25(8)
Karlsruhe (1974/75) Beer et al. (1974); Beer and Spencer (1975)	39.0 (20)	1.28(7)
Compilations
KADoNiS v1.0 (2016)	34.1 (15)	1.12(11)
KADoNiS v0.3 (2009)	38.7 (15)	1.27(5)
KADoNiS v0.2 (2006)	39 (2)	1.28(7)
Bao et al. (2000)	41 (2)	1.35(7)
Beer and Winters (1992)	43.2 (28)	1.39(9)
Evaluated libraries incl. covariances
ENDF/B-VII.1 Chadwick et al. (2011)	33.9 (33)	1.12(11)
JEFF-3.2 Koning (2014)	40.0 (60)	1.32(20)
JENDL-4.0 Shibata et al. (2011)	40.1 (20)	1.32(7)
Hauser-Feshbach models
NON-SMOKER Rauscher and Thielemann (2000)	49	1.61
MOST (2002) Goriely (2002)	78.5	2.58
MOST (2005) Goriely (2005)	72.2	2.38

Equations

$$N_{198}=\frac{C(t_m)}{{\epsilon }_{\gamma }{I}_{\gamma }{k}_{\gamma }(1-e^{-\lambda t_m})e^{-\lambda t_w}}.$$

$$k_{\gamma }=\frac{1}{d\mu (1-e^{d\mu })}.$$

$$N_{act}=N_i⟨\sigma {⟩}_{exp}{\Phi }_{tot}{f}_b.$$

$$f_b=\frac{{\int }_0^{t_a}\varphi (t)e^{-\lambda (t_a-t)}dt}{{\int }_0^{t_a}\varphi (t)dt}$$

$${\Phi }_{tot}=\frac{N_{198}}{N_{197}⟨\sigma {⟩}_{exp}{(}^{197}Au)f_b}.$$

$$⟨\sigma {⟩}_{exp}{(}^{58}\text{Ni})=\frac{N_{59}}{N_{58}}\cdot \frac{1}{{\Phi }_{tot}}.$$

$$\Phi =dN/d{E}_n\sim \sqrt{E_n}\cdot e^{-E_n/kT}.$$

Full text

Neutron capture cross section, Accelerator Mass Spectrometry, $s$-process

††preprint: APS/123-QED

I Introduction

58Ni is the most abundant stable isotope of nickel (Table 1) and of special interest for astrophysics and reactor technologies.

Neutron capture on 58Ni produces the long-lived isotope 59Ni which has an adopted half-life of $t_{1/2}$= 76(5) ka Nishiizumi et al. (1981). However, recent measurements have shown that this value could be as high as 97(9) ka Wallner et al. (2007) . Since 58Ni is an important constituent of structure materials in nuclear reactors, neutron activation leads to a potential radiation hazard. In astrophysics it is an important seed nucleus for the ”slow neutron capture” ($s$) process, and the half-life of 59Ni is long enough that under typical conditions no significant branching occurs and the main reaction flow continues via 58Ni$(n,\gamma)^{59}$Ni$(n,\gamma)^{60}$Ni.

I.1 Production of iron-group elements in stars

Woosley et al. Woosley et al. (1973) demonstrated in 1973 that in massive stars ($M>8~{}M_{\odot}$), a superposition of late burning stages of explosive oxygen and silicon burning, provides a good fit to the solar abundances in the mass region $28<A<62$. The final composition depends on the respective peak temperatures, densities, and the available amount of protons, neutrons, and $\alpha$-particles.

Explosive silicon burning occurs at T$$\geq4 GK and can be subdivided into incomplete burning, complete burning with normal freeze-out, and complete burning with $\alpha$-rich freeze-out.

Incomplete silicon burning occurs at peak temperatures of $T$= 4$-$5 GK when the temperature is not high enough for nuclear reactions to overcome the bottleneck at the magic shell closure $Z=20$ (Ca). The most abundant burning products are the same as for explosive oxygen burning, but partial leakage can produce iron-group elements.

Complete Si burning is possible for $T>5$ GK where a full Nuclear Statistical Equilibrium (NSE) is established and iron-group elements like 58Ni are produced. Complete Si burning with $\alpha$-rich freeze-out occurs at lower densities when the triple $\alpha$-reaction is not fast enough to keep the helium abundance in equilibrium. Then traces of $\alpha$ nuclei remain which were not transformed into iron-group elements.

These iron-group elements can act as seed nuclei for the weak $s$-process in future generations of stars.

I.2 The $s$-process and 58Ni

The $s$-process distribution in the solar system can be divided into three components: a ”weak” (60$<$A$<$90 Pignatari et al. (2010)), a ”main” (90$<$A$<$208 Bisterzo et al. (2014)), and a ”strong” component (mostly producing half of the solar 208Pb Gallino et al. (1998)), corresponding to different astrophysical scenarios, temperatures, and neutron densities Käppeler et al. (2011). The main and the strong $s$-process occur mainly in low- and intermediate-mass (1$-$3 M⊙) ”thermally pulsing asymptotic giant branch” (TP-AGB) stars at different metallicities Travaglio et al. (2004).

The weak $s$-process component occurs in massive stars ($M>$8 $M_{\odot}$) during the core He- and shell C-burning phases. Near He exhaustion the temperature rises to about 300 MK ($kT=26$ keV) and activates the 22Ne($\alpha,n$)25Mg reaction as main neutron source Raiteri et al. (1991a, b, 1993). While the peak neutron densities reach only moderate values of about 106 cm*-3*, this weak $s$-process phase can last several million years.

A fraction of the 22Ne survives and is re-ignited in the following convective shell C-burning phase when new $\alpha$-particles are produced via the 12C(12C,$\alpha$)20Ne reaction. At about 1 GK ($kT=90$ keV) the 22Ne($\alpha,n$)25Mg reaction works more efficiently and reaches peak neutron densities of 1010 cm*-3* for a duration of only a few years.

Starting with an iron-seed distribution produced during silicon burning of earlier generations of stars, the neutron capture on the abundant 58Ni is one of the first reactions in the weak $s$-process. An accurate knowledge of the neutron capture cross section at $s$-process temperatures is thus an important prerequisite for understanding the reaction network of the $s$-process.

I.3 Previous measurements of the 58Ni$(n,\gamma)$59Ni cross section at stellar energies

The 58Ni$(n,\gamma)$59Ni cross section has been measured at stellar energies in several time-of-flight (TOF) experiments Beer et al. (1974); Beer and Spencer (1975); Wisshak et al. (1984); Perey et al. (1993); Guber et al. (2010); Zugec et al. (2014). The overview in the ”Karlsruhe Astrophysical Database of Nucleosynthesis in Stars” (KADoNiS) Dillmann and Plag (2016a) (see also Table 8) reveals that ”older” measurements which were performed before 1993 Beer et al. (1974); Beer and Spencer (1975); Wisshak et al. (1984); Perey et al. (1993) yield a systematically higher Maxwellian-averaged cross section at $kT$= 30 keV (MACS30) compared to the two more recent TOF measurements from ORELA Guber et al. (2010) and n$\_$TOF Zugec et al. (2014). The latter two are in agreement and were used for the derivation of the new recommended MACS at $kT=30~{}$keV of $\langle\sigma\rangle_{30keV}=34.1(15)$ mbarn in the most recent release of the KADoNiS v1.0 database.

To investigate this systematic discrepancy we studied this reaction with a completely independent method. By combining the neutron activation of two Ni samples of natural isotopic composition in a quasi-stellar neutron spectrum with the subsequent atom counting of the reaction product 59Ni using accelerator mass spectrometry (AMS), the cross section of the 58Ni$(n,\gamma)^{59}$Ni reaction was extracted. The preliminary results were reported in a previous conference proceeding Rugel et al. (2007). However, the first sample suffered from a relatively high isobaric contamination of 59Co. As a consequence a chemical purification step was introduced for the second sample, as described in Sec. III. Our preliminary result ($\langle\sigma\rangle_{30keV}=30.0(23)$ mbarn Rugel et al. (2007)) is in conflict with the previous TOF measurements and the new recommended MACS ($\langle\sigma\rangle_{30keV}=34.1(15)$ mbarn). This discrepancy triggered the irradiation of a third Ni sample with a lower initial 59Co content, which did not require a chemical treatment prior to the AMS measurement.

In this paper we present the final results of all three samples, activated at KIT with a quasi-Maxwellian neutron spectrum of $kT=25~{}$keV and measured for the 59Ni content at the 14 MV tandem accelerator at the Maier-Leibnitz laboratory in Garching between April 2005 and January 2011. The neutron irradiations at the (now closed) 3.7 MV Van-de-Graaff accelerator in Karlsruhe and the determination of the neutron fluence are described in Sec. II. The AMS measurements and the chemical sample preparation for the reduction of the interfering 59Co isobar are described in Sec. III. The derivation of the resulting MACS and a comparison with previous measurements, evaluated libraries, as well as theoretical predictions, are shown in Sec. IV.

II Neutron activation

II.1 Activation setup

The activation was carried out with the Karlsruhe 3.7 MV Van de Graaff accelerator. Neutrons were produced with the 7Li($p,n$)7Be source by bombarding $20-30~{}\mu$m thick layers of metallic Li on a water-cooled Cu backing with protons of 1912 keV, 31 keV above the reaction threshold. The angle-integrated neutron spectrum at this energy almost perfectly imitates a Maxwell-Boltzmann distribution for $kT=25.0\pm 0.5~{}$keV with a maximum neutron energy of 106 keV Ratynski and Käppeler (1988), as can be seen in Fig. 1.

At this proton energy the neutrons are kinematically collimated in a forward cone with 120∘ opening angle. Neutron scattering by the Cu backing is negligible since the transmission is about 98% in the energy range of interest. To ensure a homogeneous illumination of the entire surface, the proton beam with a DC current of $\sim 100~{}\mu$A was wobbled across the Li target. In this way a mean neutron intensity over the period of the activations of $(1.6-2.1)\times 10^{9}$ s*-1* was assured at the position of the samples, which were placed in close geometry to the Li target inside the neutron cone (see Fig. 1). A 6Li-glass monitor at 1 m distance from the neutron target was used to record the time-dependence of the neutron yield in intervals of 60 s as the Li target degrades during the irradiation. In this way the proper correction of the number of nuclei which decayed during the activation (factor $f_{b}$ in Eq. 4) can be obtained. This correction is negligible for isotopes with very long half-lives like 59Ni but becomes important for comparably short-lived isotopes like 198Au ($t_{1/2}=2.6941(2)$ d), since the reaction 197Au$(n,\gamma)$ was used as the reference cross section for the neutron fluence determination.

Three samples prepared from metallic Ni powder with natural composition were used in our measurements. The sample material was pressed into thin pellets of 6 mm and 8 mm diameter, enclosed in 15 $\mu$m thick aluminum foil and sandwiched between two 30 $\mu$m thick gold foils of the same diameter. In this way the neutron fluence in our experimental neutron distribution (Fig. 1) can be determined relative to the revised neutron capture cross section of 197Au in the experimental neutron spectrum (see Sec. II.3).

The samples ”ni-1” and ”ni-2” were irradiated in the same, first activation run. The sample ”ni-3” was irradiated independently 3 years later. The net irradiation times were $\sim$ 6 d and $\sim$ 5 d, respectively, and the total neutron fluence $\Phi_{tot}$ was calculated from the $\gamma$-activity of the gold foils (see Table 2).

II.2 Determination of the neutron flux

The measurement of the induced 198Au activity after the irradiation was performed with a high purity germanium (HPGe) detector with a well defined measuring position at a distance of 76 (1) mm surrounded by 10 cm lead shielding. The relative efficiency for the 411.8 keV $\gamma$-transition into the ground-state of 198Hg was determined with a set of reference sources and yielded $\varepsilon_{\gamma}$=0.212 (4)%.

The total amount of produced 198Au nuclei, $N_{198}$, at the end of the irradiation can be deduced from the number of events $C(t_{m})$ in the particular $\gamma$-ray line at 411.8 keV registered in the HPGe detector during the measuring time $t_{m}$. The factor $t_{w}$ corresponds to the waiting time between the end of the irradiation and the start of the activity measurement:

[TABLE]

$I_{\gamma}$ accounts for the relative $\gamma$ intensity per decay of the 411.8 keV transition ($I_{\gamma}$= 95.58(12)%, Chunmei (2002)). For the measurement of the activated gold foils with the HPGe, the $\gamma$-ray self-absorption $k_{\gamma}$ has to be considered. For disk shaped samples with a thickness $d$, $k_{\gamma}$ can be calculated with the $\gamma$-absorption coefficients $\mu$ Hubbell and Seltzer (2004) via Eq. 2:

[TABLE]

This correction factor was 0.995 for all gold foils.

The number of produced atoms $N_{act}$ is determined by

[TABLE]

In this equation, $N_{i}$ is the number of sample atoms, $\langle\sigma\rangle_{exp}$ is the spectrum-averaged neutron capture cross section in the experimental neutron spectrum, and $\Phi_{tot}$ the total neutron fluence (see Table 2). The factor

[TABLE]

accounts for the decay of radioactive nuclei during the irradiation time $t_{act}$ as well as for variations in the neutron flux. This factor is calculated from the neutron flux history recorded throughout the irradiation with the 6Li-glass detector at 1 m distance from the target.

The time-integrated neutron flux $\Phi_{tot}=\int\phi(t)dt$ seen by the sample (see Table 2) was determined by averaging the neutron fluences of the two gold foils enclosing the respective sample:

[TABLE]

$\langle\sigma\rangle_{exp}$ is the experimental spectrum-averaged 197Au cross section (see discussion in the following section).

II.3 The new recommended 197Au$(n,\gamma)^{198}$Au cross section

197Au is commonly used as reference for neutron capture cross section measurements. However, it is only considered a standard for thermal energies ($kT$= 25.3 meV) and in the energy range between 200 keV and 2.8 MeV Carlson (2009). Recent high-accuracy time-of-flight measurements at n_TOF (Massimi et al., 2010; Lederer et al., 2011) and at GELINA (Massimi et al., 2014) revealed a discrepancy of 5% at $kT$= 30 keV compared to the recommended 197Au$(n,\gamma)$198Au cross section used in the previous versions of the KADoNiS database Bao et al. (2000); Dillmann et al. (2009a).

This previous recommendation was based on an activation measurement performed by the Karlsruhe group, which yielded a spectrum-averaged cross section of 586(8) mbarn for the quasi-stellar spectrum of the 7Li$(p,n)$7Be source at $E_{p}$= 1912 keV (see Fig. 1), from which a MACS of 582(9) mbarn at $kT=$ 30 keV was derived Ratynski and Käppeler (1988). The extrapolation to higher and lower energies was done with the energy dependence measured at the ORELA facility Macklin et al. (1975).

However, all recent TOF measurements Massimi et al. (2010); Lederer et al. (2011); Massimi et al. (2014) are in perfect agreement with the latest ENDF/B-VII.1 evaluation Chadwick et al. (2011), and with a new activation measurement by the group in Sevilla Jimenez-Bonilla and Praena (2014). Based on this consistency of new experimental data and data libraries, KADONIS v1.0 Dillmann and Plag (2016b) now uses the value of 613(7) mb for the 197Au(n,$\gamma$) cross section for $kT$=$30$ keV. For the astrophysically relevant energy region between $kT$=$5$ and 50 keV the values were derived by the weighted average of the GELINA measurement and the n$\_$TOF measurement. The uncertainty in this energy range was taken from the GELINA measurement Massimi et al. (2014). For the energies between $kT$= 60$-$100 keV the average of recent evaluated libraries (JEFF-3.2 Koning (2014), JENDL-4.0 Shibata et al. (2011), ENDF/B-VII.1 Chadwick et al. (2011)) was used with the uncertainty from the standard deviation given in JEFF-3.2 and ENDF/B-VII.1 (Table 3).

The new reference value for the spectrum-averaged 197Au cross section of the experimental neutron distribution (Fig. 1) becomes $\langle\sigma\rangle_{exp}$= 632(9) mbarn and was subsequently used for the determination of the neutron fluence in Eq. 5.

III Determination of the isotopic ratio via AMS

III.1 Accelerator Mass Spectrometry

Accelerator Mass Spectrometry (AMS) Synal (2013); Kutschera (2013) is an ultra-sensitive and ultra-selective analytical method for the detection of trace amounts (sub-ng range) of long-lived radioactive isotopes like 59Ni. AMS allows the determination of the concentration of the radioisotope relative to the ion current of a stable isotope (ideally of the same element). It is the most sensitive detection method for many radioisotopes and can reach down to isotopic ratios of 10*-16* for isotopes where complete background suppression is possible (e.g. 14C, 60Fe). AMS is able to outperform decay counting techniques in cases where the radioisotope of interest is either very long-lived or lacks suitable $\gamma$ transitions. However, one of the major challenges for AMS measurements is the suppression of (stable) isobaric interference.

AMS usually determines the isotopic ratio of a radioactive isotope relative to one stable isotope of the same element. In our case we have determined the ratio of 59Ni versus 58Ni, $R$=$\frac{N_{59}}{N_{58}}$. The factor $f_{b}$ (Eq. 4) is 1 for the long-lived 59Ni so we can rewrite Eq. 5 as

[TABLE]

The derived experimental spectrum-averaged cross section $\langle\sigma\rangle_{exp}$(58Ni) for the 58Ni$(n,\gamma)$59Ni reaction is given in Table 5.

A decade ago AMS has been successfully combined with astrophysical activation measurements, mainly for the determination of $(n,\gamma)$ cross sections for $s$-process nucleosynthesis (see, e.g. Nassar et al. (2005); Rugel et al. (2007); Dillmann et al. (2009b)) or for the independent measurement of actinide cross sections (235,238U$(n,\gamma)$) to resolve discrepancies in nuclear data libraries Wallner et al. (2014). But also charged-particle cross sections of astrophysical interest have been measured, e.g. the 25Mg$(p,\gamma)^{26}$Alg and 40Ca$(\alpha,\gamma)$44Ti cross sections Arazi et al. (2006); Nassar et al. (2006). An overview of cross sections measured with AMS for nuclear astrophysics so far is given in Refs. Wallner (2010) and Korschinek and Faestermann (2010).

III.2 The GAMS setup in Garching

The AMS setup GAMS (Gas-filled Analyzing Magnet System) at the Maier-Leibnitz-Laboratory (MLL) in Garching, Germany, is schematically shown in Fig. 2. Its main components are a single-cathode Cs-sputter ion source, a 90*∘* injector magnet, a 18*∘* electrostatic deflection, a 14 MV tandem accelerator, a 90*∘* analyzing magnet, and a Wien-filter, followed by a dedicated particle identification system.

To separate the radioisotope 59Ni from its stable isobar 59Co, which is orders of magnitude more abundant, the combination of a gas-filled magnet with a multi-$\Delta$E ionization chamber is employed Knie et al. (1997, 2000). In total, the ionization chamber provides five $\Delta$E signals and the signal from the Frisch-grid (proportional to the total energy deposition in the chamber). The first two anodes are diagonally segmented, providing a horizontal position information (X-position) of the incident particles. Additionally, both, the incident X- and Y-angle, can be derived from the individual signals.

The isotopic ratio of the radioisotope relative to a stable isotope is determined from the count-rate of the radioisotope detected in the ionization chamber, relative to the ion current of a stable reference isotope measured with a Faraday cup in front of the GAMS. Radionuclide and stable isotope were selected successively by adjusting the injector magnet, terminal voltage and Wien-filter voltage appropriately. The measurement relative to a standard sample of known isotopic ratio allows to cancel many types of systematic uncertainties such as the ion-source yield, stripping yields, and particle transmissions through the AMS system.

III.3 Chemical treatment of the samples and preparation of the 59Ni standard

In the first AMS beamtimes, sample ni-1 was directly pressed into sample holders without any pretreatment. This sample showed a high Co content. Therefore, the second irradiated foil (ni-2) was dissolved in 10 N hydrochloric acid (HCl) and purified by anion exchange chromatography with DOWEX AG1 resin. In a subsequent step ammonia was added until a pH value of 9 was reached, and the Ni was precipitated with dimethylglyoxim. This element-selective chelating agent was centrifuged and washed with water, and then ashed to nickel(II)oxide (NiO) which served as sample material. Due to this chemical treatment the isobar 59Co was suppressed by two orders of magnitude. The sample material for the third sample (ni-3) showed, in a first test, a much lower 59Co background rate, thus chemical treatment was not necessary.

The 59Ni standard material ’59NiO-KK92-Munich-10’ was produced via irradiation of natural Ni powder with thermal neutrons. The simultaneously produced 65Ni ($t_{1/2}$= 2.52 h) served as a neutron flux monitor for the neutron fluence. The corrections for the epithermal neutron flux and sample position were on the order of 0.5% and cancel. The activity of 65Ni was measured with a $\gamma$-ray detector utilizing the two well-known $\gamma$-ray lines at 1481.8 keV and 1115.5 keV. With the well-known thermal neutron capture cross section of 64Ni ($\sigma$= 1.52(3) barn Gryntakis and Kim (1978)) and the remeasured thermal cross section of 58Ni ($\sigma$= 4.13(5) barn Raman et al. (2004)), we calculate a ${}^{59}\text{Ni}/\text{Ni}$ ratio for our standard of 9.1(4)$\times$10*-11*. This uncertainty also includes the errors from the geometry of the sample (2%), the statistical uncertainty of the $\gamma$-ray measurement (1.8%) and the uncertainty of the HPGe efficiency calibration (152Eu standard source with 2.0% uncertainty).

III.4 AMS procedure and data analysis for 59Ni

For the determination of ${}^{59}\text{Ni}/\text{Ni}$ ratios the tandem accelerator was operated at terminal voltages between 12.5 MV and 13.0 MV. 60Ni was used as a macroscopic beam, both for tuning of the ion optics and for normalization of the 59Ni events. The ions were extracted as 59Ni- and 60Ni- from the ion source and a typical current of 100 nA 60Ni- was injected into the accelerator. On the high-energy side of the accelerator, a charge state 12+ was selected for both isotopes with the analyzing magnet, resulting in particle energies between 162 MeV and 170 MeV for 59Ni. The GAMS magnet was filled with 5.5$-$6.7 mbar of nitrogen gas. Passing through the magnet, 59Co acquires a lower average charge state than 59Ni, due to its lower element number $Z$ (see Fig. 2). This resulted in a spatial separation between the isobars of several centimeters horizontally and thus allowed to block most unwanted 59Co using an aperture in front of the ionization chamber. The main background in the detector was still due to tails of 59Co (see Fig. 3).

In the data analysis, a region of interest for 59Ni was defined by acquiring about 1000 events of 59Ni using the standard sample. Software cuts on all signals were then applied, leading to a reduced acceptance of 59Ni of between 40% and 60%. The blank level, which was measured during all AMS runs using commercial Ni powder (assuming negligible 59Ni content), was always at least three orders of magnitude lower than the ${}^{59}\text{Ni}/\text{Ni}$ concentration of the activated and the standard samples. A final suppression of background events is achieved by applying a 2-dimensional cut on one of the energy loss signals versus the X-position of the incident ions, as shown in Fig. 3.

A total suppression of 59Co of about 8 orders of magnitude was achieved, combining the GAMS magnet and all software cuts. The resulting background level obtained from the commercial Ni material was ${}^{59}\text{Ni}/\text{Ni}=6.7\times 10^{-15}$, which was considered negligible compared to the measured ratios in our samples of $(1.7-2.0)\times 10^{-11}$, see Table 2.

III.5 Error analysis

All uncertainties in this work are given as 1-$\sigma$ confidence intervals. The experimental uncertainties from the activation and AMS measurements are summarized in Table 4. Note that we have separated the uncertainties into systematic contributions (which were added linearly) and statistical contributions (which were added quadratically).

III.5.1 Uncertainties in the activation measurement

The uncertainties from the activation measurement affect mainly the measurement of the gold standard and thus the determination of the neutron fluence $\Phi_{tot}$. The uncertainty of the 58Ni abundance can be neglected (0.03%, see Table 1).

The uncertainty in the mass determination of the Au foils (0.3%) was estimated by a reading error of the used balance of $\sim$50 $\mu$g for the 20 mg foils. The neutron capture cross section of 197Au for the experimental neutron spectrum shown in Fig. 3 has an uncertainty of 1.4% Ref. Dillmann and Plag (2016b).

A random error of 1.5% was assumed to account for the uncertainty of the sample position (0.25 mm) relative to the gold foils and the neutron target during the two activations which affects the neutron flux seen by the samples. The uncertainty of the intensity of the 411.8 keV $\gamma$-line in 198Au ($I_{\gamma}$= 95.58(12)%) is 0.13%, and the counting statistics yielded an uncertainty of 0.25%. The uncertainty of the HPGe efficiency calibration was derived from the accuracy of the set of calibration sources and of the calibration procedure and yielded 2.0%. The systematic uncertainties (including the 1.4% from the neutron capture cross section of gold) for the activation measurement sum linearly up to 3.56%, whereas the statistical errors yield 1.54%.

III.5.2 Uncertainties in the AMS measurement

The AMS measurements were carried out in a ’sandwich’ type order, where the actual samples of interest were measured between two measurements of the standard sample (3 data runs each), to account for instrumental drift. Using the known concentration of 59Ni/60Ni in the standard, the transmission from the Faraday cup in front of the GAMS to the particle detector can be calculated. The typical uncertainty in transmission was 10%, which includes current readings and counting statistics for the standard sample.

Additionally, 13% statistical uncertainty were included for each 58Ni ion-current reading of the sample of interest, which was determined before and after each data run (average run time 300 s). This results in a statistical uncertainty of each individual AMS data run of 13.6%. This needs to be increased to account for the statistical uncertainty in counting statistics of 59Ni (calculated as $\sqrt{N}/N$ for typically $N=100$ events of 59Ni per data run). The results for the concentrations of 59Ni/58Ni for each sample is then calculated as an error weighted mean from all beamtimes. A total of 20 and 10 data runs were recorded for samples ni-2 and ni-3, respectively.

An exception was made for the sample ni-1, which was only measured in three data runs in a single beamtime and suffered from a high 59Co contamination. For this sample, an additional $10\%$ contribution to the uncertainty was introduced to account for statistical fluctuations in the 59Co suppression.

Subsequently, an error weighted mean concentration of 59Ni/Ni was calculated for all data runs of each individual sample, as summarized in Tab. V.

Owing to the technique of performing AMS measurements of isotope ratios relative to a standard sample of known concentration of the radioisotope in question, all systematic uncertainties related to ion-source performance, stripping yield, and transmission cancel out. The only systematic uncertainty taken into account for the AMS result in this work is thus the uncertainty of the concentration of the standard sample (4.09%).

III.6 Determination of the spectrum-averaged cross section

The experimental spectrum-averaged cross section $\langle\sigma\rangle_{exp}$ for the 58Ni($n,\gamma$)59Ni reaction was determined according to Eq. 6 with the known values for $\Phi_{tot}$ and $N_{{}^{59}\text{Ni}}$/$N_{{}^{58}\text{Ni}}$ from Table 5.

The weighted spectrum-averaged cross section from the three samples was calculated to $\langle\sigma\rangle_{exp}(^{58}\rm{Ni})$= 29.9 mbarn (see Table 5). The total systematic uncertainty (7.7%, see Table 4) is $\pm$2.3 mbarn, whereas the total statistical uncertainty is calculated as squareroot of the quadratic sum from the statistical uncertainty of each sample and yields $\pm$0.9 mbarn ($\pm$3.0%). In the following sections we will quote separately the total systematical and statistical errors (e.g. for comparison with the latest measurement from n_TOF Zugec et al. (2014)).

The spectrum-averaged cross section $\langle\sigma\rangle_{exp}=~{}29.9~{}$mbarn is used in Sec. IV for the determination of the Maxwellian-averaged cross section.

IV Calculation of Maxwellian-averaged cross sections

In an astrophysical environment with temperature $T$, interacting particles are quickly thermalized by collisions in the stellar plasma, and the neutron energy distribution can be described by a Maxwell-Boltzmann spectrum:

[TABLE]

For the calculation of a Maxwellian-averaged cross section (MACS) from our spectrum-averaged cross section $\langle\sigma\rangle_{exp}$ we applied the following procedure: the experimental neutron spectrum of the 7Li($p,n$)7Be reaction simulates the energy dependence of the flux $v~{}\cdot~{}\Phi~{}\sim~{}E_{n}~{}\cdot~{}e^{-E_{n}/kT}$ with $kT=25.0\pm$ 0.5 keV almost perfectly Ratynski and Käppeler (1988) (see Fig. 1). However, the cutoff at $E_{n}=106~{}$keV and small deviations from the shape of the ideal Maxwellian spectrum require a correction of the measured cross section $\langle\sigma\rangle_{exp}$ for obtaining a true Maxwellian average at $kT=25$ keV, $\langle\sigma\rangle$25keV. This correction factor is determined by a comparison with the energy-dependent cross sections from data libraries.

We determine a normalization factor $F_{norm}$ which gives a direct measure of the agreement between our experimentally determined cross sections $\langle\sigma\rangle_{exp}$ and the evaluated cross section $\sigma(E)$ folded with the experimental neutron spectrum of the 7Li$(p,n)$7Be source, $\langle\sigma\rangle_{eval}$. Here we assume that the energy dependence of the library data in this energy range is correct, but the absolute scale may differ.

IV.1 Evaluated cross section libraries

The energy-dependent neutron cross sections from the evaluated cross section libraries ENDF/B-VII.1 Chadwick et al. (2011), JEFF-3.2 Koning (2014), and JENDL-4.0 Shibata et al. (2011) were used for comparison. All three libraries include covariance data but with different uncertainties. JENDL-4.0 gives a 5.0% uncertainty from the covariances for the MACS at $kT$= 30 keV, JEFF-3.2 gives 15.0%, and ENDF/B-VII.1 gives 9.7%.

The cross sections were folded with our experimental neutron distribution to derive the spectrum-averaged evaluated cross section, $\langle\sigma\rangle_{eval}$ and the respective normalization factor $F_{norm}$= $\langle\sigma\rangle_{exp}$/$\langle\sigma\rangle_{eval}$.

As can be seen from Table 6, the calculated $\langle\sigma\rangle_{eval}$ cross sections do not agree for ENDF/B-VII.1 on one side, and JEFF-3.2 and JENDL-4.0 on the other side. This difference can be explained by the different resonance parameter data used to derive the resolved resonance region (RRR) and the respective statistical model which was used for the unresolved resonance region (URR) for $E_{n}>812$ keV.

The JENDL database uses the resonance parameters from an older technical report of Perey et al. Perey (1988) but not the published data of the same group in Ref. Perey et al. (1993). The data for the URR come from the statistical model code CASTHY Igarasi and Fukahori (1991).

JEFF-3.2 is based on older ENDF/B-VI.1 data and is thus identical with the JENDL-4.0 data in the RRR for $E_{n}<812$ keV. It is not obvious from the comment files in the database what was done for the URR above $E_{n}>812$ keV, but as can be seen in Fig. 4 the cross section is slightly lower than in the JENDL-4.0 database. However, this influence has only a minor effect on the MACS at higher energies.

The data used in the ENDF/B-VII.1 library is the most recent and the RRR was re-evaluated by the Oak Ridge group in 2009. The following comment is given in the header of the data file: ”The previous set of resonance parameters was based on the SAMMY analysis of ORNL neutron transmission, scattering and capture measurements by C.M Perey et al. Perey (1988). The present results were obtained by adding to the SAMMY experimental data base the capture cross sections recently measured at ORELA by K.H. Guber et al. (priv. comm. 2009) and the GELINA very high resolution transmission measurements performed by Brusegan et al. Brusegan (1994). A complete Resonance Parameter Covariance Matrix (RPCM) is obtained from the SAMMY analysis of the experimental data base made consistent by neutron energy scale adjustments, and normalization and background corrections.”

The respective normalization factor to our experimental value of $\langle\sigma\rangle_{exp}(^{58}\rm{Ni})=29.90$ mbarn is $F_{norm}=0.897$ for the ENDF/B-VII.1 library, compared to $F_{norm}=0.77$ for JEFF-3.2 and JENDL-4.0 which are based on older data. Due to this and the perfect agreement with the following publication from the ORNL group Guber et al. (2010) and the independently measured data from the n_TOF group Zugec et al. (2014) we used only the cross section from the ENDF/B-VII.1 library for our calculation of the MACS.

IV.2 Maxwellian-averaged cross sections

For the calculation of the MACS between $kT$=5$-$100 keV we have multiplied the evaluated cross section from the ENDF/B-VII.1 database Chadwick et al. (2011) with the normalization factor $F_{norm}$= 0.90. This procedure is justified since the given covariance data in this database yields MACS with uncertainties of $\pm(11.7-9.5)\%$.

The following Table 7 shows the calculated MACS from this work in comparison to the MACS from ENDF/B-VII.1 and experimental data from recent TOF measurements Zugec et al. (2014); Guber et al. (2010). Our result of $\langle\sigma\rangle_{30keV}$= 30.4 (23)syst(9)stat mbarn is slightly lower ($\sim 10\%$) than the two TOF measurements from Zugec et al. (2014); Guber et al. (2010) but still agrees within the uncertainties.

In Table 8 we compare our MACS at $kT$= 30 keV with previously measured values, recommended data from neutron-capture cross section compilations, evaluated libraries, and pure Hauser-Feshbach models. It should be noted that all previous measurements were performed with the TOF technique, and our measurement with the activation technique involves completely different systematic uncertainties and thus is an independent confirmation of the measured cross sections. The activation technique includes already the direct capture (DC) component which otherwise has to be inferred from theoretical predictions. The DC part calculated in Ref. Guber et al. (2010) at $kT$= 30 keV is $\langle\sigma\rangle_{kT=30keV,DC}$=1.36(34) mbarn, whereas in the n_TOF publication of Ref. Zugec et al. (2014) no additional $s$-wave DC component was considered due to the good global fit to existing evaluated data.

V Summary and Conclusions

We have measured the 58Ni$(n,\gamma)$59Ni cross section for the first time with the activation technique combined with subsequent 59Ni measurements using Accelerator Mass Spectrometry. A Maxwellian-averaged cross section at $kT$=30 keV of $\langle\sigma\rangle_{30keV}$= 30.4 (23)syst(9)stat mbarn could be deduced. This result is slightly lower than the two recent TOF measurements from Zugec et al. (2014); Guber et al. (2010) but agrees within the uncertainties and confirms a lower MACS30 compared to earlier TOF measurements.

The combination of the activation technique with AMS has been proven as a powerful method to determine cross sections of isotopes with long-lived reaction products, as independent confirmation of TOF measurements.

Acknowledgements.

This work was supported by the DFG Cluster of Excellence ’Origin and Structure of the Universe’ (www.universe-cluster.de). We thank E.-P. Knaetsch, D. Roller and W. Seith at the Karlsruhe 3.7 MV Van-de-Graaff accelerator and the operator and workshop teams at the MLL in Garching for their help and support during the measurements. I.D. was supported by EFNUDAT and the Excellence Cluster Universe.