Edinburgh Research Explorer Measurement of the 154Gd(n,) cross section and its astrophysical implications

The neutron capture cross section of 154 Gd was measured from 1 eV to 300 keV in the experimental area located 185 m from the CERN n TOF neutron spallation source, using a metallic sample of gadolinium, enriched to 67% in 154 Gd. The capture measurement, performed with four C 6 D 6 scintillation detectors, has been complemented by a transmission measurement performed at the GELINA time-of-ﬂight facility (JRC-Geel), thus minimising the uncertainty related to sample composition. An accurate Maxwellian averaged capture cross section (MACS) was deduced over the temperature range of interest for s process nucleosynthesis modeling. We report a value of 880(50) mb for the MACS at kT = 30 keV, signiﬁcantly lower compared to values available in literature. The new adopted 154 Gd(n, γ ) cross section reduces the discrepancy between observed and calculated solar s-only isotopic abundances predicted by s-process nucleosynthesis models.


Introduction
All the elements heavier than those in the iron group are produced by a sequence of neutron capture reactions and β decays taking place in a hot stellar environment, during different phases of stellar evolution. The two main processes involved are the slow (s) and the rapid (r) neutron capture processes. The s process [1,2] owes its name to the neutron-capture time scale, which allows β decay to occur between consecutive capture events. Consequently, a series of these reactions produce stable isotopes by moving along the β-stability valley. On the other hand, when the neutron densities are high enough [3], the neutron capture sequence is much faster than the β decays and the path, the r process path, can proceed toward many short-lived isotopes, approaching the neutron drip line.
Most nuclei receive a contribution from both the s and the r processes (see e.g. [4]). However, a few isotopes cannot receive any contribution from the r process because they are shielded against β decays by stable isobars and for this reason are called s-only isotopes. This is the case of the two gadolinium isotopes 152 Gd and 154 Gd which are shielded against the β-decay chains from the r-process region by their stable samarium isobars, as shown in Figure 1. To be precise, 152 Gd may receive an additional contribution from the p process, which proceeds via photo-disintegration. The amount of the p-process contribution to the 152 Gd abundance is still far from being precisely determined (see [5] and references therein), while a minor p-process contribution to the 154 Gd abundance cannot be excluded as well.
The almost pure s-process origin of 154 Gd (as for other s-only isotopes), makes its capture cross section crucial for testing various stellar models aiming at understanding s process nucleosynthesis in Asymptotic Giant Branch (AGB) stars, the most important stellar site for the s process. In particular, relevant hints on the shape and extension of the main s process neutron source, the so-called 13 C pocket [6], can be derived. Recently, several studies [7,8,4] have been conducted analyzing the solar s process abundances in the framework of a Galactic Chemical Evolution (GCE) model to investigate the effect of different internal structures of the 13 C pocket, which may affect the efficiency of the 13 C(α,n) 16 O reaction. In addition, Trippella and Collaborators [9] carried out a similar analysis based on single stellar models. Cristallo et al. [8] and Prantzos et al. [4] have obtained an under-production (-30%) of the 154 Gd 1 s-only nu- cleus compared to the s-only isotope 150 Sm, which is an un-branched isotope, usually assumed as a reference for the s process flow. This result is at odds with observations. The authors of ref. [8], have suggested that part of such a deviation could be connected to uncertainties in the adopted nuclear physics inputs, taken from the Karlsruhe Astrophysical Database of Nucleosynthesis in Stars (KADoNiS) version 0.3 [10], including the neutron capture cross section of 154 Gd.
In the work by Trippella et al. [9], problems for the s process production of Gd were found as well, although in this case, the discrepancy between the abundances of 150 Sm and 154 Gd is less pronounced. The need for a new 154 Gd(n,γ) measurement was underlined by the unreasonable prediction for the over-productions of 152 Gd and 154 Gd with respect to their solar abundances. In particular, the ratio 154 Gd/ 152 Gd), turned out to be lower than unity, while it is thought that 152 Gd should exhibit a higher p-process contribution as compared to 154 Gd [9]. In addition, 154 Gd was found to be produced insufficiently compared to the lighter s-only 148 Sm and 142 Nd, produced mostly by the s process and possibly partly by the p process.
The close correlation between stellar abundances and neutron capture cross sections calls for an accurate determination of the 154 Gd(n,γ) cross section. In addition, the reduction of the uncertainty related to nuclear physics inputs could rule out one of the possible causes of present discrepancies between observation and model predictions of the abundances. In fact, refined stellar models require a full set of Maxwellian Averaged Capture Cross Section (MACS) for thermal energies in the range kT = 8 − 30 keV. In the case of 154 Gd, 80% of the MACS at kT = 8 keV is determined by the capture cross section in the neutron energy region between 2.7−300 keV -hereafter we refer to this energy region as Unresolved Resonance Region (URR). At kT = 30 keV, the MACS depends almost entirely on the cross section in the URR. In this energy region, three time-of-flight 154 Gd(n,γ) cross section measurements are reported in literature, by Shorin et al. [11], Beer and Macklin [12] and Wisshak et al. [13]. They all cover the URR and the respective MACS exhibit large differences and at kT = 30 keV, they range from 878(27) mb to 1278(102) mb. Therefore, the data present in the literature, so far, are not conclusive enough to constrain stellar model calculations.
The large spread in the available experimental data could be related to the corrections for isotopic impurities which are necessarily applied in the data analysis. In particular, the poor knowledge of their cross sections, given the low natural abundance of 154 Gd (2.18%). Different discrepancies may be related to: i) the detectors used in the past experiments, which in some cases could have suffered from high neutron sensitivity; ii) the experimental determination of the neutron flux, which might have been biased in some previous measurements; iii) the quality of oxide samples and the need of canning for the container to avoid loss of material.
The present measurement reduced the impact of these limiting factors, by using the wellestablished, low neutron-sensitivity C 6 D 6 detectors [14], combined to a self-sustaining metallic sample enriched in 154 Gd, and exploiting the results of the recent 155 Gd(n,γ) measurement performed at n TOF [15]. Moreover, the gadolinium sample was characterised by a transmission measurement at the neutron time-of-flight facility GELINA at EC-JRC-Geel (Belgium).

Measurements
The neutron capture cross section measurement was performed at the neutron time-of-flight facility n TOF at CERN. In this facility, neutrons are produced by spallation reactions induced on a lead target by 20 GeV/c protons from the CERN Proton Synchrotron (PS), which provides a total of 2 × 10 15 neutrons/pulse, generated by a 7×10 12 protons/pulse primary beam. The initially fast neutrons are moderated and then collimated through two flight paths of different lengths. The present measurement was performed at the experimental area located 185 m from the spallation target. This long flight-path, combined with the 7 ns width of the proton bunches from the PS, results in a high energy resolution ranging from 3×10 −4 at 1 eV to 3×10 −3 a 100 keV [16]. 5 The neutron capture events were observed via the detection of the prompt γ-ray cascade from 155 Gd excited states. Four C 6 D 6 detectors, modified for minimizing their neutron sensitivity [14], were arranged at 125 • relative to the neutron beam direction and about 10 cm upstream from the gadolinium sample position. This configuration minimised the effect of anisotropic emission of γ cascades while reducing the background from in-beam photons scattered by the sample. The Total Energy detectors (see [17] and references therein) were used in combination with Pulse Height Weighting Technique (PHWT) [18,17]. A Au sample of the same diameter was used to normalise the measured yield, by applying the saturated resonance technique [19]. Also, two other samples with the same diameter of 3 cm were used. A lead sample enabled the estimate of the background, while a natural gadolinium sample allowed to assign observed resonances to the correct gadolinium isotope, besides confirming the isotopic content of 154 Gd in the enriched sample.
As mentioned above, the gadolinium sample was further studied through the transmission measurement at a 10-m station of the GELINA facility. The transmission, T , which was experimentally obtained from the ratio of Li-glass spectra resulting from a sample-in and a sample-out measurement, is related to the total cross section σ tot by the equation: where n = (1.431 ± 0.006) × 10 −4 atoms/b denotes the areal density of the gadolinium sample.
GELINA is particularly suitable for high-resolution transmission measurement, because of its time characteristic and the small dimensions of the neutron producing target. For this experiment, the neutron beam was collimated to a diameter of 10 mm at the sample position and filters were placed near the sample to absorb slow neutrons from the previous neutron-burst and to continuously monitor the background. The neutron beam passing through the sample was detected by a 6.4 mm thick and 76 mm wide Li-glass scintillator enriched to 95% in 6 Li. The detector was placed at 10.86 m from the neutron production target.

Data analysis and results
The experimental capture yield Y c , i.e. the probability for an incident neutron to be captured in the sample, can be deduced from the measured count rate, corrected for the detection efficiency of capture events. By applying the PHWT, the count rate, C w , is weighted in order to make the detection efficiency independent of the cascade path and γ multiplicity. The weighting functions were calculated simulating the response of the full apparatus by a GEANT4 [20] Monte-Carlo simulation. The capture yield can be written as: where N is a normalisation factor, B w is the weighted count rate representing the background and with dedicated runs using black resonance filters [17] and a fair agreement was found. In the region between 5 and 300 keV, the signal-to-total background ratio is 2.5. Although the total background level is significant, its uncertainty is small since the background is dominated by the empty-sample component, which is known within 1%. The neutron flux was evaluated with a dedicated measurement campaign using different de-8 tection systems and with neutron cross section standards [22]. The estimated systematic uncertainty on the flux determination was within 1% below 3 keV [22] and of 3.5 % up to 300 keV.
In the energy region up to 2.7 keV -hereafter referred to as Resolved Resonance Region (RRR) -, the experimental capture yield was analysed with the Bayesian R-matrix analysis code SAMMY [23]. The code can manage experimental effects such as Doppler and resolution broadening, self-shielding and multiple interactions of neutrons in the sample. Sizable discrepancies were found for some neutron resonances compared to the yields obtained using the ENDF/B-VIII.0 evaluation data set [24]. These differences were further confirmed by the transmission data. An example is shown in figure 3, where the present results of resonance shape analysis are Above this energy region, the experimental resolution became too low to resolve individual resonances and an averaged cross section was determined in the neutron energy range from 9 2.7 keV to 300 keV. The capture yield was corrected for multiple scattering and self-shielding through Monte-Carlo simulations as described in ref. [25]. The resulting correction for the two effects was lower than 2%.
The contribution of the contaminants present in the measured samples was taken into account in the experimental data analysis. In particular, for the main contaminant 155 Gd, the cross section was assumed from the previous n TOF measurement on 155 Gd. In figure 4, the capture cross section extracted from this study is compared to the data of Shorin et al. [11], Beer and Macklin [12], Wisshak et al. [13] and the ENDF/B-VIII evaluation. In the URR, the present data fairly agree with the data by Beer and Macklin [12] and they are substantially lower than the data reported by Wisshak et al. [13] and Shorin et al. [11]. This comparison seems to indicate that the results obtained with similar experimental setups are in fair agreement, while they are inconsistent if the adopted measurement technique is different. A discussion of potential reasons for the disagreement is beyond the scope of this article. MACS as a function of the thermal energy kT were calculated from the present capture data in the RRR and in the URR. The cross section in the energy region above this range (i.e. above 300 keV) was taken into account by calculations performed using the Hauser Feshbach (HF) statistical model theory, as implemented in the TALYS code [26]. The average resonance parameters, obtained in the present analysis of the RRR, were constrained to be reproduced by the calculations by adjusting the level density and the γ-ray strength function. An overall normalisation by a factor 0.737 of the resulting capture cross section was still necessary to reproduce the present experimental MACS at kT = 30 keV.
The uncertainty on the MACS takes into account the uncorrelated uncertainty attributable to counting statistics and systematic uncertainties. The uncertainty components originate from the normalisation of the capture data and the PHWT (1.3%), the shape of the neutron flux (1% below 3 keV and 3.5% above) and the subtraction of the background (on average 2%, depending on the energy region.). Another minor uncertainty is associated with the alignment of the sample and its geometrical shape. As a result, over the thermal energy range of kT= 5 − 100 keV, the uncertainty on the MACS ranges between 5 and 7%. In table 1, the present MACS are reported for the thermal energy grid proposed by KADoNiS [10,27]. In the whole energy range, the 11 MACS values from our measurement are significantly lower than KADoNiS. It is interesting to note that the disagreement worsened with the new version of the evaluation, the deviation being between 10% and 20%.

Astrophysical implications
As discussed above, a new determination of the 154 Gd neutron capture cross section was motivated by a discrepancy between stellar models and observations, as highlighted by [8] and confirmed by [4], where a lower theoretical 154 Gd/ 150 Sm ratio with respect to that measured in the Sun (and derived for the early-solar system) was found. When the present cross section is used in the models by Trippella et al. [9,31], it is interesting to notice that while the discrepancy with respect to 142 Nd, 148 Sm and 152 Gd is completely erased (due to the larger production of 154 Gd), at the same time, the ratio 154 Gd/ 150 Sm attains a value (1.15) consistent with observations, within uncertainties. In general, it appears that the approach in ref. [31] produces a flatter distribution of s process isotopes, although this was obtained in post-process computations and not in full stellar models. Therefore, a clear suggestion emerging from the present 154 Gd(n,γ) cross section measurement is that some of the remaining model ambiguities might be solved by a merging of the mixing approaches presented in FRUITY and ref. [9], something that is in an advanced stage of implementation [32].
Another important outcome from this combined experimental and theoretical study is related to the 154 Gd abundance, which largely depends on the branching at 154 Eu. For this isotope, no experimental data are available for both the neutron capture cross section and the temperaturedependent β decay rate. Therefore, s process calculations are based on purely theoretical estimations (see ref. [33] and ref. [34], respectively). A lower 154 Eu(n,γ) cross section or a faster 154 Eu(β − ) 154 Gd decay would lead to a larger 154 Gd surface abundance with respect to 150 Sm (and vice-versa). Therefore, the present result suggests that additional efforts should be spent in this direction from the experimental side, to provide experimental values as detailed as possible to stellar modelers.

Acknowledgements
The isotope used in this research was supplied by the United States Department of Energy Office of Science by the Isotope Program in the Office of Nuclear Physics.

This research was supported by the EUFRAT open access programme of the Joint Research
Centre at Geel. 3 No info on isotopic uncertainties are currently available. 13