{}^{62}Ni(n,\gamma) and {}^{63}Ni(n,\gamma) cross sections measured at n_TOF/CERN

Ni() and Ni() cross sections measured at n_TOF/CERN

C. Lederer claudia.lederer@ph.ed.uk [ University of Vienna, Faculty of Physics, Austria Johann-Wolfgang-Goethe Universität, Frankfurt, Germany    C. Massimi Dipartimento di Fisica, Università di Bologna, and Sezione INFN di Bologna, Italy    E. Berthoumieux Commissariat à l’Énergie Atomique (CEA) Saclay - Irfu, Gif-sur-Yvette, France    N. Colonna Istituto Nazionale di Fisica Nucleare, Bari, Italy    R. Dressler Paul Scherrer Institut, Villigen PSI, Switzerland    C. Guerrero European Organization for Nuclear Research (CERN), Geneva, Switzerland    F. Gunsing Commissariat à l’Énergie Atomique (CEA) Saclay - Irfu, Gif-sur-Yvette, France    F. Käppeler Karlsruhe Institute of Technology, Campus Nord, Institut für Kernphysik, Karlsruhe, Germany    N. Kivel Paul Scherrer Institut, Villigen PSI, Switzerland    M. Pignatari Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland    R. Reifarth Johann-Wolfgang-Goethe Universität, Frankfurt, Germany    D. Schumann Paul Scherrer Institut, Villigen PSI, Switzerland    A. Wallner University of Vienna, Faculty of Physics, Austria    S. Altstadt Johann-Wolfgang-Goethe Universität, Frankfurt, Germany    S. Andriamonje European Organization for Nuclear Research (CERN), Geneva, Switzerland    J. Andrzejewski Uniwersytet Łódzki, Lodz, Poland    L. Audouin Centre National de la Recherche Scientifique/IN2P3 - IPN, Orsay, France    M. Barbagallo Istituto Nazionale di Fisica Nucleare, Bari, Italy    V. Bécares Centro de Investigaciones Energeticas Medioambientales y Technologicas (CIEMAT), Madrid, Spain    F. Bečvář Charles University, Prague, Czech Republic    F. Belloni Istituto Nazionale di Fisica Nucleare, Trieste, Italy    B. Berthier Centre National de la Recherche Scientifique/IN2P3 - IPN, Orsay, France    J. Billowes University of Manchester, Oxford Road, Manchester, UK    V. Boccone European Organization for Nuclear Research (CERN), Geneva, Switzerland    D. Bosnar Department of Physics, Faculty of Science, University of Zagreb, Croatia    M. Brugger European Organization for Nuclear Research (CERN), Geneva, Switzerland    M. Calviani European Organization for Nuclear Research (CERN), Geneva, Switzerland    F. Calviño Universitat Politecnica de Catalunya, Barcelona, Spain    D. Cano-Ott Centro de Investigaciones Energeticas Medioambientales y Technologicas (CIEMAT), Madrid, Spain    C. Carrapiço Instituto Tecnológico e Nuclear (ITN), Lisbon, Portugal    F. Cerutti European Organization for Nuclear Research (CERN), Geneva, Switzerland    E. Chiaveri European Organization for Nuclear Research (CERN), Geneva, Switzerland    M. Chin European Organization for Nuclear Research (CERN), Geneva, Switzerland    G. Cortés Universitat Politecnica de Catalunya, Barcelona, Spain    M.A. Cortés-Giraldo Universidad de Sevilla, Spain    I. Dillmann Physik Department E12 and Excellence Cluster Universe, Technische Universität München, Munich, Germany    C. Domingo-Pardo GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany    I. Duran Universidade de Santiago de Compostela, Spain    N. Dzysiuk Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro, Italy    C. Eleftheriadis Aristotle University of Thessaloniki, Thessaloniki, Greece    M. Fernández-Ordóñez Centro de Investigaciones Energeticas Medioambientales y Technologicas (CIEMAT), Madrid, Spain    A. Ferrari European Organization for Nuclear Research (CERN), Geneva, Switzerland    K. Fraval Commissariat à l’Énergie Atomique (CEA) Saclay - Irfu, Gif-sur-Yvette, France    S. Ganesan Bhabha Atomic Research Centre (BARC), Mumbai, India    A.R. García Centro de Investigaciones Energeticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain    G. Giubrone Instituto de Física Corpuscular, CSIC-Universidad de Valencia, Spain    M.B. Gómez-Hornillos Universitat Politecnica de Catalunya, Barcelona, Spain    I.F. Gonçalves Instituto Tecnológico e Nuclear (ITN), Lisbon, Portugal    E. González-Romero Centro de Investigaciones Energeticas Medioambientales y Technologicas (CIEMAT), Madrid, Spain    F. Gramegna Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro, Italy    E. Griesmayer Atominstitut, Technische Universität Wien, Austria    P. Gurusamy Bhabha Atomic Research Centre (BARC), Mumbai, India    S. Harrisopulos National Centre of Scientific Research (NCSR), Demokritos, Greece    M. Heil GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany    K. Ioannides University of Ioannina, Greece    D.G. Jenkins University of York, Heslington, York, UK    E. Jericha Atominstitut, Technische Universität Wien, Austria    Y. Kadi European Organization for Nuclear Research (CERN), Geneva, Switzerland    D. Karadimos University of Ioannina, Greece    G. Korschinek Technical University of Munich, Munich, Germany    M. Krtička Charles University, Prague, Czech Republic    J. Kroll Charles University, Prague, Czech Republic    C. Langer Johann-Wolfgang-Goethe Universität, Frankfurt, Germany    E. Lebbos European Organization for Nuclear Research (CERN), Geneva, Switzerland    H. Leeb Atominstitut, Technische Universität Wien, Austria    L.S. Leong Centre National de la Recherche Scientifique/IN2P3 - IPN, Orsay, France    R. Losito European Organization for Nuclear Research (CERN), Geneva, Switzerland    M. Lozano Universidad de Sevilla, Spain    A. Manousos Aristotle University of Thessaloniki, Thessaloniki, Greece    J. Marganiec Uniwersytet Łódzki, Lodz, Poland    S. Marrone Istituto Nazionale di Fisica Nucleare, Bari, Italy    T. Martinez Centro de Investigaciones Energeticas Medioambientales y Technologicas (CIEMAT), Madrid, Spain    P.F. Mastinu Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro, Italy    M. Mastromarco Istituto Nazionale di Fisica Nucleare, Bari, Italy    M. Meaze Istituto Nazionale di Fisica Nucleare, Bari, Italy    E. Mendoza Centro de Investigaciones Energeticas Medioambientales y Technologicas (CIEMAT), Madrid, Spain    A. Mengoni Agenzia nazionale per le nuove tecnologie, l’energia e lo sviluppo economico sostenibile (ENEA), Bologna, Italy    P.M. Milazzo Istituto Nazionale di Fisica Nucleare, Trieste, Italy    F. Mingrone Dipartimento di Fisica, Università di Bologna, and Sezione INFN di Bologna, Italy    M. Mirea Horia Hulubei National Institute of Physics and Nuclear Engineering - IFIN HH, Bucharest - Magurele, Romania    W. Mondalaers European Commission JRC, Institute for Reference Materials and Measurements, Retieseweg 111, B-2440 Geel, Belgium    C. Paradela Universidade de Santiago de Compostela, Spain    A. Pavlik University of Vienna, Faculty of Physics, Austria    J. Perkowski Uniwersytet Łódzki, Lodz, Poland    R. Plag GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany    A. Plompen European Commission JRC, Institute for Reference Materials and Measurements, Retieseweg 111, B-2440 Geel, Belgium    J. Praena Universidad de Sevilla, Spain    J.M. Quesada Universidad de Sevilla, Spain    T. Rauscher Department of Physics and Astronomy - University of Basel, Basel, Switzerland    A. Riego Universitat Politecnica de Catalunya, Barcelona, Spain    F. Roman European Organization for Nuclear Research (CERN), Geneva, Switzerland Horia Hulubei National Institute of Physics and Nuclear Engineering - IFIN HH, Bucharest - Magurele, Romania    C. Rubbia European Organization for Nuclear Research (CERN), Geneva, Switzerland Laboratori Nazionali del Gran Sasso dell’INFN, Assergi (AQ),Italy    R. Sarmento Instituto Tecnológico e Nuclear (ITN), Lisbon, Portugal    P. Schillebeeckx European Commission JRC, Institute for Reference Materials and Measurements, Retieseweg 111, B-2440 Geel, Belgium    S. Schmidt Johann-Wolfgang-Goethe Universität, Frankfurt, Germany    G. Tagliente Istituto Nazionale di Fisica Nucleare, Bari, Italy    J.L. Tain Instituto de Física Corpuscular, CSIC-Universidad de Valencia, Spain    D. Tarrío Universidade de Santiago de Compostela, Spain    L. Tassan-Got Centre National de la Recherche Scientifique/IN2P3 - IPN, Orsay, France    A. Tsinganis European Organization for Nuclear Research (CERN), Geneva, Switzerland    L. Tlustos European Organization for Nuclear Research (CERN), Geneva, Switzerland    S. Valenta Charles University, Prague, Czech Republic    G. Vannini Dipartimento di Fisica, Università di Bologna, and Sezione INFN di Bologna, Italy    V. Variale Istituto Nazionale di Fisica Nucleare, Bari, Italy    P. Vaz Instituto Tecnológico e Nuclear (ITN), Lisbon, Portugal    A. Ventura Agenzia nazionale per le nuove tecnologie, l’energia e lo sviluppo economico sostenibile (ENEA), Bologna, Italy    M.J. Vermeulen University of York, Heslington, York, UK    R. Versaci European Organization for Nuclear Research (CERN), Geneva, Switzerland    V. Vlachoudis European Organization for Nuclear Research (CERN), Geneva, Switzerland    R. Vlastou National Technical University of Athens (NTUA), Greece    T. Ware University of Manchester, Oxford Road, Manchester, UK    M. Weigand Johann-Wolfgang-Goethe Universität, Frankfurt, Germany    C. Weiß Atominstitut, Technische Universität Wien, Austria    T.J. Wright University of Manchester, Oxford Road, Manchester, UK    P. Žugec Department of Physics, Faculty of Science, University of Zagreb, Croatia
July 14, 2019
Abstract

The cross section of the Ni() reaction was measured with the time-of-flight technique at the neutron time-of-flight facility n_TOF at CERN. Capture kernels of 42 resonances were analyzed up to 200 keV neutron energy and Maxwellian averaged cross sections (MACS) from  keV were calculated. With a total uncertainty of %, the stellar cross section is in excellent agreement with the the KADoNiS compilation at  keV, while being systematically lower up to a factor of 1.6 at higher stellar temperatures. The cross section of the Ni() reaction was measured for the first time at n_TOF. We determined unresolved cross sections from 10 to 270 keV with a systematic uncertainty of 17%. These results provide fundamental constraints on -process production of heavier species, especially the production of Cu in massive stars, which serve as the dominant source of Cu in the solar system.

pacs:
25.40.Lw, 25.40.Ny, 26.20.Kn, 27.50.+e

Present Affiliation: ]School of Physics and Astronomy, University of Edinburgh, UK

The n_TOF Collaboration (www.cern.ch/ntof)

I Motivation

The astrophysical slow neutron capture process ( process) in stars produces about half of the elemental abundances between Fe and Bi. The process is attributed to environments of neutron densities of typically cm, resulting in neutron capture timescales of the order of years. When an unstable nucleus is produced by neutron capture, -decays are usually faster than subsequent neutron capture, so the reaction path follows the valley of stability. The process takes place in different stellar sites. In particular, the -process abundances in the solar system are made by contributions from different generations of stars, resulting in three major components, a , a and a component (see e.g. Käppeler et al. (2011)). The main component dominates in the contributions between Zr and the Pb region and is mainly associated with thermally pulsing Asymptotic Giant Branch (AGB) stars of 1 to 3 with an initial metal content close to solar Busso et al. (1999). During the AGB phase, He burning takes place in a shell surrounding the inert C/O core of the star. Thermal pulses are caused by He shell flashes which occur because He burning cannot sustain hydrostatic equilibrium within a thin shell. As a consequence of the mixing processes and the temperature peaks induced by the thermonuclear flashes, neutrons are released in C() and the Ne() reactions, respectively Gallino et al. (1998). The strong component also originates in AGB stars but with much lower metallicities than solar Travaglio et al. (2001). It is responsible for about half of the solar Pb abundances and for the full process contribution to Bi. The weak  process takes place in massive stars () which later explode as supernova (e.g. Woosley et al. (2002)), and is producing most of the abundances in the mass region between Fe and Zr Peters (1968); Couch et al. (1974); Lamb et al. (1977); Raiteri et al. (1991a, b). In these stars, neutrons are mostly produced at the end of convective He Core burning and during the later convective Carbon Shell burning phase via Ne() reactions.
The reseulting -process abundances, , depend strongly on cross sections averaged over the stellar neutron spectrum. These Maxwellian Averaged Cross Sections (MACS) are defined as

(1)

where is the Boltzmann constant, the stellar temperature and the cross section as a function of energy . The temperatures in -process environments range from 0.09 to 1 GK (GigaKelvin), corresponding to values between 5 and 90 keV. For an accurate determination of MACSs, should be known up to a few hundred keV. Accurate cross sections are particularly important between Fe and Zr and for the light neutron poisons. The uncertainty of a single cross section may be propagated to the abundances of the following isotopes on the -process path, or over the complete -process distribution in the case of neutron poisons (see e.g. Massimi et al. (2012)). This propagation effect is a peculiar feature of the the weak process Busso and Gallino (1985); Rauscher et al. (2002).
To have accurate -process abundances derived from precise neutron capture measurements is also of great importance for -process studies because solar -process abundances are computed as residuals of the total solar abundances after subtracting :

(2)

Since current stellar cross sections in the Fe/Ni mass region exhibit fairly large uncertainties, a campaign was started at the neutron time of flight facility n_TOF at CERN to measure the neutron capture cross sections of all stable isotopes of Fe and Ni with improved accuracy. Additionally, the () cross section of the long-lived radionuclide Ni (=  yr Colle et al. (2008)) has been studied at n_TOF Lederer et al. (2013). This paper describes the measurement and data analysis of the () experiments on Ni and Ni .
Current data on Ni() include time-of-flight measurements Beer et al. (1974); Beer and Spencer (1975); Tomyo et al. (2005); Alpizar-Vicente et al. (2008) as well as activation measurements to directly determine the MACS at  keV Nassar et al. (2005); Walter (2008); Dillmann et al. (2010). Neutron capture resonances have been analyzed over a large energy range ( keV) by Beer and Spencer Beer and Spencer (1975), while there are a few other measurements investigating only the first strong resonance at 4.6 keV Hockenbury et al. (1969); Axmann et al. (1972); Litvinskiy et al. (1990). Different results for this first s-wave resonance () lead to severe differences in the low neutron energy part of evaluated cross sections, listed in libraries such as ENDF/B-VII.1 Chadwick et al. (2011), JENDL-4.0 Shibata et al. (2011) and JEFF-3.1.1 Koning et al. (2006). The n_TOF data allowed us to determine resonance capture kernels up to 200 keV neutron energy, Maxwellian averaged cross sections cross sections were determined from to 100 keV with uncertainties between 4.5 and 10.4%.
We also measured the Ni() cross section above thermal neutron energies (25 meV). Results for the resonance capture kernels and Maxwellian averaged cross sections are already published in Lederer et al. (2013). In this paper, we present results of the unresolved capture cross section between 10 and 270 keV.

Ii Measurement

ii.1 Facility

The measurements were performed at the neutron time-of-flight facility n_TOF (Phase2) at CERN. At n_TOF, a highly intense, pulsed neutron beam is produced by spallation reactions of a pulsed 20 GeV proton beam from the CERN Proton Synchrotron on a massive lead target. The initially very energetic neutrons are moderated by a water layer surrounding the spallation target. The resulting neutron flux approximates an energy dependence proportional to and ranges from thermal (25 meV) up to few GeV. Due to the long flight path of 185 m and a pulse width of 7 ns, a high resolution in neutron energy of and can be achieved at 1 eV, and at 1 MeV, respectively Guerrero et al. (2013). For a detailed description of the n_TOF facility, see Reference Guerrero et al. (2013).
The reactions on Ni and Ni were studied in separated campaigns. During the Ni campaign, additional data were taken again with the Ni sample, because Ni represented the most abundant impurity in the Ni sample. For the final Ni() cross section, results from both campaigns were combined.

ii.2 Detection setup

The prompt -ray cascade that is emitted after each neutron capture event was detected using a pair of CD scintillation detectors where the housing was made of carbon fibre Plag et al. (2003), in order to reduce their sensitivity to neutrons to the minimum possible value. This feature is important, since neutrons scattered from the sample can be captured in the detector material and produce -rays which are not distinguishable from neutron capture in the sample of interest. The CD detector system is installed perpendicular to the neutron beam and about 9 cm upstream from the capture sample. In this configuration, background due to in-beam photons, produced at the spallation target and scattered by the sample, is minimized. Additionally, angular distribution effects of -rays from resonances can be neglected in this position. The CD detectors were calibrated at 0.662, 0.898, 1.836, and 4.44 MeV using standard Cs, Y and AmBe -sources. Calibration runs were repeated every week during the measurement to monitor the detector stability. The data acquisition system records the full pulse shape using Flash ADCs at a sampling rate of 500 MHz, corresponding to a time resolution of 2 ns. A trigger signal from the Proton Synchrotron, shortly before the proton bunch hits the neutron target, starts the data acquisition. Data are recorded for 16 ms in the 8 MBytes on-board buffer memory of the digitizers, covering the neutron energy range down to 0.7 eV. In the second campaign, the data acquisition system was adjusted to a recording time of 80 ms, thus extending the minimum measurable neutron energy to 27 meV.

ii.3 Samples

The Ni sample consisted of 2 g metal powder, which was pressed into a stable pellet 20 mm in diameter and about 1 mm in thickness. The Ni sample was produced about 30 years ago by breeding a highly enriched Ni sample in the ILL high flux reactor at Grenoble Harder et al. (1992); Muthig (1984); Trautmannsheimer (1992). A first analysis of this material confirmed that it was free of any detectable impurities apart from the ingrown Cu component. After a chemical separation of the Cu, the remaining Ni fraction was converted into NiO grains typically 1 to 2 mm in size and with a total mass of 1156 mg. Finally, the grains were sealed in a light cylindrical container made from polyether-ether-ketone ([CHO], PEEK, wall thickness 0.15 mm), with a total weight of 180 mg. Mass spectroscopic analysis of the sample yielded a Ni to Ni ratio of . This sample was used for measuring the Ni() cross section Lederer et al. (2013) and for fitting the first large Ni() resonance at 4.6 keV due to its smaller thickness (see Section IV.1.1 for details). Additionally to the Ni samples, a Au sample of the same geometry as the Ni samples was used to normalize the cross section. A summary of the samples is shown in Table 1.

Sample Mass Enrichment (w%) Thickness Chemical
(mg) Ni Ni (10 atoms/b) form
Ni 1989 98.0 - 6.20 metal pellet
Ni 1156 69.4 8.4 5.68 oxide grains
Au 596 - - 0.584 metal foil
Table 1: Sample characteristics. All samples were of cylindrical shape and 2 cm in diameter.

Iii Data Analysis

iii.1 Determination of the Capture Yield

All time-of-flight spectra were corrected for dead-time effects, which never exceeded 1%. The count rate measured in a capture experiment is related to the capture yield via

(3)

with being the number of neutrons hitting the sample, the detection efficiency for capture events, and the background reactions. To obtain the detection efficiency which is independent of the de-excitation path of the compound nucleus, we applied the Pulse Height Weighting Technique Macklin and Gibbons (1967). Usually, the detection efficiency for a single -ray depends strongly on its energy, but by subjecting a pulse height dependent weight to each recorded signal, one can achieve a detection efficiency

(4)

which is a linear function of the excitation energy of the compound nucleus, regardless of the decay pattern of the capture cascade. The excitation energy is the sum of the reaction Q-value (6.84 MeV and 9.66 MeV for Ni and Ni, respectively) and the neutron energy in the center of mass system. The weights can be parametrized with a polynomial function of the energy deposited in the detector. Weighting functions were determined by simulating the detector response to mono-energetic -rays using GEANT-4 Agostinelli et al. (Geant4 Collaboration) (2003), implementing a detailed geometry of the experimental setup.
After weighting, the capture yield can be calculated as

(5)

where is the weighted count rate, the weighted background, a normalization factor, and the neutron flux incident on the sample. We used a neutron flux evaluated using long term measurements with several detectors and Monte Carlo simulations Barbagallo et al. (2013). The uncertainty in the neutron flux is 2% below 10 keV and above 100 keV, and 4-5% between 10-100 keV neutron energy. To obtain the absolute capture yield, the absolute detection efficiency, and the fraction of the neutron flux incident on the sample (beam interception factor) need to be known. After applying weighting functions, the efficiency to detect a capture event for each isotope only depends on the excitation energy of the compound nucleus. The systematic uncertainty in the capture yield ascribed to the Pulse Height Weighting Technique is 2% Abbondanno and the n_TOF Collaboration (2004). The normalization factor for obtaining the absolute detection efficiency is then the same for all measured isotopes after scaling the weighted counts with the excitation energy . The beam interception, together with the normalization factor was determined with the saturated resonance technique at the  eV resonance in Au, using a Au sample of the same diameter as the Ni samples. If the Au sample is chosen sufficiently thick, no neutrons are transmitted through the sample at the resonance energy. Since the capture width is bigger than the neutron width for this resonance, almost all neutrons interacting with the sample get captured. It has been demonstrated in Ref. Borella et al. (2007) that a normalization obtained from this saturated resonance in Au is nearly independent of even large changes in the resonance parameters.
Since the neutron beam profile changes with neutron energy, the beam interception factor depends slightly on neutron energy as well. This effect was determined by Monte Carlo simulations Guerrero et al. (2013). In the investigated neutron energy range the beam interception factor never changed by more than % compared to the value at 4.9 eV. We estimated the systematic uncertainty of the final cross section due to the normalization and the beam interception, including a possible misalignment of the sample which would affect the energy dependence of the beam interception, as 1%. The resulting total systematic uncertainty for determining the absolute capture yield is consequently 3% up to 10 keV and from 100-200 keV, and 5.5% from 10-100 keV neutron energy.
The effective neutron flight path, and thus the neutron energy calibration, was determined relative to low energy resonances in Au, which have been recently measured at the time-of-flight facility GELINA with high precision Massimi et al. (2011).

iii.2 Backgrounds

The background for capture measurements at n_TOF consists of a number of different components.
Ambient background is coming from cosmic rays, natural radioactivity and a possible radioactivity of the sample itself. This background is determined by runs without neutron beam.

Sample-independent background, due to reactions of the neutron beam with any structure material, is determined in runs with an empty sample holder.

Sample-dependent background consists of two components. Neutrons, scattered from the sample into the experimental area where they are captured, and photons, which are produced at the spallation target and are scattered from the sample into the detector. The latter background, called in-beam background, appears at neutron energies between 10 and 300 keV. It stems mainly from neutron capture on the hydrogen of the moderator and could be significantly improved in the second campaign by using borated water as moderator. This improvement is demonstrated in Fig. 1, which shows a comparison of the Ni capture yields from both campaigns, using water in the first, and borated water in the second campaign.

Sample dependent backgrounds can be investigated using black resonance filters installed about halfway between the spallation target and the sample. These filters are sufficiently thick that the neutron spectrum is left void of neutrons at the energies of certain strong resonances. Accordingly, events in these energy windows are due to background reactions. We checked this background for neutron energies below 1 keV by comparing sample spectra with filters with the spectrum of the empty sample holder with filters and found no indication for such a sample related background. For higher neutron energies, this comparison was not possible due to lack of statistics. Since this background, however, is varying smoothly with neutron energy, it can be assumed as being constant over the width of the resonance and therefore be fitted while fitting the resonance shape. This approach could be cross checked by analyzing the Ni data from two different campaigns, each having different backgrounds (for the second campaign borated water was used as moderator, reducing the photon background). The capture kernels of Ni resonances mostly agreed within statistical uncertainties for both campaigns. For the few exceptions, the standard deviation of the two fits was used as uncertainty of the capture kernel.

Figure 1: (Color online) Capture yield of Ni using water (black) and borated water (red) as moderator. The addition of boron yields a significant reduction of the photon induced background in the keV region.

Multiple scattering (MS) is a background that arises when a neutron is captured in the sample after it had been scattered within the sample itself. This background can be large in resonances with high scattering-to-capture ratios and depends also strongly on the sample geometry. The MS corrections are considered by the SAMMY code Larson (2003), which was used for analyzing the neutron resonances in Ni. For the unresolved cross section of Ni no such corrections could be applied due to the unknown scattering cross section. However, the effect is small since the Ni sample was relatively thin. A possible overestimation of the cross section due to this effect is included in the systematic uncertainty of the cross section.
A further sample related background consists of -rays originating from inelastic scattering of neutrons. This background can be neglected in this measurement since the first excited state in Ni and the first excited state above the detector threshold of 250 keV in Ni are above 0.5 MeV. In both cases population of those levels was not possible on the investigated neutron energy range Singh (2007).
The capture yields of Ni and Ni together with the ambient and sample-independent background components are shown in Figures 2 and 3, respectively.

Figure 2: (Color online) (Top) Capture yield of Ni (black, solid line) compared with backgrounds due to neutron reactions in surrounding materials (pink, solid line, measured with empty sample holder) and ambient background (blue, shaded line). While the ambient background is 2 orders of magnitude smaller than the signal over the whole energy range, the empty background plays a crucial role in the higher keV range. (Bottom) Zoom into the neutron energy region from 6 to 100 keV.
Figure 3: (Color online) Capture yield of Ni (green) compared with backgrounds due to neutron reactions on Ni in the sample (black) and with surrounding materials (pink, shaded line, measured with empty sample container), and ambient background (black, shaded line). The spectrum recorded with the Ni sample was scaled to the areal density of Ni in the Ni sample.

Iv Results on N()

iv.1 Resonance Analysis

Neutron resonances up to about 200 keV neutron energy were identified and analyzed using the multi-level R-matrix Code SAMMY Larson (2003). The fitting procedure applied in SAMMY to find the ’best fit’ values of parameters and the associated parameter covariance matrix is based on the Bayes’ theorem. The resonance shapes were fitted using the Reich-Moore approximation, including corrections for self shielding, multiple scattering and impurities in the sample, which were mainly other Ni isotopes. Experimental effects, such as Doppler broadening and the resolution of the capture setup, were taken into account. Because the measured resonance widths were in most cases larger than the natural widths due to the broadening, only the capture kernel could be determined. It is related to the resonance area via

(6)

where denotes the de Broglie wavelength at the resonance energy, and , the neutron and capture widths of the resonance. The statistical spin factor is determined by the resonance spin , the neutron spin and the spin of the target nucleus. The results obtained from the SAMMY fits with their statistical uncertainties are listed in Table 2 for resonances up to 200 keV. We used the partial neutron widths obtained by Beer and Spencer Beer and Spencer (1975) for resonances to fit the radiative width . For resonances with , no experimental data for partial widths were available, so the capture kernel is given in the table. Examples for resonance fits are shown in Fig. 4. Table 2 lists the combined result and propagated statistical uncertainties of both measurement campaigns. The systematic uncertainties due to the pulse height weighting (2%), the normalization (1%), and the neutron flux shape (2-5%) are not included in Table 2. This leads to a total systematic uncertainty in the capture kernel of 3% for resonances up to 10 keV and from 100-200 keV, and 5.5% for resonances from 10-100 keV.

Figure 4: (Color online) (a-d) Examples for resonances fitted with the program SAMMY Larson (2003). The dots are the measured data, the line represents the result of the resonance fit. Panel a shows the fit of the 4.6 keV resonance which was analyzed using the spectra obtained with the Ni sample. The data in panels b-d are from the first Ni campaign.
(eV) (meV) (meV) (meV)
1
1 340000
1 70000
1 2500000
1 4600000
1 140000
1 90000
Table 2: Resonance energies and capture kernels of the Ni() reaction. When possible, values have been fitted using spin assignments and values from Beer and Spencer Beer and Spencer (1975). Resonances, which were not seen in any previous measurement are marked by an asterisk.

iv.1.1 Resonance at  keV

The shape of the neutron resonance at =4.6 keV is highly affected by background from multiple scattering, due to its very high scattering-to-capture ratio of 800. It was found impossible to fit this resonance with the relatively thick Ni sample, therefore data measured with the thinner Ni sample, where multiple scattering is less important, were used to analyze this resonance. Since the estimated multiple scattering background varies with the neutron width , the resonance was fitted while keeping constant. The resonance was assigned as due to its shape. Using two previously measured values for the neutron width,  keV Litvinskiy et al. (1990) and  keV Axmann et al. (1972), values of 2.4 meV and 2.7 meV were obtained in the SAMMY fits, respectively. A resonance fit was not possible using a third experimental value for of 1.3 keV Garg et al. (1971). Since this resonance is an s wave, the two possible options for the fit yield different contributions to the cross section at lower energies. In fact, the thermal cross section obtained with the two choices is 16.2 barn for  meV, but only 12.8 barn for  meV. Previous measurements of the thermal cross section result in reported values between 14.0 and 21 barn Pomerance (1952); McMullen et al. (1956); Horrocks and Harkness (1962); Sims and Juhnke (1970); Ishikawa (1973); Michael et al. (1974); Ishaq et al. (1977); Venturini and Pecequilo (1997), with the majority of values grouped around 14.5 barn Pomerance (1952); Horrocks and Harkness (1962); Sims and Juhnke (1970); Michael et al. (1974); Ishaq et al. (1977). Due to this large spread, these previous measurements cannot give us a hint on the correct value. A new measurement of this resonance using a much thinner sample would be desirable in the future, especially since this resonance contributes about 50% to the Maxwellian averaged cross section (MACS) at =30 keV.

iv.1.2 Level Spacing

It is expected that the average level density of the compound nucleus is constant over the investigated energy range. Figure 5 shows that the accumulated number of observed levels as a function of neutron energy follows the expected linear behaviour up to about 80 keV. The increasing number of missing levels is due to the weakening signal-to-background ratio combined with the decreasing energy resolution of the n_TOF setup. We find an average level spacing of roughly 28 keV for s-wave resonances and 3.4 keV for resonances. The consequences of missing resonances for the Maxwellian averaged cross sections are discussed in section IV.2.

Figure 5: (Color online) Accumulated number of levels as a function of neutron energy. The black dots represent the data, the red line is a linear fit from 0 to 80 keV.

iv.2 Maxwellian Averaged Cross Sections

We calculated Maxwellian averaged cross section from  keV using the resonance parameters obtained from the SAMMY fits. Resonances parameters from 200 keV onwards were taken from the JENDL-4.0 library Shibata et al. (2011). The MACS values from  keV together with their statistical and systematic uncertainties are listed in Table 3 and Table 4 details the uncertainties for three typical values of . Systematic uncertainties include the Pulse Height Weighting Technique, the normalization, and the neutron flux. The impact of the two different fits for the 4.6 keV resonance according to the different multiple scattering corrections has been included as separate systematic uncertainty (called ”‘MS at  keV”’ in Table 4).
To investigate the effect of missing levels on the MACS values an average cross section was calculated from our data in the energy range from 81 to 200 keV, using simulated self shielding and multiple scattering corrections. These corrections were obtained by means of Monte Carlo simulations taking into account the sample geometry and neutron capture and scattering cross sections. The MACS values of this approach were between 3% and 7% higher in the range  keV than the results calculated from resonance data only. We included this difference as additional systematic uncertainty in Table 4 (missing levels).

(keV) MACS (mb) Uncertainty (%)
Statistical Systematic
 5 181.2 0.6 5.2
10 83.2 0.6 4.9
15 50.8 0.6 4.8
20 35.8 0.7 4.4
25 27.4 1.0 4.3
30 22.2 1.5 4.2
40 16.0 2.7
50 12.5 3.8
60 10.2 4.7
80 7.44 6.0
100 5.75 6.7
Table 3: Maxwellian averaged cross sections of the Ni() reaction from 5 to 100 keV together with statistical and systematic uncertainties.
(keV) 5 30 100
Weighting Functions 2 2 2
Normalization 1 1 1
Neutron Flux Shape 2.0 2.7 2.9
MS at  keV 4.2 2.3 0.9
Missing Levels - - +7
Counting Statistics 0.6 1.5 6.7
Total 5.2 4.5 -7.7/+10.4
Table 4: Contributions to the uncertainties (in %) for the stellar Ni() cross sections (see text for details).

A comparison of our results to previous measurements and evaluations is shown in Fig. 6. For  keV, the n_TOF data are in agreement with the results of Alpizar-Vicente et al. Alpizar-Vicente et al. (2008). At 25 keV and 30 keV, our MACS is in excellent agreement with activation measurements of Nassar et al. Nassar et al. (2005) and Dillmann et al. Dillmann et al. (2010), while being significantly lower than a previous time-of-flight measurement by Tomyo et al. Tomyo et al. (2005). Towards higher values, our data start to deviate from the results of Alpizar-Vicente et al. Alpizar-Vicente et al. (2008), being systematically lower up to a factor of 1.8. As investigated by Monte Carlo simulations, missing levels due to high background at high neutron energies cannot account for that difference. For , our data are in fair agreement with MACS calculated using resonance parameters of the JENDL-4.0 evaluation Shibata et al. (2011), which is mainly based on a measurement by Beer and Spencer Beer and Spencer (1975).

Figure 6: (Color online) Maxwellian Averaged Cross sections from 5 to 100 keV compared to previous measurements (Alpizar-Vicente et al. Alpizar-Vicente et al. (2008), Nassar et al. Nassar et al. (2005), Dillmann et al. Dillmann et al. (2010) and Tomyo et al. Tomyo et al. (2005)). The results obtained with data from the JENDL-4.0 evaluation (dashed line, Shibata et al. (2011)) and the recommended MACS values of the KADoNiS compilation (solid line, Dillmann et al. (2009)) are included as well.

V Results for N()

The resonance analysis for the Ni() reaction has already been described and published in Ref. Lederer et al. (2013). In this section, the results for the unresolved cross section of Ni() are presented. From 10 keV onwards, we calculated an averaged cross section, since the high background, mainly due to reactions of neutrons with Ni and with the sample container prevented us from analyzing more resonances. The Ni() capture yield was calculated by subtracting the background due to Ni() reactions using the spectra recorded with the Ni sample and the known Ni abundance in the Ni sample. Background from reactions on oxygen is negligible, due to the low reaction cross section. The average cross section was calculated using the thin target approximation

(7)

where is the areal density of the sample and the neutron capture yield. As for Ni, systematic uncertainties are coming from the Pulse Height Weighting Technique (2%), the neutron flux (2%-5%), and the normalization (1%). Additionally, the Ni/Ni ratio in the sample contributed an uncertainty of %. The background subtraction due to reactions on Ni in the sample introduces the largest systematic uncertainty, which we estimated as 15% based on different ways to treat the background at Ni resonances. Assuming a high multiple scattering correction of 5%, the total systematic uncertainty of this measurement amounts to 17%. The cross sections from 10-270 keV, along with statistical uncertainties, are listed in Table 5. MACS values and the implications of the Ni cross section for stellar nucleosynthesis have been published in Lederer et al. (2013).

Neutron Energy (eV) Cross Section (mb)
10104 12136
12136 14577
14577 17506
17506 21023
21023 30304
30304 43664
43664 62871
62871 90456
90456 130027
130027 186705
186705 267743
Table 5: Average Ni() cross sections between 10 and 270 keV laboratory neutron energy with statistical uncertainties. The total systematic uncertainty is 17%.

Vi Astrophysical Implications

In addition to the cross sections of the target nuclei in their ground states, as measured here, reactions on thermally excited states have to be considered in the determination of stellar reaction rates to be used in astrophysical models. For Ni(), the population of excited states is negligible across the full energy range of  process temperatures. Thus, the measured laboratory cross sections directly allow to derive the stellar rates. Due to the higher nuclear level density of Ni, only a fraction of the stellar rate can be constrained by a measurement of Ni() cross sections and theoretical corrections have to be applied as described in Lederer et al. (2013).
The impact of our new results on Ni() and Ni() on the weak  process in massive stars was investigated for a full stellar model for a 25  star with an initial metal content of Z=0.02 Pignatari et al. (2013). The complete nucleosynthesis was followed with the post-processing NuGrid code MPPNP Pignatari and Herwig (2012).

Figure 7: (Color online) (Top) Final isotopic  process abundances between Fe and Ga normalized to solar system abundances. The red circles represent the abundances using the Ni() MACS of this work and the Ni() MACS reported in Ref. Lederer et al. (2013). This distribution is compared to the results using the recommended MACS of Ni and Ni of the KADoNiS compilation Dillmann et al. (2009). As a reference, the overabundance of O is shown as black continuous line, divided and multiplied by 2 (black dashed lines). (Bottom) Ratio between the abundances using the new cross sections and the abundances using KADoNiS cross sections.

Figure 7 shows the -process abundance distribution in the mass region from Fe to Ga after the convective core He and the convective C shell burning phase. Although the solar system -process abundances in the Ni-Cu-Zn region may be partially affected by the following core-collapse supernova event (e.g. Rauscher et al. (2002); Pignatari et al. (2010)), the pre-explosive -process distribution is relevant as it serves as seed for the later explosive nucleosynthesis. The abundance distribution calculated with the MACSs of Ni and Ni from this work and Ref. Lederer et al. (2013) is compared to the abundances calculated with the recommended MACS data of the KADoNiS compilation v0.3 Dillmann et al. (2009). Because the Ni MACS of this work is smaller than the value in KADoNiS for  keV, neutron capture rates of Ni in the C shell burning phase, where temperatures correspond to  keV, are smaller and the final abundance of Ni increases by 20%. The corresponding lower production of Ni results in lower abundances of Cu and Zn. This decrease is compensated for Cu and above Zn by the fact that the Ni MACS itself is a factor of 2 higher than the MACS value in KADoNiS, resulting in a stellar rate that is about 40% larger than the KADoNiS rate at typical shell C burning temperatures after considering the contribution from neutron capture on excited states in Ni Rauscher (2012). Accordingly, the  abundances in this region differ only by 1-2%. For Cu, which is mainly produced by the radiogenic decay of Ni after C shell burning, the effect of a smaller Ni MACS and a higher Ni MACS causes a 40% lower abundance of Cu. Because the Cu abundance remains essentially unchanged, the isotopic ratio Cu/Cu is reduced after C shell burning. These results will allow to better define the following explosive contribution to the copper inventory of the solar system.

Vii Summary

We measured the cross sections of the Ni() and Ni() reactions at the neutron time-of-flight facility n_TOF at CERN.
For Ni(), the resonance analysis was performed up to 200 keV neutron energy. In total, 42 levels could be identified, of which 12 were not seen in previous experiments. The Maxwellian averaged cross sections, calculated from resonance parameters is in good agreement with previous measurements for values up to 50 keV. At higher energies our results are systematically lower than the data by Alpizar-Vicente et al. Alpizar-Vicente et al. (2008), but in good agreement with the evaluations in the data libraries JENDL Shibata et al. (2011) and ENDF/B-VII Chadwick et al. (2011), which are mainly based on a measurement by Beer and Spencer Beer and Spencer (1975). Our MACS at 100 keV is also a factor of 1.6 lower than the currently recommended value of the KADoNiS compilation.
For the Ni() reaction, the neutron resonance analysis together with the stellar cross sections are published elsewhere Lederer et al. (2013). We determined averaged cross sections between 10 and 270 keV with systematic uncertainties of 17%.
The impact of the new stellar ) cross sections of Ni and Ni has been studied with a stellar model for a 25 star with Z=0.02. We find significant changes in the  abundances of Ni (+20%) and Cu (-40%), whereas the changes for heavier  process isotopes are less than 2%. These results are particularly important to understand the solar system abundances of Cu, which is dominantly produced in massive stars.

Acknowledgements.
The authors would like to thank H. Danninger and C. Gierl of the Technical University of Vienna for their help preparing the Ni sample. This work was partly supported by the Austrian Science Fund (FWF), projects P20434 and I428 and by the Federal Ministry of Education and Research of Germany, project 05P12RFFN6. M.P. acknowledges support from the Ambizione grant of the SNSF (Switzerland), from NuGrid thanks to the EU MIRG-CT-2006-046520, from the NSF grants PHY 02-16783 and PHY 09-22648 (Joint Institute for Nuclear Astrophysics, JINA), and from EuroGenesis (MASCHE). T.R. acknowledges the Swiss NSF, the European Research Council, and the THEXO Collaboration within the 7 Framework Program ENSAR of the EU.

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