Resonance neutron-capture cross sections of stable magnesium isotopes and their astrophysical implications

Abstract

044615-1 0556-2813/2012/85(4)/044615(15) ©2012 American Physical Society C. MASSIMI et al. We have measured the neutron capture cross sections of the stable magnesium isotopes 24,25,26 Mg in the energy range of interest to the s process using the neutron time-of-flight facility n_TOF at CERN. Capture events from a natural metal sample and from samples enriched in 25 Mg and 26 Mg were recorded using the total energy method based on C 6 2 H 6 detectors. Neutron resonance parameters were extracted by a simultaneous resonance shape analysis of the present capture data and existing transmission data on a natural isotopic sample. Maxwellian-averaged capture cross sections for the three isotopes were calculated up to thermal energies of 100 keV and their impact on s-process analyses was investigated. At 30 keV the new values of the stellar cross section for 24 Mg, 25 Mg, and 26 Mg are 3.8±0.2 mb, 4.1±0.6 mb, and 0.14±0.01 mb, respectively.

Full text

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PHYSICAL REVIEW C 85, 044615 (2012)
Resonance neutron-capture cross sections of stable magnesium isotopes and
their astrophysical implications
C. Massimi,1,2,*P. Koehler,3S. Bisterzo,4N. Colonna,5R. Gallino,4F. Gunsing,6F. K¨ appeler,7G. Lorusso,5A. Mengoni,8,9
M. Pignatari,10G. Vannini,1,2U. Abbondanno,11G. Aerts,6H.´Alvarez,12F.´Alvarez-Velarde,13S. Andriamonje,6
J. Andrzejewski,14P. Assimakopoulos,15,†L. Audouin,16G. Badurek,17M. Barbagallo,5P. Baumann,18F. Beˇ cv´ aˇ r,19
F. Belloni,11M. Bennett,20E. Berthoumieux,6M. Calviani,9F. Calvi˜ no,21D. Cano-Ott,13R. Capote,8,22C. Carrapic ¸o,23,6
A. Carrillo de Albornoz,23P. Cennini,9V. Chepel,24E. Chiaveri,9G. Cortes,25A. Couture,26J. Cox,26M. Dahlfors,9S. David,16
I. Dillmann,7R. Dolfini,27C. Domingo-Pardo,28W. Dridi,6I. Duran,12C. Eleftheriadis,29M. Embid-Segura,13
L. Ferrant,16,†A. Ferrari,9R. Ferreira-Marques,24L. Fitzpatrick,9H. Frais-Koelbl,8K. Fujii,11W. Furman,30
I. Goncalves,23E. Gonz´ alez-Romero,13A. Goverdovski,31F. Gramegna,32E. Griesmayer,8C. Guerrero,13B. Haas,33
R. Haight,34M. Heil,35A. Herrera-Martinez,9F. Herwig,36R. Hirschi,20M. Igashira,37S. Isaev,16E. Jericha,17Y. Kadi,9
D. Karadimos,15D. Karamanis,15M. Kerveno,18V. Ketlerov,30V. Konovalov,29S. Kopecky,38E. Kossionides,39M. Krtiˇ cka,19
C. Lampoudis,29,6H. Leeb,17C. Lederer,40A. Lindote,24I. Lopes,24R. Losito,9M. Lozano,22S. Lukic,18
J. Marganiec,14L. Marques,23S. Marrone,5T. Mart´ ınez,13P. Mastinu,32E. Mendoza,13P. M. Milazzo,11C. Moreau,11
M. Mosconi,7F. Neves,24H. Oberhummer,17S. O’Brien,26M. Oshima,41J. Pancin,6C. Papachristodoulou,15
C. Papadopoulos,42C. Paradela,12N. Patronis,15A. Pavlik,40P. Pavlopoulos,43L. Perrot,6M. T. Pigni,17R. Plag,7A. Plompen,38
A. Plukis,6A. Poch,25J. Praena,22C. Pretel,25J. Quesada,22T. Rauscher,10R. Reifarth,34G. Rockefeller,34M. Rosetti,44
C. Rubbia,27G. Rudolf,18J. Salgado,23C. Santos,23L. Sarchiapone,9R. Sarmento,23I. Savvidis,29C. Stephan,16G. Tagliente,5
J. L. Tain,28D. Tarr´ ıo,12L. Tassan-Got,16L. Tavora,23R. Terlizzi,5P. Vaz,23A. Ventura,44D. Villamarin,13V. Vlachoudis,9
R. Vlastou,42F. Voss,7S. Walter,7H. Wendler,9M. Wiescher,26and K. Wisshak7
(n_TOF Collaboration)
1Dipartimento di Fisica, Universit` a di Bologna, Bologna, Italy
2Istituto Nazionale di Fisica Nucleare, Bologna, Italy
3Oak Ridge National Laboratory, Physics Division, Oak Ridge, Tennessee 37831-6369, USA
4Dipartimento di Fisica Generale, Universit` a di Torino, Torino, Italy
5Istituto Nazionale di Fisica Nucleare, Bari, Italy
6CEA/Saclay, IRFU, Gif-sur-Yvette, France
7Karlsruhe Institute of Technology (KIT), Campus Nord, Institut f¨ ur Kernphysik, Germany
8International Atomic Energy Agency (IAEA), Nuclear Data Section, Vienna, Austria
9CERN, Geneva, Switzerland
10Department of Physics, University of Basel, Switzerland
11Istituto Nazionale di Fisica Nucleare, Trieste, Italy
12Universidade de Santiago de Compostela, Santiago de Compostela, Spain
13Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, Madrid, Spain
14University of Lodz, Lodz, Poland
15University of Ioannina, Ioannina, Greece
16Centre National de la Recherche Scientifique/IN2P3-IPN, Orsay, France
17Atominstitut der¨Osterreichischen Universit¨ aten, Technische Universit¨ at Wien, Vienna, Austria
18Centre National de la Recherche Scientifique/IN2P3-IReS, Strasbourg, France
19Charles University, Prague, Czech Republic
20Keele University, Newcastle-under-Lyme, Staffordshire, United Kingdom
21Universidad Politecnica de Madrid, Madrid, Spain
22Universidad de Sevilla, Seville, Spain
23Instituto Tecnol´ ogico e Nuclear (ITN), Lisbon, Portugal
24LIP-Coimbra and Departamento de Fisica da Universidade de Coimbra, Coimbra, Portugal
25Universitat Politecnica de Catalunya, Barcelona, Spain
26University of Notre Dame, Notre Dame, USA
27Universit` a degli Studi Pavia, Pavia, Italy
28Instituto de F´ ısica Corpuscular, CSIC-Universidad de Valencia, Valencia, Spain
29Aristotle University of Thessaloniki, Thessaloniki, Greece
30Joint Institute for Nuclear Research, Frank Laboratory of Neutron Physics, Dubna, Russia
31Institute of Physics and Power Engineering, Kaluga region, Obninsk, Russia
32Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro, Padua, Italy
33Centre National de la Recherche Scientifique/IN2P3-CENBG, Bordeaux, France
34Los Alamos National Laboratory, New Mexico, Los Alamos 87545, USA
35GSI Helmholtzzentrum f¨ ur Schwerionenforschung GmbH, Darmstadt, Germany
36Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia, Canada
044615-1
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C. MASSIMI et al.
PHYSICAL REVIEW C 85, 044615 (2012)
37Tokyo Institute of Technology, Tokyo, Japan
38EC-JRC-IRMM, Geel, Belgium
39NCSR, Athens, Greece
40University of Vienna, Faculty of Physics, Vienna, Austria
41Japan Atomic Energy Research Institute, Tokai-mura, Japan
42National Technical University of Athens, Athens, Greece
43Pˆ ole Universitaire L´ eonard de Vinci, Paris La D´ efense, France
44ENEA, Bologna, Italy
(Received 9 January 2012; revised manuscript received 22 February 2012; published 20 April 2012)
We have measured the neutron capture cross sections of the stable magnesium isotopes24,25,26Mg in the
energy range of interest to the s process using the neutron time-of-flight facility n_TOF at CERN. Capture
events from a natural metal sample and from samples enriched in25Mg and26Mg were recorded using the
total energy method based on C62H6detectors. Neutron resonance parameters were extracted by a simultaneous
resonance shape analysis of the present capture data and existing transmission data on a natural isotopic sample.
Maxwellian-averaged capture cross sections for the three isotopes were calculated up to thermal energies of
100 keV and their impact on s-process analyses was investigated. At 30 keV the new values of the stellar cross
section for24Mg,25Mg, and26Mg are 3.8±0.2 mb, 4.1±0.6 mb, and 0.14±0.01 mb, respectively.
DOI: 10.1103/PhysRevC.85.044615 PACS number(s): 26.20.Kn, 28.20.Np, 29.30.Hs, 21.10.Hw
I. INTRODUCTION
The slow neutron-capture process (s process) [1–4] in stars
is responsible for the origin of about one half of the elemental
abundances beyond iron that we observe today. In this process
mostoftheneutronsareprovided bythe13C(α,n)16Oreaction
and by the22Ne(α,n)25Mg reaction. Most of the produced
neutronsarecapturedbylightspeciesincompetitionwith56Fe,
that is the main seed for s-process nucleosynthesis on heavy
elements. Among light neutron poisons,25Mg and26Mg may
have a relevant impact on neutron balance, and their neutron-
capture cross sections need to be known with high precision,
in order to obtain robust s-process calculations. Additionally,
these results yield some constraints for the yet poorly known
22Ne(α,n)25Mg cross section by studying the states of the
25Mg+n compound nucleus.
Another aspect of the capture cross section of the stable
magnesium isotopes is related to the open question of the
production of the radioisotope
sensitivity study of Iliadis et al. [5] has demonstrated that
the cross section of the24Mg(n,γ) reaction is important for
the origin of26Al, because its main production mechanism
in massive stars is strongly affected by the uncertainties of
several cross sections, including that of24Mg(n,γ).
The capture cross sections of the Mg isotopes in current
nuclear data libraries exhibit deficiencies in the resolved res-
onance region (RRR), in particular concerning the assignment
of resonance spins. The respective evaluations are based on
the Japanese Evaluated Nuclear Data Library (JENDL) 3.2 [6]
version, which adopted the Brookhaven National Laboratory
compilation [7] in the RRR. Because the energy range of
interest for s-process temperatures is slightly larger than the
onecoveredbytheevaluation,Koehler[8]recentlyreanalyzed
26Al in the cosmos. The
*Cristian.Massimi@bo.infn.it
†Deceased.
existing data [9] to derive an improved set of resonance
parameters. His analysis included very high resolution data
for the total cross section obtained with a metallic sample
of natural Mg and high-resolution capture data measured
with an enriched25Mg sample, both from experiments at
the Oak Ridge Electron Linear Accelerator (ORELA) neutron
time-of-flight facility [10].
Although the evaluation of Ref. [8] is more accurate than
that in Ref. [6], there are three problems [11] with the former
work (Ref. [8]). First, the scattering widths given in Tables I
and II of Ref. [8] are actually ?nand not g?n, where g is
the statistical spin factor. Second, and more importantly, the
sample thickness used in the transmission analysis was 10%
too small. Third, the transmission data used in that analysis
were too much averaged near the 475-keV resonance, so the
quoted parameters for that resonance are not very accurate.
Previous experiments comprise a series of neutron time-
of-flight (TOF) measurements onnatMg as well as on enriched
samples. Typically, these experiments covered only a limited
energy region, and capture data were taken with large detec-
tors, less suited for capture cross-section studies on isotopes
in the mass region of Mg, where the cross sections are by
far dominated by the elastic-scattering channel. While the
most abundant isotope24Mg has been investigated several
times[12–15],therearefewneutrondatafor25,26Mg.Because
theresonance-dominatedcapturecrosssectionsofallthreeMg
isotopesarerelativelysmall,themeasurementscanbestrongly
affectedbyvariouskindsofbackgroundandexhibit,therefore,
rather large discrepancies. For instance, spin and parity of the
first neutron resonance in25Mg+n have been reported as
Jπ= 3+[16], 3−[17], and 2+[18] but was assigned as 2−
in the JENDL evaluation, although the parity assignment of
Ref. [18] is consistent with an independent26Mg(γ,n)25Mg
experiment [19].
Concerning26Mg+n reaction, the observed differences
between the only TOF data from Ref. [9] and activation
experiments by Mohr et al. [20,21] are consistent with the
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TABLE I. Characteristics of the Mg samples.
SampleIsotopic abundance (%)TotalAreal density
(atoms/b)a
ID
24Mg
25Mg
26Mgmass (g)
natMg
25Mg
26Mg
78.7
3.05
2.46
10.13
95.75
1.28
11.17
1.20
96.26
5.2393
3.1924
3.2301
0.03415
0.01234
0.01219
aAreal density of the Mg isotopes.
direct radiative capture (DRC) component [22] that is not
covered by the TOF technique. For this part, the thermal
capture cross section reported in Ref. [23] provides an
additional constraint for normalization of the 1/v slope of
the cross section (v being the neutron velocity).
In view of the uncertain and incomplete cross-section data
oftheMgisotopes,whichmaybeduetotheneutronsensitivity
of previous experiments, a set of capture measurements was
performed at n_TOF to update the (n,γ) cross sections of
24,25,26Mg. In these measurements particular care was devoted
to minimizing systematic uncertainties due to scattered neu-
trons. In addition, enriched samples were used to improve the
assignment of some doubtful resonances.
The experiment and the procedure for the data reduction
are described in Secs. II and III, respectively. The resonance
analysis is discussed in Sec. IV and the corresponding
stellar cross sections are given in Sec. V. The astrophysical
implications are illustrated in Sec. VI and the conclusions are
in Sec. VII.
II. EXPERIMENT
The capture experiment was performed at n_TOF, the
neutron time-of-flight facility at CERN [24], which provides a
white neutron spectrum from thermal to about 1-GeV neutron
energy. Neutrons are produced in a massive lead target by a
pulsed 20-GeV proton beam from the CERN/PS accelerator
complex.Thisspallationneutronsourceischaracterizedbythe
highintensityof7 × 1012protonsperpulse,ashortpulsewidth
of 6 ns, a low repetition rate of 0.4 Hz, and a long flight path of
185 m. Two collimators are present in the neutron beam. They
provide a nearly symmetric Gaussian-shaped beam profile
at the sample position, with an energy-dependent standard
deviation, which is about 0.77 cm at low neutron energies. A
full description of its characteristics and performance can be
found in Refs. [25,26]. The background level is kept low, in
the experimental area, thanks to several massive concrete and
iron shieldings and by means of a strong sweeping magnet.
A. Capture apparatus
The capture apparatus consisted of two C62H6 liquid
scintillators. The deuterated benzene liquid scintillators used
in the present measurement consisted of cylindrical cells
127.3 mm in diameter and 78 mm in length with an active
volume of about 1000 cm3. Deuterated benzene was chosen
foritsverysmallneutronsensitivity.Theneutronsensitivityof
FIG. 1. (Color online) Sketch of sample changer and detectors in
the experimental area at a flight path of 185 m (D denotes deuterium,
2H).
thedetectorswasfurtherminimizedbycouplingathincarbon-
fiber cell directly to the EMI 9823QKA photomultipliers
[27]. The detectors were placed perpendicular to the beam,
9.2 cm upstream from the sample center in order to reduce
the background due to scattered photons. This geometrical
configuration also allowed us to reduce the effects of the
angular distribution from primary neutron capture γ rays
following neutron capture in ? = 1 p-wave resonances. The
setup of the sample-detector geometry is sketched in Fig. 1.
The total energy detection method in combination with the
pulse height weighting technique (PHWT) [28] was used for
this experiment. The neutron fluence at the sample position,
about 185 m from the neutron source, was measured with
a well-calibrated6Li-based neutron monitor [29]. It is an
in-beam detector, consisting of a6Li deposit (300 mg/cm2and
6 cm in diameter) on a Mylar foil and four off-beam silicon
(6 × 4 cm2) detectors measuring the particles from the6Li(n,
α)3H reaction. The monitor was located about 3 m upstream
of the sample position.
Thedetectorsignalswererecordedusingfastdigitizerswith
a sampling rate of 500 Msamples/s [30]. This configuration
made it possible to record the detector signals over the
entire TOF interval from relativistic neutron energies down
to approximately 1 eV. The effective length of the flight path,
L = 185.07 ± 0.01 m, was calibrated using the first s-wave
resonances of Au as explained in Ref. [31]. The TOF data
were converted to neutron energy by
En= mnc2
⎡
⎣
c
?
c2−?L
?t
?2− 1
⎤
⎦,
(1)
where mn is the neutron mass and c the speed of light.
The TOF interval of a neutron ?t was determined by the
time between the start signal, based on the reference signal
provided by the prompt γ-flash tγ, and the stop signal tn(both
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C. MASSIMI et al.
PHYSICAL REVIEW C 85, 044615 (2012)
detected in the C62H6detectors) according to the following:
?t = tn− tγ+ L/c.
B. Samples and measurements
Enriched samples of25Mg and26Mg were borrowed from
the Science-Technical Centre “Stable Isotopes” (Obninsk,
Russia) in the form of magnesium oxide powder. The powder
was sealed in very thin aluminum cans with total masses
of 350 mg. The enriched samples were complemented by a
metal disk of natural magnesium. All samples were 22 mm in
diameter.
The composition of the samples is listed in Table I. The
specified impurities of the enriched samples included traces
of Be, Sb, Fe, Al, Sn, Mn, Cu, Ca, Mo, Ni, Ag, and Pb [32].
From the resonance shape analysis (RSA) of the capture data,
some traces of In were found in addition. The concentration
of impurities was verified and it resulted to be very low. For
instance,themostimportantimpurities(115In,121,123Sb,117Sn,
and95Mo) were at the level of tens of ppm. The mass of the
sampleswasquotedintheaccompanyingdocumentationwith-
out uncertainties. Furthermore, no information was available
on the procedure used for the preparation, nor on the final
homogeneity of the powder samples. Because MgO is highly
hygroscopic, the Mg content might have been overestimated
by the absorption of moisture before the powder was sealed
in the Al cans. Unfortunately, it was not possible to heat the
samplesforremovingabsorbedwaterasdescribedinRef.[20].
In fact, the comparative analysis of the first s-wave
resonance at 19.86 keV in the25Mg(n, γ) cross section,
which was observed with the enriched25MgO sample and
with the metallic natural sample, provided clear evidence that
the quoted25Mg mass was overestimated by about 30% (see
Sec. IVB). An alternative explanation could be possible inho-
mogeneities of the sample, related to the spatial distribution
of the powder inside the canning. Nevertheless, a procedure
described in the analysis section allowed determination of
the25Mg mass with an uncertainty of approximately 12%.
Unfortunately, the same procedure could not be applied to
the
herein may be underestimated by as much as 30% for this
isotope.
Additional samples of Au, Pb, and C (all 22 mm in
diameter) have been used in the experiment. The Pb and C
(corresponding to an areal density of 2.99 × 10−3atoms/b
and 2.018 × 10−2atoms/b, respectively) disks were used to
determine various background components. A gold sample,
0.25 mm in thickness (corresponding to an areal density of
1.498 × 10−3atoms/b), served to normalize the capture data
via the saturated resonance technique [33]. This technique
can be applied when the macroscopic total cross section is
much larger than unity. In this particular case, all incoming
neutrons, with energies in the vicinity of the resonance energy,
interact with the sample. Therefore, since all neutrons are
absorbedinthesample,theprobabilityofacaptureeventinthe
sample is 1.
The measurements with the different samples were cycled
every2daysandtheywereinterspersedwithenergycalibration
of the scintillators.
26Mg sample. Therefore, the cross section presented
III. DATA REDUCTION
The use of the PHWT, by which the TOF spectrum is
modifiedonthebasisofthesignalamplitude,requiresacareful
energycalibrationofthecapturedetectorsincombinationwith
proper study of the detector resolution [34]. During the entire
experiment, the pulse height response of the C62H6detectors
was calibrated in regular intervals with standard sources, i.e.,
with137Cs,60Co, and a composite238Pu/C source, which
yields 6.13-MeV γ rays through the13C(α,n)16O∗reaction.
Data were taken with a digitizer threshold corresponding to a
deposited energy of about 160 keV, but a fixed threshold of
200 keV was later applied in the off-line processing.
By the use of fast digitizers for data acquisition the dead
time could be reduced to an effective value of less than
25 ns, related to the pulse reconstruction algorithm. In the
off-line event processing, we applied a fixed dead time of
30 ns and used this value in the calculation of the correction
due to counting-rate losses. When an event was observed, all
subsequent signals occurring within the dead time of 30 ns in
bothdetectorswerediscardedinordertoeliminatecoincidence
counting. The dead time correction never exceeded 1%.
A. Capture yield
The capture yield Y(En), which represents the probability
of a neutron to be captured by the sample, can be deduced
from the background-subtracted counts in the TOF spectrum
C(En) registered by the C62H6array,
C(En) = Y(En)?(En)Aεc,
(2)
where ?(En) represents the intensity of the neutron beam, A
the sample area, and εcthe efficiency for detecting a capture
event.
In the PHWT, the proportionality of the capture efficiency
to the total γ energy released in the capture event εc∝
Ec, where Ec is the sum of the neutron separation energy
and the kinetic energy (Ec= Sn+ Kc.m.), is obtained by a
weighting function, which modifies the detection efficiency so
εcbecomes independent of the γ cascade. The weighted count
rate spectrum is
CW(En) = NY(En)?(En)Ec,
(3)
where the absolute normalization N of the capture data is
obtained by means of the saturated resonance in Au at 4.9 eV.
Since the Au disk was 0.25 mm in thickness, the attenuation
of the γ rays in the Au sample was considered as described in
Ref. [28]. The corresponding correction of the normalization
constant was of the order of 1%.
The measured capture yields are shown in Fig. 2.
B. Background studies
The background components have been determined by
comparisonoftheMgcaptureyieldswiththerespectiveyields
measured with the Pb and C samples as illustrated in Fig. 3.
The main source of background in the keV region is
generated by in-beam γ rays, which are scattered from the
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0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
110
Neutron energy (eV)
10
2
10
3
10
4
10
5
10
6
natMg(n,γ)
25Mg(n,γ)
26Mg(n,γ)
Capture yield (in units of 102)
FIG. 2. (Color online) Capture yield of thenatMg(n, γ),25Mg(n,
γ), and26Mg(n, γ) reactions.
sample and detected by the capture setup. These γ rays
arise mainly from neutron capture on hydrogen in the water
moderatorsurroundingthespallationtargetandareresponsible
for most of the background in the keV region. This component
is most pronounced in the yield of the Pb sample, which is
particularly sensitive to in-beam γ rays due to high atomic
number of lead. Accordingly, the effect for the C and Mg
samples is much weaker as illustrated in Fig. 3.
Another important background is produced by sample-
scattered neutrons, which are captured in the detection setup
and in surrounding materials. This background component is
studied with the C sample that can be considered as a pure
neutron-scatterersample.Theshapeofthecarbonyieldisvery
similar to that of25Mg, because the nonresonant elastic cross
sectionσn(theso-calledpotentialscattering)issmoothforboth
elementsinthisregionandtheelasticyieldnσn(wherenisthe
areal density in atoms per barn) is similar for both samples.
The comparison of the two components shows that the
overall background was dominated by the effect of sample-
10
-5
10
-4
10
-3
110
Neutron energy (eV)
10
2
10
3
10
4
10
5
10
6
25Mg + n
natC + n
natPb + n
Yield (not normalized)
FIG. 3. (Color online) Capture yield of the25Mg+n reaction
together with the spectra of the C and Pb measurements.
scattered neutrons. Since the background displays a smooth,
nonresonant behavior as a function of energy, it was not
subtracted but was fitted in the resonance analysis. In this
way, the uncertainty related to the background was included
in the uncertainty of the resonance parameters.
IV. SIMULTANEOUS RESONANCE SHAPE ANALYSIS
The present capture data were analyzed together with
transmission data from ORELA [9], available from the
Experimental Nuclear Reaction Data (EXFOR) database
[35], using the R-matrix code SAMMY [36]. A simultaneous
resonance shape analysis of capture and transmission data
results in much more reliable resonance parameters than can
be obtained through independent analyses of the various data
sets.Experimentaleffectsduetoneutronmultiplescatteringin
the sample, self-shielding (i.e., shielding of the inner atoms in
the sample by the outer atoms closer to the surface), Doppler
broadening, and experimental resolution are properly taken
into account within the SAMMY code.
As shown in Eq. (3), the efficiency, and, hence, the
calculated capture yield, is inversely proportional to Ec.
However, only a single Sn(typically chosen to be that of the
most abundant isotope in the sample) can be used in weighting
the data. Therefore, in the analysis of the capture data, the
abundances of the other Mg isotopes in the sample must be
scaled according to their Snvalue. In particular, the neutron
separation energies used were 7.33, 11.09, and 6.44 MeV for
25Mg,26Mg, and27Mg, respectively.
Resonance parameters reported in Ref. [8] were used as
initial values in the RSA, with the following exceptions.
An average reaction width ?γ= 3.5 eV was kept fixed to
fit capture data when a resonance was not visible in the
transmissiondata.Spin-parityassignmentofresonancesabove
500 keV were taken from known results of a neutron elastic-
scatteringexperiment[13].Allresonancesupto700keVwere
includedintheR matrix.Theavailabilityofcapturedatainthe
fullenergyrangeallowedustoassigntheobservedresonances
to the respective isotopes in the fit of the transmission data up
to 700 keV. The RSA of the capture data was limited to below
about700-keVneutronenergy,whereinelasticscatteringstarts
to interfere.
Inthefittingprocedure,theresonanceenergyandthepartial
widths (?n and ?γ) were allowed to vary while spin and
angular momentum were kept fixed. The nuclear radii for
24Mg+n and25Mg+n were allowed to vary in the fits of the
transmission data as explained in Ref. [8]. The results are radii
of 5.4 and 3.8 fm for s and p waves in24Mg+n, respectively,
and 5.1 fm common to s and p waves in25Mg+n. Figure 4
shows the quality of the fit to the transmission data.
Parameters of the resonances at negative energy were
changed with respect to the assumptions in Ref. [6] to repro-
ducethethermal-neutroncapturecrosssectionreportedinRef.
[23].TheirenergywastakenfromthelevelschemeinRef.[37].
A.
24Mg+n resonances
The capture yield considered for this analysis was obtained
from thenatMg+n measurement. The problems described in
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0
0.1
0.2
0.3
0.4
0.5
0.6
0100
Neutron energy (keV)
200300400500600700
natMg+n
SAMMY RSA
I
Transmission
FIG. 4. (Color online)natMg+n transmission data (red symbols)
and the SAMMY fit (blue line).
Sec. IIB for the oxide samples do not apply for this metal
sample.
In Table II the results of the RSA are reported together with
the uncertainties from the fitting procedure. Examples of the
fits are given in Figs. 4 and 5.
In the present analysis, the 68.5-keV resonance, assigned
to
resonance. Indeed, it was visible in the26Mg(n,γ) data and
with much reduced size in thenatMg(n,γ). Moreover, the
doubtful resonance at 177 keV was confirmed as belonging
to24Mg.
The capture kernels
24Mg in the literature, has been found to be a
26Mg
ωγ = g?γ?n/(?γ+ ?n),
(4)
calculatedfrompresentresonanceparameters,arecomparedto
those from Ref. [9] in Fig. 6. In particular ratios of the capture
kernels as a function of neutron energy and of the g?n/?γ
values are shown. It has been shown [38] that some kernels
TABLE II.24Mg+n resonance parameters extracted from the
simultaneous R-matrix analysis. The quoted uncertainties were
obtainedbytheSAMMYfit.SpinandparityfromRef.[8]andRef.[13].
En(keV)
?Jπ
?γ(eV)
?n(eV)
−100
46.347 ± 0.001
83.940 ± 0.004
176.67 ± 0.01
257.182 ± 0.001
267.48 ± 0.01
430.79 ± 0.01
475.359 ± 0.004
498.285 ± 0.004
551.04 ± 0.03
642.012 ± 0.004
659.95 ± 0.01
aAssumed reaction width. See text for details.
00.5+
(0.5−)
1.5−
(0.5−)
(1.5+)
0.5−
1.5−
2.5+
1.5−
(2.5+)
0.5−
0.5+
133000
(1)
1
(1)
(2)
1
1
2
1
(2)
1
0
1.4 ± 0.2
4.1 ± 0.2
3.5a
1.8 ± 0.1
7 ± 3
6.7 ± 0.6
1.2 ± 0.2
0.25 ± 0.1
8 ± 7
1.5 ± 0.3
(13 ± 1)
1.44 ± 0.06
7607 ± 4
0.4 ± 0.2
20.9 ± 0.5
83270 ± 20
28180 ± 20
13.9 ± 0.5
752 ± 2
1.2 ± 0.4
1459 ± 8
17470 ± 40
0
45
Incoming neutron energy (keV)
0.005
0.01
0.015
Capture yield
0.02
45.5 4646.5 47
24Mg(n,γ)
SAMMY RSA
I
(a)
0
0.05
0.1
0.15
260 280 300
24Mg(n,γ)
SAMMY RSA
I
(b)
Incoming neutron energy (keV)
Capture yield (in units of 102)
FIG. 5. (Color online) Fits of the capture yield of the24Mg+n
reaction in different energy regions.
from previous ORELA measurements for resonances having
large g?n/?γwere systematically too large, presumably due
to an underestimation of the neutron-scattering background
(so-called neutron sensitivity effect). The differences between
the present capture kernels and those of Ref. [9] do not appear
to indicate this neutron sensitivity effect.
B.
25Mg+n resonances
The capture yield of25Mg was obtained from the spectrum
measuredwiththeenrichedoxidesampleafteritsarealdensity
was scaled to reproduce the resonance parameters determined
from the natural Mg sample, where the first s-wave resonance
in
correction, ?γ values of 1.7 ± 0.2 and 1.16 ± 0.06 eV
were found using the data measured with the natural and
the enriched MgO sample, respectively. This disagreement
suggestedthatthearealdensityoftheoxidesamplewas27.5%
too high, indicating a significant water contamination of the
oxide sample.
25Mg+n at 19.86 keV is well isolated. Without that
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RESONANCE NEUTRON-CAPTURE CROSS SECTIONS OF ...
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0
0.5
1
1.5
2
2.5
3
0100
Neutron energy (keV)
200 300400 500600 700
(a)
Kernel ratio (this work/Weigmann)
0
0.5
1
1.5
2
2.5
3
10
-210
-1
110
gΓn/Γγ
10
2
10
3
10
4
(b)
Kernel ratio (this work/Weigmann)
FIG. 6. CapturekernelratiosofthepresentworktoWeigmann[9]
as functions of neutron energy (a) and g?n/?γ values (b) for24Mg
resonances.
If the shape of a resonance is distorted by experimental
effects, e.g., by Doppler and resolution broadening, the
remaining observable is the capture kernel (proportional to the
area under the resonance) and the areal density of the sample
[39].Accordingly,theRSAissensitivetong?γ?n/(?γ+ ?n).
Because ?n? ?γfor the 19.86-keV resonance, this quantity
reduces to ng?γ, and because the statistical spin factor is
knownfrompreviousmeasurements,theeffectivearealdensity
n can be derived via RSA from the capture data obtained with
the oxide sample. This procedure is valid only if the resonance
parameters, and in particular the reaction width, is kept fixed
in the fit. In this way, the effective areal density turned out to
be (8.6 ± 1.0) × 10−3atoms/b, where the 12% uncertainty is
given by the uncertainty on ?γ.
This adjusted areal density was used in the RSA of the
enriched25Mg sample. As shown in Fig. 7, the capture yield
of the oxide sample can be reproduced with the same accuracy
either by fitting the reaction width or the areal density of
the sample. On the contrary, the calculation of the yield
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
15
Incoming neutron energy (keV)
202530
25Mg(n,γ)
n=0.0118 atoms/b
Γγ=1.7 eV
n=0.0086 atoms/b
Γγ=1.7 eV
n=0.0118 atoms/b
Γγ=1.16 eV
I
Capture yield (in units of 103)
FIG. 7. (Color online) The capture yield of the
resonance at 19.86 keV. The data measured with the oxide sample
(symbolswitherrorbars)areclearlyoverestimatedwiththeresonance
parameters obtained from the metallic sample and the originally
declared areal density (black line). The resonance analysis with
SAMMY shows that the data are reproduced treating the areal density
n or the capture width ?γ as free parameters (blue and green lines,
respectively). Consistency with the result obtained with the metal
sample requires adopting the reduced areal sample density.
25Mg(n,γ)
assuming n = 0.01182 atoms/b (i.e., the originally declared
value) and ?γ= 1.7 eV (derived from the metallic sample)
does not reproduce the data. It is obvious that the results
for the 19.86-keV resonance can be reconciled only if the
reduced areal density is adopted for the enriched sample. The
correspondingresultsoftheRSAarelistedinTableIIItogether
with the uncertainties from the SAMMY fits. Examples of the
RSA analysis are given in Figs. 4 and 8.
The parameters of the 19.86-keV resonance derived from
the metallicnatMg sample are in agreement with those of
Ref. [9]. Moreover, the spin and parity assignment of this
level was confirmed since the χ2/DOF (χ2is chi-squared and
DOF is the number of degrees of freedom) value of the fit (in
the energy range 15–30 keV) was 1.6 assuming Jπ= 2+and
5.6 assuming Jπ= 3+. The spin and parity of the 72.66 keV
was confirmed as well: the χ2/DOF value of the fit (in the
energy range 60–80 keV) was 4.6 assuming Jπ= 2+and 7.9
assuming Jπ= 3+. The parity of the 62.727-keV resonance
was changed to negative according to a recent photoexcitation
experiment by Longland et al. [40]. The doubtful resonances
at ≈102 and 107 keV were found to improve the quality of the
simultaneous RSA and are, therefore, included in Table III.
However, they affect the resonance parameters of the large s
wave at 100.03 keV and capture data with an enriched sample
andveryhighstatisticarerequiredtosolvethispoint.Thespin
and parity of the 211.14-keV resonance was changed from 3−
[8] to 2−, because the simultaneous RSA of the transmission
and capture data were more satisfactory. In particular, the
χ2/DOF value of the fit (in the energy range 200–220 keV)
was 1.1 assuming Jπ= 2−and 3.5 assuming Jπ= 3−. For
theresonancesabove450keVthelargestatisticaluncertainties
prevented a meaningful RSA of the capture data.
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C. MASSIMI et al.
PHYSICAL REVIEW C 85, 044615 (2012)
TABLE III.25Mg+n resonance parameters extracted from the simultaneous R-matrix analysis, uncertainties include the one from the
sample mass. Spin and parity from Ref. [8]. Resonances and values in brackets must be considered with some caution.
En(keV)
?Jπ
?γ(eV)
?n(eV)
−154.25
19.86 ± 0.05
62.727 ± 0.003
72.66 ± 0.03
79.29 ± 0.03
81.117 ± 0.001
93.60 ± 0.02
100.03 ± 0.02
[101.997 ± 0.009]
[107.60 ± 0.02]
156.34 ± 0.02
188.347 ± 0.009
194.482 ± 0.009
200.20 ± 0.03
200.944 ± 0.006
203.878 ± 0.001
[208.27 ± 0.01]
211.14 ± 0.05
226.255 ± 0.001
242.47 ± 0.02
244.60 ± 0.03
245.552 ± 0.002
253.63 ± 0.01
261.84 ± 0.03
279.6 ± 0.2
311.57 ± 0.01
362.04 ± 0.02
387.57 ± 0.04
423.43 ± 0.01
451.24 ± 0.06
514.88 ± 0.03
536.0 ± 0.02
aSpin and parity assignment based on Ref. [40].
bParity assignment based on Ref. [19].
cObserved in22Ne(α,n)25Mg reaction.
dSpin assignment based on χ2.
0
0
1a
0
(0)
0b
(1)
0
[1]
[0]b
(1)
0
(1)
1b
(2)
(1)
[1]
(1)
(1)
(1)
1
(1)
(1)
(1)
(0)
(2)
2
(3)
1
(1)
(1)
(1)
2+
2+
1+a
2+
(3+)
(2)+
(1−)
3+
[2−]
[3+]
(2−)
(2)+
4(−)
1−
(2+)
(2−)
[1−]
(2−)d
(1−)
(1−)
1−c
(1−)
(1−)
4(−)
(2+)
(5+)
4+c
(5−)c
(1−)c
(3−)c
(2−)
(4−)
6.530000
2310 ± 30
28 ± 5
5080 ± 80
1560 ± 80
0.8 ± 0.7
0.6 ± 0.2
5240 ± 40
[4 ± 3]
[2 ± 1]
5520 ± 20
590 ± 20
1730 ± 20
1410 ± 60
0.7 ± 0.7
2 ± 1
[230 ± 20]
12400 ± 100
0.4 ± 0.2
0.3 ± 0.2
50 ± 20
0.5 ± 0.2
0.1 ± 0.1
3490 ± 60
3290 ± 50
(240 ± 10)
2020 ± 40
(8910 ± 80)
(25 ± 10)
(3000 ± 100)
(1800 ± 100)
(840 ± 40)
1.7 ± 0.2
4.1 ± 0.7
2.5 ± 0.4
3.3 ± 0.4
3 ± 2
2.3 ± 2
1.0 ± 0.1
[0.2 ± 0.1]
[0.3 ± 0.1]
6.1 ± 0.4
1.7 ± 0.2
0.2 ± 0.1
0.3 ± 0.3
3.0 ± 0.3
0.8 ± 0.3
[1.2 ± 0.5]
3.1 ± 0.7
4 ± 3
6 ± 4
3.5 ± 0.6
2.3 ± 2
3.1 ± 2.7
2.6 ± 0.4
1.9 ± 0.7
(0.84 ± 0.09)
2.2 ± 0.2
(1.7 ± 0.3)
(20 ± 10)
(6.6 ± 0.8)
(8.6 ± 0.8)
(2.7 ± 0.3)
C.
26Mg+n resonances
This analysis is based on the capture yield measured with
the enriched26MgO sample. The RSA results are reported
in Table IV together with the uncertainties from the fitting
procedure. As indicated by the capture yields in Fig. 2, the
mass of the26Mg sample seemed less affected by adsorption
of moisture. Nevertheless, this possibility still implies a
significant uncertainty, because none of the resonances could
be seen with the natural Mg sample. Therefore, the ?γvalues
(and, correspondingly, the capture cross section) may be
underestimated by as much as 30%.
It is worth noting that capture kernels have been estimated
in Ref. [21] on the basis of activation data and a theoretical
calculation for the DRC component. The ωγ values for the
68.5-and219.4-keVresonancesaregivenas0.067±0.016eV
and 1.34 ± 0.24 eV, respectively. In the present work we
measured ωγ = 0.09 ± 0.02 eV for the 68.5-keV resonance
and 2.17 ± 0.12 eV for the 219.2-keV resonance. This
disagreement would even be enhanced by a possible reduction
of the sample mass. Examples of the simultaneous RSA
analysis are given in Fig. 9.
TABLE IV.26Mg+n resonance parameters extracted from the
simultaneous R-matrix analysis. The quoted uncertainties were
obtained by the SAMMY fit. Spin and parity from Ref. [8].
En(keV)
?Jπ
?γ(eV)
?n(eV)
−60
68.529 ± 0.001
219.395 ± 0.002
302.34 ± 0.1 ± 0.08
427.23 ± 0.02
438.59 ± 0.09
500.50 ± 0.01
aValues may be underestimated by as much as 30%.
00.5+
(0.5−)
1.5+
0.5−
(0.5+)
(0.5−)
(1.5−)
32400
48 ± 2
80 ± 2
61200 ± 200
90 ± 20
11900 ± 200
260 ± 10
(1)
2
1
(0)
(1)
(1)
0.09a± 0.02
1.10a± 0.06
6.3a± 0.9
2.7a± 0.5
3.4a± 0.9
0.48a± 0.08
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RESONANCE NEUTRON-CAPTURE CROSS SECTIONS OF ...
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TABLE V. Maxwellian-averaged capture cross sections of24,25,26Mg (in mb) for different temperatures compared with the values in the
KADoNiS database [41].
Thermal energyThis workKADoNiS [41]
(keV) ResonancesDRCTotalResonancesTotal
24Mg(n,γ)25Mg
5
8
10
15
20
23
25
30
40
50
60
80
90
100
0.17 ± 0.01
0.38 ± 0.02
0.67 ± 0.04
1.7 ± 0.1
2.7 ± 0.1
3.1 ± 0.2
3.3 ± 0.2
3.7 ± 0.2
3.8 ± 0.2
3.6 ± 0.2
3.2 ± 0.2
2.6 ± 0.2
2.4 ± 0.3
2.1 ± 0.2
0.04
0.05
0.06
0.08
0.09
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.21 ± 0.01
0.43 ± 0.02
0.71 ± 0.04
1.71 ± 0.1
2.7 ± 0.1
3.2 ± 0.2
3.4 ± 0.2
3.8 ± 0.2
3.9 ± 0.2
3.7 ± 0.2
3.4 ± 0.2
2.8 ± 0.2
2.6 ± 0.3
2.3 ± 0.3
0.11
0.48
1.3
2.3
2.9
3.3 ± 0.4
3.6
3.4
3.1
2.7
2.1
25Mg(n,γ)26Mg
5
8
10
15
20
23
25
30
40
50
60
80
90
100
3.5 ± 0.4
4.9 ± 0.6
5.1 ± 0.6
4.9 ± 0.6
4.6 ± 0.4
4.5 ± 0.6
4.3 ± 0.6
4.0 ± 0.6
3.4 ± 0.6
2.8 ± 0.5
2.4 ± 0.4
1.8 ± 0.3
1.5 ± 0.2
1.3 ± 0.2
0.02
0.03
0.03
0.03
0.04
0.05
0.05
0.05
0.06
0.07
0.08
0.09
0.1
0.1
3.5 ± 0.4
4.9 ± 0.6
5.1 ± 0.6
4.9 ± 0.6
4.6 ± 0.4
4.6 ± 0.6
4.4 ± 0.6
4.1 ± 0.6
3.5 ± 0.6
2.9 ± 0.5
2.5 ± 0.4
1.9 ± 0.3
1.6 ± 0.2
1.4 ± 0.2
4.8
5.0
5.5
6.0
6.2
6.4 ± 0.4
6.2
5.7
5.3
4.4
3.6
26Mg(n,γ)27Mg
5
8
10
15
20
23
25
30
40
50
60
80
90
100
0.067a± 0.002
0.050a± 0.001
0.047a± 0.001
0.056a± 0.003
0.069a± 0.005
0.07a± 0.01
0.08a± 0.01
0.09a± 0.01
0.12a± 0.01
0.17a± 0.02
0.21a± 0.02
0.29a± 0.04
0.31a± 0.05
0.34a± 0.05
0.02
0.02
0.03
0.03
0.04
0.04
0.04
0.05
0.06
0.06
0.07
0.08
0.09
0.09
0.087b± 0.002
0.070b± 0.001
0.077b± 0.001
0.086b± 0.003
0.109b± 0.005
0.11b± 0.01
0.12b± 0.01
0.14b± 0.01
0.18b± 0.01
0.23b± 0.02
0.28b± 0.02
0.37b± 0.04
0.40b± 0.05
0.43b± 0.05
0.103
0.091
0.098
0.110
0.124 ± 0.008
0.126 ± 0.009
0.143
0.161
0.165
0.226
0.084 ± 0.005
0.265
aValues may be underestimated by as much as 30%.
bValues may be underestimated by as much as 20%.
V. STELLAR CROSS SECTIONS
A. Resonance contributions
The cross sections determined using the resonance param-
eters in Secs. IVA, IVB, and IVC have been convoluted with
a Maxwellian neutron energy distribution to obtain the actual
stellar cross section (MACS). The results are listed in the
Table V for thermal energies between kT = 5 and 100 keV,
including the specific values for the common s-process sites,
e.g., for kT = 8 and 23 keV related to He shell burning in
low-mass AGB stars and kT = 25 and 90 keV for the case
of core He and shell C burning in massive stars. The value
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C. MASSIMI et al.
PHYSICAL REVIEW C 85, 044615 (2012)
0
60
Incoming neutron energy (keV)
0.05
0.1
0.15
0.2
0.25
0.3
0.35
7080
25Mg(n,γ)
SAMMY RSA
I
(a)
Capture yield (in units of 102)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
125
Incoming neutron energy (keV)
150 175 200
25Mg(n,γ)
SAMMY RSA
I
(b)
Capture yield (in units of 103)
FIG. 8. (Color online) Fits of the capture yield of the25Mg+n
reaction in different energy regions.
for kT = 30 keV is traditionally used for comparison with
previous work.
In the resonance analysis, the DRC component is not
consideredand,therefore,thiscomponenthasbeencalculated,
asexplainedinthenextsection,Sec.VB.TheDRCcomponent
in the capture process varies smoothly with neutron energy. In
a TOF measurement, it cannot be easily disentangled from the
background, unless itis much larger than the background level
itself. This is not the case in the present experiment, therefore,
DRCwasconsideredasabackgroundandwassubtractedfrom
the capture yield and from the resonance cross section as well.
In order to obtain the actual MACS we added the calculated
DRC cross section to those extracted by the resonance shape
analysis.
B. Direct capture contributions
An estimate of the DRC component can be provided by
model calculations. In the present work, we adopted the
method described in Ref. [42] based on Lane-Lynn theory,
developed in the 1960s. Bound-state and scattering-state wave
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
50
Incoming neutron energy (keV)
100150 200250300350
26Mg(n,γ)
SAMMY RSA
I
Capture yield (in units of 103)
FIG. 9. (Color online) Fits of the capture yield of the26Mg+n
reaction.
functions are derived from a mean-field interaction potential
of Woods-Saxon shape with the following common geometric
parameters: radius r0= 1.236 fm, diffuseness d = 0.62 fm,
and spin-orbit strength Vso= 7.0 MeV. The potential strength
for the bound states (final states in the capture process) were
fixed assuming the experimental binding energies of the rele-
vant low-lying states. For25Mg and26Mg, the spectroscopic
strengthswereassumedtobeunityforthestateswithdominant
1d5/2, 2s1/2, and 1d3/2single-particle character, whereas, for
27Mg, experimental values available from the neutron transfer
(d,p) reaction were used.
For the calculation of the scattering-state wave functions,
two cases have been considered: a plane-wave approximation
and a mean interaction potential, whose strength had to be
adjustedusingsomeadditionalassumption.Forthelattercase,
one could consider the same potential strength that binds the
ground state of the composite system. Alternatively, a way
to derive the mean-field interaction potential could be that
of reproducing the neutron-scattering length which, however,
wouldbeaccurateforincidents-waveneutrons,whereasinthe
present case the dominant electromagnetic transition strength
for dipole transitions are for incident p-wave neutrons. Given
this indetermination, we will provide the result of the MACS
for a very wide range of interaction potentials, namely for
strengths between V0= 40 MeV and V0= 50 MeV.
The results of the calculations for the MACS at kT =
25 keV are shown in Table VI. As can be seen, the resulting
DRC cross sections depend strongly on the interaction poten-
tial used to derive the scattering-state wave functions. This is
duetothefactthatforthesenuclei,thesingle-particle2p3/2and
2p1/2orbits are located close to the neutron separation energy
of the composite systems. The matrix elements are, therefore,
inthisparticularcase,verysensitivetotheinteractionpotential
strength. As mentioned above, the interaction strength can
be constrained further using the information of the neutron-
scattering length. For24Mg and26Mg this leads to interaction
potential strengths of V0≈ 46 MeV and V0≈ 48 MeV,
respectively. With these two limiting cases for the potential
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TABLEVI. DRCcomponentsofthecrosssections.MACSvalues
in μb at kT = 25 keV are given for the different assumptions on the
strength of the interaction potential used in the calculation of the
scattering wave function. For the Woods-Saxon potential, the two
limits correspond to interaction strengths of V0= 40 and 50 MeV.
The recommended values are derived as described in the text.
Target Plane waveWoods-SaxonRecommended
24Mg
25Mg
26Mg
68.4
25.1
34.7
48.6 – 172.4
21.4 – 91.7
33.1 – 180.6
102 ± 15
48 ± 8
44
strength we have derived the recommended values shown in
the fourth column of Table VI.
For24Mg and25Mg, the DRC component of the cross
section remains a small fraction of the resonant component
derived from the present analysis, even assuming the largest
value resulting from the strongest scattering potential.
For26Mg, the DRC component can be estimated from
the difference between the MACS measured via activation
(0.124 ± 0.008 mb [20], which includes both DRC and
resonance components) and our resonance results in Table V.
The result (0.08 ± 0.01 mb) indicates that the DRC is about
40% of the total capture cross section for this nuclide. The
wide range of the results of the DRC model calculation shown
in Table VI is compatible with this estimate.
C. Discussion of uncertainties
In Table II, Table III, Table IV, and Table V the results
of the present experiment are presented together with their
uncertainties. These uncertainties are the sum of uncorrelated
or statistical uncertainties and systematic uncertainties.
The first component, attributable to counting statistic was
obtained from the resonance shape analysis. In particular in
the sequential RSA of capture and transmission data, the
covariance matrix was used to propagate uncertainties on
resonance parameters.
The correlated uncertainties consisted of several compo-
nents. They come from the PHWT, from the background
determination, and from the absolute neutron flux determina-
tion. The uncertainty related to the influence of the weighting
function was important in this case, since the capture data
were normalized to another isotope. The γ-ray spectra differ
markedly because of the large difference in the number
of levels available for decay after capture. Therefore, the
influence of the detector threshold may play a role. The
comparison of partial widths extracted independently from
transmission and from capture data gave coherent results
within few percentages. From these considerations, we could
assignanuncertaintyof3%fromtheapplicationofthePHWT.
The background determined by the measurement without
samplewasnormalizedbymeansofthenumberofprotonsper
pulse, which carries an uncertainty of 2%. For the estimation
of the uncertainty of the shape of the neutron flux, we adopted
an uncertainty of 2%. An uncertainty in the absolute level
of the flux is not relevant since we normalized the yield
on the saturated resonances. The uncertainty related to the
alignment of the sample was estimated to be less than 1%. The
combination of these components resulted in a total correlated
uncertainty of 4%.
An additional component arises for the powder samples. In
the case of25Mg it was possible to quantify this uncertainty to
be 12%, yielding a total systematic uncertainty of 13%. In the
case of26Mg we can argue only that the present result may be
underestimated by as much as 30%, which is the magnitude of
the correction for25Mg.
The values of the total uncertainty were obtained using
SAMMY. The systematic uncertainty was included by prop-
agating the uncertainty of few parameters: the background,
the normalization, and, only for the25Mg sample, the areal
density. The uncertainty on background parameter was 20%
and its effect was found to be negligible. The normalization
parameter grouped together with the remaining sistematyc
uncertaities; therefore, its uncertainty was 4%. In the analysis
of25Mg the areal density was allowed to vary within 12%. Its
effect was verified by repeating the RSA of25Mg with a lower
(higher) value of the areal density by 12%. Coherent results
were obtained.
In order to propagate the uncertainties from resonances
parameters to the stellar cross section, a parametric procedure
was adopted. In this procedure, the MACS (in Table V) were
calculatedusingresonanceparametersrandomlyvariedwithin
uncertainties.
VI. ASTROPHYSICAL IMPLICATIONS
A. Impact on s-process abundances
The inventory of the s-process abundances in the solar
systemisprovidedbythecontributionofdifferenttypeofstars.
The so-called main component originates from low-mass
asymptoticgiantbranch(AGB)starsintherangeof1to3solar
masses (M?) and is responsible for the s component of the
elementsbetweenSrandthePb/Biregion.Thecomplementary
weak component is provided by massive stars with M ? 8M?
and is responsible for the production of most of the s-process
species between Fe and Sr.
Neutron production in low-mass stars occurs during the
He shell burning phase of evolution by recurrent H and He
burning episodes. By far most of the neutrons are produced by
(α,n) reactions on13C during the quiescent H burning stage
and only about 5% of the neutron balance is contributed by
22Ne(α,n)25Mg reactions at the higher temperatures reached
in the relatively short He flashes. Accordingly, the production
of Mg is limited so the neutron poisons affecting the main
componentaredominatedbythelighterelementswithZ ? 20.
Theconsequencesfortheabundancesproducedbythemain
s component has been studied for the cases describing the
solution for the solar s component [43]. In these calculations,
only marginal differences of less than 1% were found if
the MACS values of the KADoNiS compilation [41] were
replaced by the present results. The main reasons for this
negligible impact are (i) that the MACS of
thermal energy of kT = 8 keV, which is characteristic of
the dominant neutron source provided by the13C(α,n)16O
25Mg at the
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PHYSICAL REVIEW C 85, 044615 (2012)
reaction, is nearly identical to the KADoNiS value and (ii)
that the22Ne(α,n)25Mg reaction is only marginally activated
in low-mass AGB stars with nearly solar metallicity.
In contrast to low-mass AGB stars, neutron production in
massive stars is dominated by the22Ne(α,n)25Mg reaction
during the convective core He burning and convective shell C
burningphases.Carbonmainlyburnsviathereactionchannels
12C(12C,α)20Ne and12C(12C,p)23Na, thus providing the α
particles for22Ne(α,n)25Mg reactions on the22Ne, left behind
at previous core He exhaustion.
Convective C shell burning is characterized by a short time
scale of the order of 1 year, and a by high neutron density
of up to 1012cm−3. The s-process nucleosynthesis during
this phase was first studied in detail 20 years ago [44] and
was confirmed by full stellar evolution calculations up to the
supernova explosion [45–47]. In a typical 25 M? star, the
convectiveCshellburningzoneextendsfromabout2to6M?,
closetothemaximum extension of theprevious convective He
burningcore.Theabundancesfromtheinnerzonebelowabout
3.5 M?that are ejected are modified in the final supernova
explosion, which essentially destroys the previously produced
s-process abundances by photodisintegration. The major part
of the s-process material in the outer zones of the C burning
shell is ejected almost unchanged, forming most of the s-
process yields of a 25 M?star [48–50].
Because of the dominance of the22Ne(α,n)25Mg reaction
as a neutron source in massive stars, a
produced along with practically each free neutron. Therefore,
becauseofitsrelativelyhighMACS,25Mgisarelevantneutron
poison. In this section, we study the impact of the present Mg
MACS on full stellar model calculations for a 25 M?star,
with solar metallicity, which were performed with an updated
postprocessing code described in Ref. [51].
The effect of the Mg cross sections from this work is
illustrated in Fig. 10. Figure 10(a) shows the s-process
abundance distributions calculated with the set of MACS
values from the KADoNiS database [41] (blue squares) and
after the MACS of the Mg isotopes were replaced by the
present results (red circles). The relative differences of the two
distributions are emphasized by their ratio in Fig. 10(b). In the
massregionoftheweaks processbetweenA ≈ 60and90one
finds a significant enhancement of the abundance distribution,
indicatingareducedpoisoningeffect.Thisreductionismainly
due to the lower MACS of25Mg.
Neutron-rich species following the branching points along
the s-process path (64Ni,70Zn,76Ge,82Se,86Kr,96Zr, and
100Mo in Fig. 10) show a strongest enhancement compared
to other isotopes in the same mass region. Some of them,
like76Ge and100Mo, are considered to be mostly produced in
r-process conditions. The reason of this specific effect is that
the reduced poisoning effect results not only in an enhanced
efficiency propagated over all the s-process distribution but
also in a higher neutron density, causing a stronger neutron
channel at the different branching points. Apart from these
cases, the average enhancement of about 30% underlines the
importance of reliable cross-section data for the light isotopes
below the mass range of the Fe peak. As demonstrated by the
presentresultsfortheMgisotopes,theseelementscanstrongly
influence the neutron balance of the s process with significant
25Mg nucleus is
FIG. 10. (Color online) (a) Abundance distribution of the weak s
process calculated with MACS values from the KADoNiS database
[41] (blue squares) and with the MACS of the Mg isotopes by the
present results (red circles). (b) The ratio of the two distributions
indicates an average enhancement of 30% due to the reduced neutron
poisoning effect.
consequences for the overall abundance distribution as well as
for the analysis of s-process branchings.
B. Constraints for the22Ne(α,n)25Mg reaction
As outlined in the previous section, the (α,n) reaction
on22Ne represents an important s-process neutron source.
Despite several attempts to measure the reaction cross section
[52–55], these experiments failed to reach the low α energies
ofastrophysicalrelevance,mostlybecausecosmic-rayinduced
background starts to dominate the experimental signatures
below Eα= 0.5 MeV. A series of indirect measurements via
α-particletransferreactions have been performed toovercome
this limitation [56,57]. Alternatively, the
reaction can be used to populate the same excited states as
shown in Fig. 11.
The reaction rates for the22Ne+α reaction at s-process
temperatures are determined by the level structure of the com-
poundnucleus26Mgabovetheα threshold(Q = 10.615MeV)
and near the neutron threshold (Sn= 11.093 MeV). Previous
evaluations [52] have assumed that all states observed by
neutron spectroscopy below the lowest observed resonance
at Eα= 832 keV can contribute to the reaction rate. This
approach overestimates this contribution because in the
22Ne(α,n)25Mgreactionthe26Mgcompoundstatesareformed
25Mg(n,γ)26Mg
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FIG. 11. Levelscheme(nottoscale)of26Mgwiththe22Ne+αand
25Mg+n entrance channels. The reaction Q values and the neutron-
separationenergySnareinMeV.Spinandparityvaluesofresonances
are given together with the level energies. Note the negative Q value
for the22Ne(α,n)25Mg reaction.
through spin 0 particles. Therefore, the resonance states have
natural spin and parity (0+, 1−, 2+, ...) and correspond
only to a subset of
the25Mg(n,γ)26Mg reaction. In fact, s-wave neutron capture
populates 2+, 3+states, whereas 1−, 2−, 3−, 4−are reached
by p-wave capture and 0+, 1+, 2+, 3+, 4+, 5+by d-wave
capture. Therefore, only a subset of levels was selected from
indirect measurements in Ref. [58] but included still some
non-natural states. Recent information on the level scheme
of26Mg, obtained from nuclear resonance fluorescence [40]
experiments, were used by Longland [59] to improve the
calculation of the reaction rate.
The present study provides strong evidence for natural
parityfortheresonancesat19.86keV(Ex= 11.112MeV)and
72.66keV(Ex= 11.163MeV).Moreover,thepresentworkis
compatiblewiththeresultsoftheexperimentbyLongland[40]
which gives strong indications for non-natural parity for the
resonances at 62.727 keV (Ex= 11.154 MeV). For other
resonances in the energy region of interest (En? 250 keV),
the spin and parity assignments remain uncertain.
Thecontribution ofnarrow
22Ne(α,n)25Mg reaction rate (in cm3/s/mole) can be
26Mg states, which are populated in
resonancestothe
1
10
102
103
0 0.20.40.60.81
19.86- and 72.66-keV resonances
Resonances up to 200 keV
19.86- and 72.66-keV resonances
Resonances up to 200 keV
T9 (GK)
Reaction rate ratio
FIG. 12. (Color online) Ratio of the upper and lower limits of the
22Ne(α,n)25Mg reaction rates and of the recommended values from
NACRE [61] as a function of temperature. Blue curves are calculated
using ?αfrom Ref. [58], and red curves are calculated using ?αfrom
Ref. [52].
estimated [60] as
NA?σv?r∼=1.54 × 105(2J + 1)?α
A3/2T3/2
9
e11.605ER/T9
,
(5)
where J is the spin of the resonance, ?α the α width (in
eV), A the reduced mass, and T9 the temperature in GK
(T9= T/109K). ER denotes the resonance energy in the
center-of-masssystem(inMeV).Thecalculationwasrepeated
assuming different values for ?α (a quantity that cannot be
determined by neutron spectroscopy). Lower limits of ?α
are from Ref. [58], and upper limits are from Ref. [52]. In
Table VII the contributions of the resonances observed in
the this work are summarized. In particular, two groups have
been considered: (i) the natural-parity resonances at 19.86 and
72.66 keV and (ii) resonances from this work below 244 keV
(Eα= 832 keV), where the assignment of natural parity is
uncertain (En= 81.117, 93.6, 188.347, 200.2, 200.944, and
208.27 keV).
Below 0.2 GK the reaction rate is dominated by the natural
parity resonances at 19.86 and 72.66 keV. The rate uncertainty
is determined by the ?α value but not by the energy [see
Eq. (5)], which is precisely inferred from the analysis of
the neutron data. However, there are still a few resonances
with uncertain spin and parity assignments which could
contribute to the22Ne(α,n)25Mg reaction rate at and above
0.2 GK. Therefore, a combined transmission and capture
experiment with highly enriched25Mg samples would be
highly desirable for obtaining unambiguous spins and parities.
Moreover, the
missing experimental information on ?α. This is illustrated in
Fig. 12 by the comparison of the calculated reaction rate from
this work and from the Nuclear Astrophysical Compilation of
Reaction rate (NACRE) evaluation [61].
22Ne(α,n)25Mg rate is still suffering from
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C. MASSIMI et al.
PHYSICAL REVIEW C 85, 044615 (2012)
TABLE VII. Neutron-resonance contributions (in %) to the rate of the22Ne(α,n)25Mg reaction at different temperatures.
T9
Group (i)Group (ii)
?αfrom Ref. [58]
?αfrom Ref. [52]
?αfrom Ref. [58]
?αfrom Ref. [52]
0.12
0.2
0.3
0.4
0.5
0.6
1.0
98
30
2
<1
–
–
–
83
40
24
17
12
1
–
2
8
3
17
60
74
76
74
72
2
<2
–
–
–
VII. CONCLUSIONS
We have measured the resonance neutron-capture cross
section of the three stable isotopes of Mg from 1 eV
to about 700 keV neutron energy. The measurement has
been performed with a capture setup optimized for capture
cross-section measurement of isotopes showing very large
elastic-to-reaction-channel ratios. We have updated the (n,γ)
cross sections of24,25,26Mg by combining the present capture
data with high-resolution transmission data from ORELA. In
this way, the parametrization of the cross section in terms
of resonance parameters could be significantly improved.
The use of highly enriched samples permitted us to assign
doubtful resonances, e.g., the 68.5-keV resonance could be
assignedto26Mgandthe177-keVresonanceto24Mg.Thespin
and parities of the 62.727-keV and 211.14-keV resonances
in
The present parametrization, including resonances at negative
25Mg were changed and the evaluation was extended.
energies, was adapted to reproduce the experimental value
of the cross section at thermal energy. Maxwellian average
cross sections determined from the present data were found
to differ significantly from earlier work. These values were
about 20% higher for24Mg and about 40% lower for25Mg
than recommended previously.
The26Mg results are in agreement with existing data,
but with a possible underestimation by 20%, due to sample
features. It was shown that the new values reduce the effect of
25Mg as a neutron poison for the s process in massive stars,
leadingtoahigherproductionpropagatedoverallthes-process
distribution. In particular, the largest variation is obtained in
the Kr-Rb region, with an increase up to 50–70%.
Constraints of the present results for the s-process neutron
source reaction22Ne(α,n)25Mg have been discussed, and a
new experiment for obtaining definite spin-parity assignments
of the important26Mg levels was proposed.
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