文部科学省 [先端研究基盤共用・プラットフォーム形成事業 成果報告]
兵庫県立大学 高度産業科学技術研究所 ニュースバル放射光施設

レーザー逆コンプトンガンマ線を用いた光中性子断面積測定
所属

甲南大学理工学部

ビームライン

ＢＬ01

利用者氏名

宇都宮 弘章

利用分野

量子ビーム技術

利用年度

2015年度活用技術

ガンマ線利用

利用成果の概要
209Bi(gamma,xn), (x=1-3) 断面積 データを7 - 40 MeVのエネルギー領域で取得した。ELI-NP
研究所（ルーマニア）とモスクワ大学（ロシア）との共同研究として実施した。
7Li(gamma,n)断面積データを2 - 5 MeVのエネルギー領域で取得した。甲南大学理工学部物理学科卒業研究および自然科学研究科物理学専攻修士課程の研究として行った。
205Tl(gamma,n), 203Tl(gamma,n), 89Y(gamma,n)断面積データを7.7 - 20 MeVのエネルギー領域で取得した。9Be(gamma,xn), (x=1,2)断面積データを17 - 32 MeVのエネルギー領域で取得した。
オスロ大学（ノルウェー）、ELI-NP（ルーマニア）との共同研究として実施した。レーザー逆コンプト
ンガンマ線の生成と診断は甲南大学理工学部物理学科卒業研究となる。また、9Be核データは自然科学研究科物理学専攻修士課程の学位取得の基になる。
<利用目的>
次の光中性子断面積データを取得するためにレーザー逆コンプトンガンマ線を利用する。
1. 209Bi(gamma,xn), (x=1-3) 断面積 データ
2. 7Li(gamma,n)断面積データ
3. 205Tl(gamma,n), 203Tl(gamma,n), 89Y(gamma,n)断面積データ
4. 9Be(gamma,xn), (x=1,2)断面積データ<実験方法>
上記1, 4の(gamma,2n), (gamma,3n)核データを取得するために、レーザー逆コンプトンガンマ線
をINAZUMA (Nd:YVO4)Q-switchレーザーの２倍高調波532nmを用いて生成した。電子エネル
ギーは630- 1100 MeVの範囲で変化させた。Pockels CellとPolarizerを用いてINAZUMAの周波数
16.67 kHz（パルス間隔60ms）を1.04 kHz（パルス間隔960ms）に間引いた。中性子はエネルギー領域0 - 5 MeVで全検出効率が約40%の平坦効率中性子検出器で検出した。
上記2の(gamma,n)核データを取得するために、レーザー逆コンプトンガンマ線をCO2 CWレー
ザーの10.5915mmを用いて生成した。電子エネルギーは1020-1460 MeVまで変化させた。上記1,
3, 4の(gamma,n)核データを取得するために、レーザー逆コンプトンガンマ線をINAZUMA(Nd:YVO4)Q-switchレーザーの基本波1064nmを用いて生成した。電子エネルギーは651- 1061
MeVの範囲で変化させた。INAZUMAレーザーを20 kHzで動作させた。中性子は1MeV以下のエネ
ルギー領域で60%以上の全検出効率を持つ高効率中性子検出器で検出した。
<実験結果>
上記核データ1, 2, 3, ,4をそれぞれ取得することができた。現在、甲南大学、ELI-NP研究所、オスロ大学でそれぞれ分担してデータ解析を行っている。

http;//www.lasti.u-hyogo.ac.jp/NS/

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文部科学省 [先端研究基盤共用・プラットフォーム形成事業 成果報告]
兵庫県立大学 高度産業科学技術研究所 ニュースバル放射光施設<今後の見通し>上記核データ1と4は、国際研究プロジェクトIAEA-CRP F41032 Updating the photonuclear satalibraryに提供する。核データ3は国際研究プロジェクトIAEA-CRP F41032 Generating a reference
dayabase for photon strength functionsに提供する。研究成果を基に、2016年9月11-16日にブルージュ（ベルギー）で開催される国際会議ND2016(International Conference on Nuclear Data
for Science and Technology, http://www.nd2016.eu）で口頭発表３件、ポスター発表２件を予定している。

問い合わせ先兵庫県立大学 高度産業科学技術研究所
ニュースバル放射光施設 共用促進室〒678-1205 兵庫県赤穂郡上郡町光都1-1-2
TEL : 0791-58-2543 FAX : 0791-58-2504
E-mail : kyoyo@lasti.u-hyogo.ac.jp

http;//www.lasti.u-hyogo.ac.jp/NS/

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PHYSICAL REVIEW C 90, 064616 (2014)

Photoneutron cross sections for samarium isotopes:
Toward a unified understanding of (γ ,n) and (n,γ ) reactions in the rare earth region
D. M. Filipescu,1,2 I. Gheorghe,1,2,3 H. Utsunomiya,4,5 S. Goriely,6 T. Renstrøm,7 H.-T. Nyhus,7 O. Tesileanu,1 T. Glodariu,2T. Shima,8 K. Takahisa,8 S. Miyamoto,9 Y.-W. Lui,10 S. Hilaire,11 S. Péru,11 M. Martini,6,11,12 and A. J. Koning13
1
Extreme Light Infrastructure Nuclear Physics, 407 Atomistilor Str., P.O. Box MG6, Bucharest-Magurele, Romania
National Institute for Physics and Nuclear Engineering Horia Hulubei, 407 Atomistilor Str., P.O. Box MG6, Bucharest-Magurele, Romania
3
Faculty of Physics, University of Bucharest, RO-077125, Bucharest, Romania
4
Department of Physics, Konan University, Okamoto 8-9-1, Higashinada, Kobe 658-8501, Japan
5
Center for Nuclear Study, University of Tokyo, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
6
Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles, Campus de la Plaine, CP-226, 1050 Brussels, Belgium
7Department of Physics, University of Oslo, N-0316 Oslo, Norway
8
Research Center for Nuclear Physics, Osaka University, Suita, Osaka 567-0047, Japan
9
Laboratory of Advanced Science and Technology for Industry, University of Hyogo, 3-1-2 Kouto, Kamigori, Ako-gun, Hyogo 678-1205, Japan
10
Cyclotron Institute, Texas A&M University, College Station, Texas 77843, USA
11
CEA, DAM, DIF, F-91297 Arpajon, France
12
Department of Physics and Astronomy, Ghent University, Proeftuinstraat 86, B-9000 Gent, Belgium
13
Nuclear Research and Consultancy Group, P.O. Box 25, NL-1755 ZG Petten, The Netherlands(Received 6 October 2014; revised manuscript received 24 November 2014; published 22 December 2014)
2

Photoneutron cross sections were measured for the seven stable samarium isotopes 144,147,148,149,150,152,154 Sm
near the neutron threshold with quasi-monochromatic laser-Compton scattering γ rays. Our photoneutron crosssections are found to be low by 20%–37% relative to existing data. The photoneutron data are analyzed with
the TALYS reaction code by considering the Skyrme Hartree-Fock-Bogoliubov (HFB) plus quasiparticle random
phase approximation (QRPA) model and the axially symmetric deformed Gogny HFB plus QRPA model of theE1 γ -ray strength. Using the γ -ray strength function constrained by the present photoneutron data, we madea thorough analysis of the reverse (n,γ ) cross sections including the radioactive nucleus 151 Sm with a half-lifeof 90 yr. The radiative neutron capture cross section for 153 Sm with the half-life of 1.928 d is deduced with theγ -ray strength function method.
DOI: 10.1103/PhysRevC.90.064616

PACS number(s): 25.20.Lj, 25.40.Lw, 27.60.+j, 26.20.Kn

I. INTRODUCTION

Radiative neutron capture on radioactive nuclei along theline of β stability in the medium- to heavy-mass region of thechart of nuclei is an important issue in nuclear astrophysics andnuclear engineering. In nuclear astrophysics, the cross sections
are important to determine the s-process path at branching
points where neutron capture and β decay compete [1].
The neutron capture data are also essential for nuclear
transmutation of long-lived fission products known as nuclear
waste in the field of nuclear engineering [2]. The γ -ray strength
function (γ SF) method was recently devised for constraining
the (n,γ ) cross section of radioactive nuclei, which cannot
be measured directly [3,4]. This method relies on the Brink
hypothesis linking photodeexcitation to photoabsorption [5]and aims at determining the γ SF, a nuclear statistical quantitythat is commonly important to quantify radiative neutron
capture and photoneutron cross sections. Photoneutron crosssections provide a stringent experimental constraint in absolute
scale on the γ SF around the neutron emission threshold Sn . The
method requires a systematic measurement of photoneutron
cross sections for neighboring stable isotopes of a radioactive
nucleus of interest, in addition to the existing (n,γ ) data which
serve as experimental constraints on the γ SF below Sn . Thus,a unified understanding of (n,γ ) and (γ ,n) cross sections
throughout an isotopic chain offers detailed information on
0556-2813/2014/90(6)/064616(9)the γ SF for a given nucleus formed by neutron captureon the radioactive nucleus. Such a systematic approach withthe γ SF method has been applied to zirconium [6], tin [7],molybdenum [8], and neodymium [9] isotopes.
We now apply the γ SF method to the Sm isotopic chain.
The γ SF method requires a systematic measurement ofphotoneutron cross sections for stable Sm isotopes in thevicinity of the radioactive Sm isotopes. Figure 1 illustrates
the photoneutron emission and radiative neutron captureof Sm isotopes studied in the present paper. The present
photoneutron measurement involved seven stable isotopes
including the p-process nucleus 144 Sm, the s-only nuclei 148 Sm
and 150 Sm, and the r-only nucleus 154 Sm as shown by the leftpointing arrows in Fig. 1. The photoneutron emissions studied
constitute a part of the reaction network of the p-process
nucleosynthesis [10] in which photodisintegration plays aprimary role in reprocessing the preexisting nuclei produced by
the s-process and r-process [11]. Photoneutron cross sections
for two odd-N nuclei, 147 Sm and 149 Sm, are measured forthe first time. The 147 Sm(γ ,n) reaction is important for the
production of the p-process 146 Sm chronometer [10]. The
photodisintegration of 144 Sm also contributes to the destructionof this p-process nucleus.
We present radiative neutron capture cross sections for153
Sm (half-life of 1.928 d) and 151 Sm (half-life of 90 yr)
determined with the γ SF method. The latter cross section

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D. M. FILIPESCU et al.

PHYSICAL REVIEW C 90, 064616 (2014)

FIG. 1. (Color online) The chart of nuclei depicting our systematic analysis of (γ ,n) and (n,γ ) cross sections for Sm isotopes in the context
of the γ -ray strength function method. Photoneutron cross sections measured in the present experiment are shown by left-pointing arrows.
Radiative neutron capture cross sections discussed in the present systematic analysis are shown by right-pointing arrows. The radiative neutron
capture cross section of the radioactive nucleus 153 Sm is deduced with the γ -ray strength function method.

is compared with the direct measurement carried out at the
CERN-nTOF facility [12,13].
The outline of the paper is given as follows: The experimental procedure is described in Sec. II, while details regarding
the data analysis are given in Sec. III. The theoretical analysis
for the photoneutron emission is described in Sec. IV. The
radiative neutron capture cross sections, together with thedetermination of the 153 Sm(n,γ )154 Sm cross section throughthe γ SF method, are analyzed in Sec. V . Finally, conclusions
are drawn in Sec. VI.
II. EXPERIMENTAL PROCEDURE

Photoneutron cross section measurements for the stable isotopes of samarium have been performed by using
γ -ray beams produced by the Compton backscattering oflaser photons on relativistic electrons (LCS γ rays) at the
NewSUBARU synchrotron radiation facility [14]. We present
here details about γ beam production, beam energy profile, target preparation, neutron detection, and beam flux monitoring.
A. Gamma production and energy profile measurements

LCS γ -ray beams were produced with a high power
Q-switch Nd : YVO4 laser INAZUMA (Spectra-Physics) andelectron beams at energies between 573 and 850 MeV. The
maximum energy of the LCS γ -ray beams was varied fromthe corresponding neutron emission threshold (Sn ) of each Sm
isotope (the lowest value of which is 5.87 MeV for 149 Sm)
to 13 MeV, in the fundamental mode of the laser operation(λ = 1064 nm; power = 40 W). The laser was operated at
a 20-kHz frequency and had a pulsed, 10-Hz macroscopic
time structure of 80 ms beam-on and 20 ms beam-off. The
electron beam intensity varied from 200 to 65 mA, decreasing
by approximately 12–13 mA per hour.
The γ -ray beamline of the NewSUBARU synchrotron
radiation facility is depicted in Fig. 2. The laser beam was
focused in the vicinity of the midpoint (P2) of the straightsection of the ring used for laser-electron interactions, where
the electron beam has a minimum transverse profile and theprobability of LCS interactions becomes maximum [14]. The
LCS γ -ray beams were collimated with a 10-cm-thick lead
block with a 2-mm opening (C2 collimator in Hutch 1) thatis located 18.47 m from the interaction point. The collimator
mounted on an x-y-θ stage driven by stepping motors wasaligned to optimize the γ -ray flux by monitoring with a
NaI(Tl) detector. The γ -ray beamline is equipped with a double
collimation system with a 10-cm C1 lead collimator with 6- or
3-mm opening, which is located in the accelerator vault 3.00 m
upstream from the C2 collimator. The experiment was carriedout with and without the C1 collimator.

The γ -ray energy profile was measured with a largevolume 3.5 × 4 lanthanum bromide (LaBr3 : Ce) detectorin Hutch 2, GACKO (Gamma Collaboration Hutch of Konan
University). Hourly measurements were performed for eachγ -ray beam energy with the laser operated in the continuouswave mode at a reduced power in order to avoid pile-up effects.
The LaBr3 : Ce detector was calibrated by using thestandard calibration sources 137 Cs and 60 Co including the
2.5-MeV sum peak of 60 Co, the 1436-keV peak resulting
from the electron capture decay of 138 La, and the maximum
energy of each LCS γ -ray beam produced in this experiment.
The energy calibration of the LaBr3 : Ce detector is shown in
Fig. 3. The calibration points were fitted with a second-orderpolynomial by using the χ 2 method. The energy resolutionof the detector was studied by using γ transitions from the137
Cs and 60 Co sources. An upper limit of 2% was obtainedfor√energies above 2.5 MeV by fitting the data points with a
1/ E function, where E is the γ -ray energy.
The maximum energy of the LCS γ -ray beams is obtainedby the known energy of the electrons and laser photons(1.164 eV). The electron beam energy was recently calibrated
between 550 and 974 MeV in nominal energy with an accuracyof the order of 10−5 [15]. For this, a grating-fixed CO2 laser(λ = 10.5915 μm) was used to produce low-energy LCS
γ -ray beams below 1.7 MeV at the interaction point P1.
The produced γ -ray beams were measured with a calibrated
hyperpure Germanium (HPGe) detector. It was found that there

FIG. 2. (Color online) The γ -ray beamline at the NewSUBARU
synchrotorn radiation facility.

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PHYSICAL REVIEW C 90, 064616 (2014)

FIG. 3. (Color online) Energy calibration of the LaBr3 : Ce detector with 137 Cs, 60 Co, and 138 La and the maximum energies of LCS
γ -ray beams produced using a Nd : YVO4 laser and electron beams
at energies between 573 and 850 MeV.

is a systematic difference of approximately 10 MeV between
the nominal electron energy given by the beam optics of thestorage ring and the calibrated energy.
The Compton backscattering of laser photons on relativistic
electrons and the electromagnetic interactions of the γ -raybeams inside the LaBr3 : Ce detector were simulated by using
the GEANT4 Monte Carlo code [16,17]. The kinematics of
the inverse Compton scattering is implemented in the Monte
Carlo code with inclusion of the effect of the electron beamemittance. The energy spectra of the LCS γ -ray beams incident
on the targets were obtained by reproducing the LaBr3 : Ce
detector response. A detailed description of the GEANT4
simulation is given in a separate paper [18].
Figure 4 shows a typical spectrum of the LCS γ -ray
beam recorded with the LaBr3 : Ce detector (solid line)
along with the GEANT4 simulations of the detector response

FIG. 5. (Color online) Typical spectra of the γ -ray beams
recorded with the LaBr3 : Ce detector (solid lines) and the simulationsof the response function (dotted lines) and of the incident γ -ray beam(gray lines). A double collimation with a C1 collimator of 6-mm
aperture and a C2 collimator of 2-mm aperture was employed.

function (dotted line) and the incident γ -ray beam (grayline). The spectra are renormalized for better visualization.
The experimental response function was obtained without theC1 collimator. One can see a broad low-energy bump around
3 MeV in the response function. This bump is characteristicof spectra obtained without the C1 collimator, which was
confirmed experimentally under the presence and absence of
the C1 collimator. The bump corresponds to the laser photons
Compton-scattered around 0◦ with large cross sections in
the rest frame of electrons which, after a Lorentz boost by
relativistic electrons in the laboratory frame, punched throughthe 10-cm C2 collimator. The punch-through component isseen in the low-energy region of the incident γ -ray spectrum.
Figure 5 shows typical spectra of the LCS γ -ray beams
recorded with the LaBr3 : Ce detector (solid lines) along with
the GEANT4 simulations of the detector response function(dotted lines) and the incident γ -ray beam (gray lines). The
experimental response functions were obtained by using the
double collimation system with a C1 collimator of 6-mm
aperture. The low-energy component is absent in the response
function obtained with the double collimation system, which
confines the scattering angles into a narrower cone along
the electron beam axis with a total thickness of 20 cm. The
experimental response functions are well reproduced by the
GEANT4 simulation. Energy spreads of 1.2%, 1.4%, and 1.6%
at full width at half maximum (FWHM) were obtained for thethree incident γ -ray beams of maximum energy of 6.5, 10.0,
and 13.0 MeV, respectively. Thus the LaBr3 : Ce detector issuitable for recording energy spectra of the γ -ray beams.
B. Target preparation

FIG. 4. (Color online) A typical spectrum of the γ -ray beamrecorded with the LaBr3 : Ce detector (solid line) and the simulationsof the response function (dotted line) and of the incident γ -ray beam(gray line). A single collimation with a C2 collimator of 2-mm
aperture was used.

Enriched samples of 144 Sm, 147 Sm, 148 Sm, 149 Sm, 150 Sm,
Sm, and 154 Sm in oxide form (Sm2 O3 ) placed in purealuminum containers with inner diameter of 8 mm were
irradiated by the γ -ray beams. The samples were dehydrated
by baking in vacuum at temperatures up to 393◦ C for 4 h before

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D. M. FILIPESCU et al.

PHYSICAL REVIEW C 90, 064616 (2014)

TABLE I. Enrichment and areal density of samples.
SamplePurity(%)

Areal density(mg/cm2 )

144

88.80
94.00
99.94
97.72
94.68
99.47
98.69

1102
1042
2102
2242
862
1959
2253

Sm
Sm
148
Sm
149
Sm
150
Sm
152
Sm
154
Sm
147

being placed inside the aluminum containers. The sample
masses were determined by weighing the containers before andafter the filling. The γ -ray beam was positioned at the centerof the target by monitoring the visible synchrotron radiation as
a guide. According to the GEANT4 simulation, the beam spot
on target is 2.3 mm in diameter, which is sufficiently smaller
than the diameter of the target. The enrichment and the areal
density of each sample are listed in Table I.
C. Neutron detection

The number of (γ ,n) reactions was determined by detecting
the reaction neutrons with a calibrated neutron detection array.
The samarium samples were mounted at the center of a 4π
neutron detector composed of 20 3 He proportional countersembedded in a 36 × 36 × 50 cm3 polyethylene moderator.
The 3 He counters were placed in three concentric rings of four,
eight, and eight proportional counters located 3.8, 7.0, and10.0 cm from the beam axis, respectively. The moderator was
surrounded by additional polyethylene plates with cadmium tosuppress background neutrons. Every 100 ms of γ irradiation,
reaction plus background neutrons were recorded for 80 msof laser-on and background neutrons were recorded for 20 msof laser-off. The average energy of the reaction neutrons was
obtained using the “ring ratio technique” originally developedby Berman and Fultz [19] and used to determine the detection
efficiency. More details of the neutron detection are found in
the literature [20].
Neutron detection efficiencies of the three rings were
measured after the present experiment by using a calibrated
252
Cf source with an emission rate of 2.27 × 104 s−1 with
2.2% uncertainty at the National Metrology Institute of Japan.
The measurement excellently reproduced the results obtainedin 2006 at the same institute, which can be seen in Ref. [20].

collimator aperture, and the probability of interaction between
the laser photons and the relativistic electrons.
The number of recorded γ photons was obtained by using
the “pile-up method” described in [21], which is based on the
Poisson fitting method originally developed at the Electrotechnical Laboratory [22,23]. The uncertainty of the Poisson fitting
method is estimated to be 3%, which is attributed to thefitting and the energy linearity of the γ -ray detector in its
response to multiphotons. For each neutron measurement run
we recorded the γ -ray spectra, when the laser is on in the fullpower mode. Multiple photons were detected simultaneously,
generating a so-called pile-up spectrum. Before or after eachneutron measurement run the laser power is reduced in orderto obtain a single-photon spectrum, where it is most likely
to measure only one photon at a time. A typical exampleof the experimental pile-up energy spectrum, along with thesingle-photon spectrum, is shown in Fig. 6.
The number of γ rays detected in the NaI detector, Nγ ,det ,is given byipileup  ,(1)nipileupisinglewhere i = ( xi ni )/( ni ) gives the average channel ofthe pile-up and single-photon spectrum, and ni is the numberof counts in the ith channel. Note that the ratio of i in
Eq. (1) gives the average number of γ photons involved ina γ -ray beam pulse, while the sum pile-up events give thenumber of γ -ray beam pulses. As the targets are quite thick,the attenuation of the γ rays in the target amounts to 2%–3%.
Furthermore, to calculate the average γ -ray flux incident on
the target we have to take into account the attenuation in the
NaI detector as well,Nγ ,det =Nγ =Nγ ,det

 NaI
 ,

exp − μρtt tt 1 − exp − μρNaI
tNaI

(2)

D. Beam flux monitoring

The γ -ray beam flux was monitored with a 6 × 5 NaI(Tl)detector placed at the end of the LCS γ -ray beam line. The Nd :YVO4 (λ = 1.064 μm) laser operated at 20-kHz frequency
produces pulses of light of 60 ns in duration. The electron beam
bunches have a time structure of 2-ns interval (500 MHz) and
60-ps width. Thus, the LCS γ rays are generated in bunches
corresponding to each laser light pulse. The number of LCS
γ rays per bunch is given by a Poisson distribution [21] with amean which depends on the laser and electron beam intensity,

FIG. 6. (Color online) Experimental pile-up energy spectrum of
the LCS γ -ray beam obtained with a 6 × 5 NaI(Tl) detector.
A single-photon spectrum is also shown by the dashed line. The
maximum energy of the LCS γ -ray beam is 13.03 MeV (electron
beam energy of 860.8 MeV). The average number of photons per
beam pulse is 1.78.

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PHYSICAL REVIEW C 90, 064616 (2014)

where tt and tNaI give the thickness (in g/cm2 ) of the target
and the NaI detector, respectively, and μρ represents the massattenuation coefficient (in cm2 /g), tabulated in Ref. [24].
The systematic uncertainty for the cross section breaks
down to 3% for the number of incident photons, 3.2% for
the neutron detection efficiency, 0.5%–0.7% for the numberof target nuclei, and 0.2%–0.9% for the total attenuation
coefficient. Thus, the overall systematic uncertainty amounts
to 4.5% by summing the uncertainties of the breakdown inquadrature.

(1) We use the monochromatic cross section found from
Eq. (6), σ (0) (Eav ) = σγmonon (Eav ), as our starting pointand fit it with a Lorentzian function multiplied by apower law which dominates near Sn energies,
σ (E) = σc

The photoneutron cross section is given bynγ (Eγ )σγ n (Eγ )dEγ =

Sn

Nn
,
Nt Nγ ξ n g(3)

where nγ (Eγ ) gives the energy distribution of the γ -ray beam
normalized to unity and σγ n (Eγ ) is the photoneutron crosssection to be determined. Furthermore, Nn represents thenumber of neutrons detected, Nt gives the number of target
nuclei per unit area, Nγ is the number of γ rays incident
on target, n represents the neutron detection efficiency, andfinally ξ = (1 − eμt )/(μt) gives a correction factor for a thicktarget measurement. The factor g represents the fraction of γ
flux above the neutron threshold Sn ,g=EMaxnγ (Eγ )dEγ
Sn
.
EMax
nγ (Eγ )dEγ
0(4)

As a first approximation we assume a monochromatic γ -raybeam, by replacing the γ -energy distribution n(Eγ ) in Eq. (3)by a delta function, δ(Eγ − Eav ). Here, Eav is the averageenergy of the LCS γ beam,
Eav =

EMax
Eγ nγ (Eγ )dEγ
Sn
.
EMax
nγ (Eγ )dEγ
Sn(5)

We obtain the following cross section in the monochromatic
approximation:
σγmonon (Eav ) =Nn.
Nt Nγ ξ n g

p

1

2
2
1 + E − ER2 /(E 2

2)

, (9)

where σc , p, ER , and are treated as free parameters [20].
(2) The fitted function σ (E) is further divided into small
regions of 300 keV, and each region is fitted by a thirdorder polynomial.
(3) The third-order polynomials are in turn used to calculate the derivatives σγ(i)n (Eav ) in Eq. (8).
(4) Combining Eqs. (6) and (7), we get σ (Eav ) by

III. DATA REDUCTIONEMax

E − SnSnσγ(1)n (Eav ) = σγmonon (Eav ) − s2 (Eav ) − s3 (Eav ). (10)Here, we notice that the s1 term cancels out.
The calculated photoneutron cross section σγ(1)n (Eav ) isused for the next iteration; this procedure is followed
until convergence is achieved.
We find that the series converges rather fast. Since the energy
distribution of the beam is very sharp, the overall correction
remains small, i.e., 0.5%–9%. As shown in Fig. 7, only crosssections located at the highest average energies are subject toa significant correction.
Our final photoneutron cross sections are compared in
Figs. 8–14 with previous measurements, including the Saclay
data [26]. Significant discrepancies are observed between ourcross sections and those of Saclay for all Sm isotopes. Our
experiment leads to cross sections lower by 20%–37%. Suchan overestimate by the Saclay photodata was also reported inprevious comparisons for 142 Nd with a renormalization by afactor of 0.86 [31], for 144 Sm by a factor of 0.80 [32], and for(6)

The next step is to take into account the measured energy distribution of the γ -ray beam. A Taylor expansion method [25]is used to solve the integral of Eq. (3) with respect to σγ n (Eav )in the following manner:

Nn
,
(7)
σγ n (Eav ) +si (Eav ) =Nt Nγ ξ n giwhere
si (Eav ) =

EMax
1 (i)
σγ n (Eav )nγ (Eγ )(Eγ − Eav )i dEγ , (8)n!
Sn

and where σγ(i)n (Eav ) represents the ith derivative of σγ n (Eav ).
In order to determine σγ(i)n (Eav ), one must assume an energy
dependence; hence an iteration procedure must be applied. The
iteration procedure consists of the following four steps:

FIG. 7. (Color online) The monochromatic cross section and thenonmonochromatic cross section of 148 Sm. The arrow-indicated Sn
gives the neutron threshold of this nucleus.

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PHYSICAL REVIEW C 90, 064616 (2014)

FIG. 8. (Color online) Comparison between the present photoneutron emission cross sections and previously measured ones [26]for 144 Sm. Also included are the predictions from Skyrme
HFB+QRPA (based on the BSk7 interaction) [27] and axiallydeformed Gogny HFB+QRPA models (based on the D1M interaction) [28].

Rb, nat Sr, 89 Y, 90 Zr, 93 Nb, 127 I, 197 Au, and 208 Pb by a factorof 0.80–0.93 [33].

nat

IV. THEORETICAL ANALYSISThe photoneutron cross-section data are now comparedwith theoretical calculations obtained with the TALYS nuclear
reaction code [34,35] and two different models of the γ SF,
namely, the Skyrme Hartree-Fock-Bogoliubov (HFB) plus
quasiparticle random phase approximation (QRPA) model [27]based on the BSk7 interaction and the axially symmetricdeformed Gogny HFB plus QRPA model based on the
D1M interaction [28,36–38]. Both models are based on the
QRPA approach but make use of different interactions andapproximations. The BSk7+QRPA model introduces somephenomenological corrections to take the damping of the collective motion as well as the deformation effects into account.
In contrast, the D1M+QRPA model allows for a consistentdescription of axially symmetric deformations and includes

FIG. 10. (Color online) Same as Fig. 8 for 148 Sm.

phenomenologically the impact of multiparticle-multihole
configuration as a function of their densities [28,37]. Bothmodels have proven their capacity to reproduce experimental
photoabsorption data relatively well.
As seen in Figs. 8–14, cross sections around the neutron
threshold are rather well described by the D1M+QRPA model,
provided a scaling within typically 10%–20% is applied to thestrength function to reproduce the absolute experimental crosssections. The agreement around the neutron threshold is rather
satisfactory and there is no reason to invoke the presence of
extra low-lying strength from the present data, at least in thevicinity of the neutron threshold and as seen in some previous
photodata [3,6,7,39]. In contrast, larger deviations are seen
for the predictions obtained with the BSk7+QRPA strength
where some extra strength is usually predicted around 11 MeV.
Similar quantitative and qualitative results were obtained in theanalysis of the photoneutron data for the Nd isotopes [9].
V. RADIATIVE NEUTRON CAPTURE AND
THE γ SF METHOD

We now turn to the reverse radiative neutron capturechannel. It should be kept in mind that the corresponding

FIG. 9. (Color online) Same as Fig. 8 for 147 Sm.

FIG. 11. (Color online) Same as Fig. 8 for 149 Sm.
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PHYSICAL REVIEW C 90, 064616 (2014)

FIG. 12. (Color online) Same as Fig. 8 for 150 Sm.

FIG. 14. (Color online) Same as Fig. 8 for 154 Sm. Experimental
photoabsorption data from Ref. [30] are also included.

cross section for incident keV neutrons depends sensitively on
the γ SF, but in a rather lower energy range below the neutron
threshold, typically around 6 MeV of γ -ray energy for the
stable Sm isotopes, corresponding to the major contributing
energy range in the folding of the γ SF with the nuclear
level density (NLD) [11,27]. The predicted tail of the strength
function at low energies therefore plays a fundamental role.
On the basis of the Gogny HFB plus QRPA γ -raystrength [28], the reverse radiative neutron capture cross sections are now estimated with the TALYS reaction code [34,35]
for the stable and experimentally known 147,148,149,150,151,152 Sm
isotopes and compared with the experimental cross sections [26,29,30] in Fig. 15. Note that, in addition to theE1 contribution to the γ SF, the smaller M1 and otherhigher multipolarities are included, following the prescriptions
recommended in Refs. [34,35,54]. On top of the E1 strength
function, the cross section calculation also depends on the
adopted NLD. We have used here two versions of the HFB plus
combinatorial model, namely, the original one from Ref. [55]and the latest version based on the temperature-dependent
HFB model of Ref. [56]. Both of them are normalized tothe experimental s-wave spacing D0 values [54] wheneveravailable.

As can be seen in Fig. 15, the TALYS calculation agrees
well with experimental data for all six Sm isotopes, whichshows that, within the uncertainties affecting the experimental
γ SF and D0 value, all γ SF data are compatible with both thephotoabsorption above the threshold and the radiative capturechannels below the threshold. Experimental data exist forthe 151 Sm(n,γ )152 Sm cross section and our predictions are
in rather good agreement with the measurements. The corresponding TALYS Maxwellian-averaged cross section amounts,
at the thermal energy of 30 keV, to 3200 ± 800 mb, where
the uncertainty stems from the use of our two different NLD
models [55,56]. This value is in agreement with the value of3031 ± 68 mb found experimentally [13].
The γ SF method can now be applied to the experimentally unknown neutron capture cross section of 153 Sm. The
D1M+HFB E1 strength function positively tested on thephotoneutron and radiative capture cross section is used. As
far as the NLD is concerned, here also both versions of
the HFB plus combinatorial models [55,56] are considered.
No experimental information exists on the resonance spacingat the neutron binding energy for 154 Sm. The major uncertainty in the estimate of the neutron capture cross section
therefore stems from the adopted NLD model. The final
prediction is shown in Fig. 16. The Japanese JENDL-4.0
and American ENDF/B-VII.1 evaluations [57] are seen to
be in relatively good agreement with our estimate, but theRussian ROSFOND-2010 evaluation gives rather lower crosssections below 10 keV. The resulting Maxwellian-averaged
cross section of astrophysical interest amounts, at 30 keV,
to 1285 ± 360 mb. Our estimate (and, consequently, also the
ENDF/B-VII.1 and JENDL-4.0 ones) is found to be larger
than the theoretical Maxwellian-averaged cross sections of1095 ± 175 mb recommended in Ref. [58].
VI. CONCLUSIONS

FIG. 13. (Color online) Same as Fig. 8 for 152 Sm. Experimental(γ ,n) data from Ref. [29] are also included.

Photoneutron cross sections were measured for all sevenstable Sm isotopes near the neutron threshold with quasimonochromatic laser-Compton scattering γ rays. Our photoneutron cross sections are found to be about 20%–37%064616-7

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PHYSICAL REVIEW C 90, 064616 (2014)

FIG. 15. (Color online) Comparison between the Sm measured radiative neutron capture cross sections [13,40–53] with a TALYS calculation
making use of the D1M+QRPA calculation for the E1 strength. The hashed area corresponds to the sensitivity to the NLD.

lower relative to the 1974 measurements in Saclay [26].
The new data are analyzed with HFB+QRPA models of E1
γ -ray strength. The D1M+QRPA strength function is foundto be able to reproduce fairly well the photodata in all theenergy range above the neutron threshold and simultaneously

the experimental neutron capture cross sections which aresensitive to the γ SF below the threshold. A thorough analysisof the reverse (n,γ ) cross sections is made including theradioactive nucleus 151 Sm with a half-life 90 yr and 153 Sm
with a half-life 1.928 d through the γ -ray strength function
method. While neutron capture measurements exist for 151 Sm,
the new constraint on the 154 Sm E1 strength leads to a153
Sm(n,γ )154 Sm cross section sensitively higher than the one
predicted in previous works.

ACKNOWLEDGMENTS

FIG. 16. (Color online) Prediction of the 153 Sm(n,γ )154 Sm crosssection. The dotted, dashed, and dashed-dotted curves correspondto the Japanese JENDL-4.0, American ENDF/B-VII.1, and Russian
ROSFOND-2010 evaluations [57], respectively.

This work was supported by the Japan Private School
Promotion Foundation and by the JSPS-FNRS bilateral program. We are grateful to M. Igashira of the Tokyo Institute ofTechnology for making the 148,149,152,154 Sm samples available
for the present experiment. We thank Florin Rotaru of the
National Institute for Physics and Nuclear Engineering Horia
Hulubei for initiating us into GEANT4 coding and for fruitful
discussions. We acknowledge PRACE for awarding us accessto the resource CURIE based in France at TGCC-CEA.
D.M.F., I.G., and O.T. acknowledge financial support from theExtreme Light Infrastructure Nuclear Physics (ELI-NP) Phase
I project, a project co-financed by the European Union through064616-8

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PHYSICAL REVIEW C 90, 064616 (2014)

the European Regional Development Fund. H.T.N. and T.R.
acknowledge financial support from the Norwegian ResearchCouncil (NFR), Project No. 210007. S.G. acknowledges thefinancial support from the FNRS.

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Photoneutron cross sections for neodymium isotopes: Toward a unified understandingof (γ ,n) and (n,γ ) reactions in the rare earth region
H.-T. Nyhus,1 T. Renstrøm,1 H. Utsunomiya,2,3 S. Goriely,4 D. M. Filipescu,5 I. Gheorghe,5,7 O. Tesileanu,5 T. Glodariu,6
T. Shima,8 K. Takahisa,8 S. Miyamoto,9 Y.-W. Lui,10 S. Hilaire,11 S. Péru,11 M. Martini,4,11,12 L. Siess,4 and A. J. Koning13
1

Department of Physics, University of Oslo, N-0316 Oslo, Norway
Department of Physics, Konan University, Okamoto 8-9-1, Kobe 659-8501, Japan
3
Center for Nuclear Study, University of Tokyo, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
4
Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles, Campus de la Plaine, CP-226, 1050 Brussels, Belgium
5
ELI-NP, “Horia Hulubei” National Institute for Physics and Nuclear Engineering (IFIN-HH), 30 Reactorului,077125 Bucharest-Magurele, Romania
6“Horia Hulubei” National Institute for Physics and Nuclear Engineering (IFIN-HH), 30 Reactorului, 077125 Bucharest-Magurele, Romania
7
Faculty of Physics, University of Bucharest, RO-077125, Bucharest, Romania
8
Research Center for Nuclear Physics, Osaka University, Suita, Osaka 567-0047, Japan
9
Laboratory of Advanced Science and Technology for Industry, University of Hyogo, 3-1-2 Kouto, Kamigori, Ako-gun, Hyogo 678-1205, Japan
10
Cyclotron Institute, Texas A&M University, College Station, Texas 77843, USA
11
CEA, DAM, DIF, F-91297 Arpajon, France
12
Department of Physics and Astronomy, Ghent University, Proeftuinstraat 86, B-9000 Gent, Belgium
13
Nuclear Research and Consultancy Group, P.O. Box 25, NL-1755 ZG Petten, The Netherlands(Received 3 October 2014; revised manuscript received 20 November 2014; published 22 January 2015)2

Photoneutron cross sections were measured for five stable Nd isotopes, 143,144,145,146,148 Nd, near neutron
threshold with highly monochromatic laser-Compton scattering γ rays. The photoneutron data were comparedwith the calculations performed with the TALYS reaction code with inputs of the Skyrme Hartree-Fock-Bogoliubov(HFB) plus quasi-particle random phase approximation (QRPA) model and the axially symmetric deformed
Gogny HFB plus QRPA model of E1 γ -ray strength. Using the γ -ray strength function constrained by thepresent photoneutron data, a thorough analysis of the reverse (n,γ ) cross sections is made. Radiative neutron
capture cross sections for an s-process branching-point nucleus in the rare earth region, 147 Nd with the half-life
10.98 d, are deduced with the γ -ray strength function method. The impact of the newly evaluated 147 Nd(n,γ )148 Nd
cross section on s-process nucleosynthesis is discussed.
DOI: 10.1103/PhysRevC.91.015808

PACS number(s): 25.20.Lj, 21.10.Pc, 25.40.Lw, 27.60.+j

I. INTRODUCTION

Radiative neutron capture on nuclei along the line of βstability in the medium- to heavy-mass region of the chartof nuclei is an important issue in nuclear astrophysics andnuclear engineering. In nuclear astrophysics, the cross sections
are important to determine the s-process path at branching
points where neutron capture and β decay compete [1]. The
neutron capture data are also of essential importance fornuclear transmutation of long-lived fission products known as
nuclear waste in the field of nuclear engineering [2]. Following
the preceding paper for samarium isotopes [3], this paper
for neodymium isotopes constitutes the second part of ourinvestigations in the rare earth region.
Although experimental data of radiative neutron capture
cross sections for stable nuclei are well documented [4], thosefor radioactive nuclei are scarce due to the difficulty of direct
measurements that requires both an intense neutron beam andradioactive samples. While some of radioactive nuclei withhalf-lives (T1/2 ) of the order of years have become objectives
for direct measurements, for example, 151 Sm (T1/2 = 90 yr)[5,6] and 63 Ni (T1/2 = 100 yr) [7] at CERN/n-TOF, 147 Pm(T1/2 = 2.62 yr) at Karlsruhe [8], 244 Cm (T1/2 = 18.1 yr) [9]at J-Parc (Tokai), and 173 Lu (T1/2 = 1.73 yr) [10] in progress
at LANSCE (Los Alamos), those with T1/2 of the order of days
and shorter are far beyond the experimental scope at present.
0556-2813/2015/91(1)/015808(7)The well-established γ -ray strength function (γ SF) method
can be used for constraining the (n,γ ) cross sections for radioactive nuclei [11,12]. Relying on the Brink hypothesis [13]linking the photo-deexcitation process to photoabsorption,
the method determines the γ SF which commonly quantifies
radiative neutron capture and photoneutron cross sections. The(n,γ ) cross section is governed by primary γ transitions from aneutron capture state at the excitation energy E to all possible
nuclear states below the neutron threshold. Thus, the γ SF at
γ -ray energies εγ below the neutron separation energy (Sn )and the nuclear level density at the final state (E − εγ ) play
an essential role in this capture reaction [14]. Photoneutron
cross sections provide a stringent experimental constraint in
absolute scale on the γ SF around Sn . When auxiliary (γ ,γ  )and particle-γ coincidence data that help to construct the γ SF
below Sn are unavailable, the method requires a systematic
measurement of photoneutron cross sections for neighboring
stable isotopes of the radioactive nucleus of interest, in
addition to existing (n,γ ) data that serve as experimental
constraints on the γ SF below Sn . Thus, a unified understandingof (n,γ ) and (γ ,n) cross sections throughout an isotopic
chain offers detailed information on the γ SF for a given
nucleus formed by neutron capture on the radioactive nucleus.
Such a systematic approach with the γ SF method has been
applied to zirconium [15], tin [16], and molybdenum [17]isotopes.

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PHYSICAL REVIEW C 91, 015808 (2015)

FIG. 1. (Color online) The chart of nuclei depicting our systematic analysis of (γ ,n) and (n,γ ) cross sections for Nd isotopes in
the context of the γ -ray strength function method. Photoneutron
cross sections measured in the present experiment are shown by leftpointing arrows. Radiative neutron capture cross sections discussed in
the present systematic analysis are shown by right-pointing arrows.
Photoneutron cross sections for the radioactive nucleus 147 Nd are
deduced with the γ -ray strength function method.

Figure 1 depicts photoneutron emission (←) and radiative
neutron capture (→) on Nd isotopes of interest in the present
paper. We measured photoneutron cross sections for fiveneodymium isotopes, 143–146,148 Nd. Combining the present(γ ,n) data with existing (n,γ ) data for six Nd isotopes,
142–146,148
Nd, we determine 147 Nd(n,γ ) cross sections with theγ SF method. The present systematic measurement included
two odd-A nuclei, 143 Nd and 145 Nd, for which photoneutron
cross sections are presented near the neutron threshold for the
first time.
In this paper, we present radiative neutron capture cross sections for 147 Nd with T1/2 = 10.98 d, an s-process branchingpoint nucleus located in the rare earth region [1,18]. Its β decay
leads to the subsequent branchings at 147,148 Pm [8], which inturn affect the s-process production ratio of 147 Sm to 148 Sm.
We discuss a possible impact of the new cross section for 147 Ndon the abundance ratio of 148 Nd to the s-only nucleus 148 Sm
in asymptotic giant branch (AGB) stars.
The outline of the paper is given as follows. A descriptionof the experimental procedure and the data reduction is limited
to a minimum in Sec. II, yielding a detailed description to thepreceding paper [3]. The theoretical analysis of the photoneutron cross sections is given in Sec. III. The radiative neutron
cross sections are analyzed in Sec. IV. The 147 Nd(n,γ )148 Nd
cross section is determined with the γ SF method in Sec. V,
followed by a possible impact of the cross section on thes-process nucleosynthesis in Sec. VI. Finally, conclusions are
drawn in Sec. VII.
II. EXPERIMENTThe experiment was performed at the experimental hutch
GACKO (Gamma Collaboration Hutch of Konan University)of the γ -ray beamline BL01 of the NewSUBARU synchrotron
radiation facility [19]. In the BL01, energy-tunable andhighly monochromatic γ -ray beams [20] are produced throughinverse Compton scattering between Nd : YVO4 laser photons(λ = 1064 nm) and relativistic electrons in the NewSUBARU
storage ring. Fine pencil-like beams of the laser Compton
scattering (LCS) γ rays were produced and measured with a
3.5 × 4.0 LaBr3 (Ce) detector. The response function of the
LaBr3 (Ce) detector to the LCS γ rays was reproduced with a
GEANT4 simulation code implemented with the kinematics ofthe laser inverse Compton scattering to obtain the energy distribution of the γ -ray beam. The energy spread of the LCS γ -ray
beam with a low-energy tail was 1%–2% in full width at half

maximum (see Figs. 4 and 5 of [3]). Details of the GEANT4 simulation will be given in a forthcoming paper [21], where alsoa more in-depth description of the experimental setup can befound.
Samples of 143–146,148 Nd enriched to 90.85%–98.07% all
in the oxide form of Nd2 O3 with areal densities of 1.35–
2.78 g/cm2 were encapsulated in pure-aluminum containers
and irradiated with LCS γ -ray beams. The samples were
dehydrated by baking at temperatures up to 393 ◦ C for
4 h in vacuum before being placed inside the aluminum
containers. The sample masses were determined by weighing
the containers before and after the filling.
The γ -rays flux was determined by the pile-up methodof Ref. [22] after detecting the beam with a 6 × 5 NaI(Tl)detector mounted at the end of the beamline. Typically 20%
corrections were made for the transmission rate of the LCS γ
rays through the NaI(Tl) detector.
Neutrons were detected with a high-efficiency 4π neutron
detector consisting of 20 3 He proportional counters embedded
in a polyethylene moderator of 36 × 36 × 50 cm3 fully
covered by additional 5-cm-thick polyethylene plates with
1-mm-thick cadmium for background neutron suppression.
Neutrons were moderated in the polyethylene before being
detected with three rings of 4, 8, and 8 3 He counters placed at
distances of 3.8, 7.0, and 10.0 cm, respectively from the γ -ray
beam axis. The average neutron energy was determined by theso-called ring-ratio technique originally developed by Berman
and Fultz [23]. The total neutron detection efficiency is morethan 60% for neutrons with energies less than 1 MeV. Moredetails of the neutron detection can be found in Ref. [24].
Neutron detection efficiencies of the three rings were remeasured after the present experiment using a calibrated 252 Cf
source with an emission rate of 2.27 × 104 s−1 with 2.2%
uncertainty at the National Metrology Institute of Japan. The
measurement excellently reproduced the results obtained at
the same institute in 2006.
Photoneutron cross sections are deduced with the Taylor
expansion method [25], which takes into account the energy
spread of the LCS γ -ray beam. Corrections were also madefor the contributions to the cross section coming fromthe isotopic impurities in the Nd samples. The correction
remains small, being 1%–7% for the energy spread of thehighly monochromatic LCS γ -ray beam and 2% even for
the isotopic impurities of the less-enriched (90.85% and91.73%) 143,145 Nd samples. The systematic uncertainty ofthe present cross sections is 4.4% with the breakdown of
3% in the photon flux and 3.2% in the neutron detection
efficiency.
Our photoneutron cross sections are compared in Fig. 2
with the Saclay measurements [26]. While a good agreement
is obtained in the 146,148 Nd cases, significant discrepancies
are observed for the light Nd isotopes. In particular, ourexperiment leads to cross sections lower by typically 30%
for 143 Nd, 20% for 144 Nd, and 27% for 145 Nd. Such an
overestimate by the Saclay photodata was also reported
in previous comparisons for 142 Nd with a renormalization
by 0.86 [27], for 144 Sm by 0.80 [28], and for nat Rb,
nat
Sr, 89 Y, 90 Zr, 93 Nb, 127 I, 197 Au, and 208 Pb by a factorof 0.80–0.93 [29].

015808-2

( ,n) [mb]PHOTONEUTRON CROSS SECTIONS FOR NEODYMIUM . . .

10

Present
Carlos et al. (1971)
BSk7+QRPA
D1M+QRPA

1

10

143

Nd( ,n)142Nd( ,n) [mb]

100

(b)

102
101

144

Nd( ,n)143Nd( ,n) [mb]

100

(c)

102
101

145

Nd( ,n)144Nd

100( ,n) [mb]and the axially symmetric deformed Gogny HFB plus QRPA
model [33–35] based on the D1M interaction [36]. The
BSk7+QRPA model introduces phenomenological corrections to take the damping of the collective motion as well as thedeformation effects into account. (Note, however, that deformation parameters are consistently extracted from the HFB-7
mass model based on the BSk7 Skyrme functional [37].) In
contrast, the D1M + QRPA model allows for a consistentdescription of axially symmetric deformations and includes
phenomenologically the impact of multiparticle-multihole
configurations as a function of their densities [34]. Bothmodels have proven their capacity to reproduce experimental
photoabsorption data relatively well.
As seen in Fig. 2, cross sections around the neutron
threshold are rather well described by the D1M + QRPA
model, although some deviations can be seen. The agreement
around the neutron threshold is rather satisfactory and there is
no reason to invoke the presence of extra low-lying strengthfrom the present data, at least in the vicinity of the neutron
threshold, as seen in some previous photodata [11,15,16,38]. In
contrast, larger deviations are seen for the predictions obtainedwith the BSk7 + QRPA strength, in particular around 11 MeV,
but also at lower energies in the 145,146 Nd cases.

(a)

2

(d)

102

B. Radiative neutron capture cross sections

101
146

Nd( ,n)145Nd

100( ,n) [mb]

(e)
102

101
148

Nd( ,n)147Nd

0

10

PHYSICAL REVIEW C 91, 015808 (2015)

6

8

10

12

E [MeV]

14

16

FIG. 2. (Color online) Comparison between the present photoneutron emission cross sections and previously measured ones [26]for 143–146,148 Nd. Also included are the predictions from Skyrme
HFB + QRPA (based on the BSk7 interaction) [32] and axiallydeformed Gogny HFB + QRPA models (based on the D1M
interaction) [34].
III. THEORETICAL ANALYSIS
A. Photoneutron cross sections

Our new photoneutron cross sections shown in Fig. 2
have been compared to theoretical calculations obtained with
the TALYS nuclear reaction code [30,31] and two different
models of the γ SF, namely, the Skyrme Hartree-FockBogoliubov (HFB) plus quasi-particle random phase approximation (QRPA) model [32] based on the BSk7 interaction

We now turn to the reverse radiative neutron capturechannel. It should be kept in mind that the corresponding
cross section for incident keV neutrons depends sensitively
on the γ SF, but in a rather lower energy range below theneutron threshold, typically around 6 MeV of γ -ray energy.
The predicted tail of the γ SF at low energies therefore plays afundamental role.
On the basis of the Gogny HFB plus QRPA γ -raystrength [34], the reverse radiative neutron capture cross sections are now estimated with the TALYS reaction code [30,31]
for the stable and experimentally known 142–146,148 Nd isotopes
and compared with experimental cross sections in Fig. 3.
In addition to the E1 strength function, the cross section
calculation also depends on the adopted nuclear level density.
We have used here the temperature-dependent HFB plus combinatorial model [39] normalized to the experimental s-wave
spacing D0 values at the neutron binding energy [14]. Note thatexperimental s-wave spacings are available, so uncertainties
related to the adopted NLD model are rather small, typically
10%, as shown in Fig. 3, where the hashed areas correspondto uncertainties on experimental D0 values. Similarly, theuncertainties related to the adopted neutron optical potential
are negligible in the energy range of astrophysical interest, i.e.,in the keV–MeV region.
Based on the radiative neutron capture cross section,
the laboratory (i.e., without including the contribution of
excited states) Maxwellian-averaged cross sections (MACS)
have been estimated and compared with experimental dataat an energy of kT = 30 keV in Table I. The theoreticalerror bars stem from the NLD uncertainties affecting the D0
values. Here also, our TALYS predictions are compatible withexperimental data, with theoretical values being usually higher
than the measurements, except in the 142 Nd and 144 Nd cases.

015808-3

H.-T. NYHUS et al.

PHYSICAL REVIEW C 91, 015808 (2015)

103

104
Kononov et al. (1977)
Musgrove et al. (1978)
Wisshak et al. (1998)
Wisshak et al. (1998b)(E) [mb]

(a)

TALYS

103
Musgrove et al. (1978)
Nakajima et al. (1978)
Bokhovko et al. (1985)
Wisshak et al. (1998)
Veerapaspong et al. (1999)

(b)

103

Kononov et al. (1977)
Musgrove et al. (1978)
Wisshak et al. (1998)
Wisshak et al. (1998b)

(c)

2

10

102
102
142

Nd(n, )143Nd

1

10
0.001

0.01

143

Nd(n, )144Nd

0.1
Musgrove et al. (1978)
Nakajima et al. (1978)
Bokhovko et al. (1985)
Wisshak et al. (1998)
Veerapaspong et al. (1999)
Hockenbury et al. (1975)(d)(E) [mb]

104

1 0.001
104

0.01

144

Nd(n, )145Nd

0.1
Musgrove et al. (1978)
Nakajima et al. (1978)
Wisshak et al. (1998)
Veerapaspong et al. (1999)
Kononov et al. (1977)
Trofimov (1993)

(e)

103

1 0.001
104

0.01

0.1

1

Musgrove et al. (1978)
Nakajima et al. (1978)
Wisshak et al. (1998)
Johnsrud et al. (1959)
Kononov et al. (1977)
Trofimov (1993)
Afzal Ansari et al. (1999)

(f)

103

103
102

102

2

10

145

0.001

Nd(n, )146Nd
0.01

146

Nd(n, )147Nd

0.1

1 0.001

0.01

E [MeV]148

Nd(n, )149Nd

0.1

E [MeV]

1 0.001

0.01

0.1

1

E [MeV]

FIG. 3. (Color online) Comparison between the measured radiative neutron capture cross sections [40–50] with TALYS calculations making
use of the D1M + QRPA E1 strength (solid line). The hashed area corresponds to uncertainties related to the NLD model and their normalization
on experimental s-wave spacings at the neutron binding energy.

It should however be stressed that the MACS [42,43] havebeen measured relative to the radiative neutron capture crosssection of 197 Au, which has been recently re-evaluated andfound to deviate systematically by more than 5% from the crosssection that is recommended as a reference for astrophysicalapplications [51].
As a conclusion, the TALYS calculation agrees well with themost recent experimental data for all six stable Nd isotopes,
which shows that, within the uncertainties affecting theexperimental γ SF and D0 value, all γ SF data are compatible
TABLE I. Comparison of experimental (laboratory) MACS of
stable Nd isotopes [42,43] with the TALYS predictions at an energy of
30 keV. MACS are given in millibarns.
TargetExp. [42,43]

TALYS

142

35.0 ± 0.7
245 ± 381.3 ± 1.5425 ± 591.2 ± 1
147 ± 231 ± 2267 ± 2363 ± 4478 ± 5096 ± 8157 ± 11

Nd
Nd
144
Nd
145
Nd
146
Nd
148
Nd
143

with both the photoabsorption above the threshold and theradiative capture channels below the threshold.
C. Determination of the 147 Nd(n,γ )148 Nd cross section

The γ SF method can now be applied to the experimentally
unknown cross section 147 Nd(n,γ )148 Nd by making use of
the same nuclear inputs. In the case of 148 Nd, experimental
information exists on the resonance spacing at the neutronbinding energy, namely, D0 = 4.0 ± 1.5 eV [14]. The 40%
error on D0 corresponds to the major uncertainty still affecting
the prediction of the 147 Nd(n,γ )148 Nd cross section, giving
rise to a range of predicted cross sections within typically
20%–30%, as shown in Fig. 4. The ENDF/B-VII.1 evaluation [52] is seen to be in relatively good agreement with
our estimate, but the ROSFOND-2010 evaluation [53] gives
rather lower cross sections above typically a few keV andthe JENDL-4.0 evaluation [54] gives larger values above
typically 100 keV. The resulting MACS of astrophysicalinterest are shown in Fig. 5 and compared with the theoretical
determination recommended in Ref. [55]. Our MACS (and,consequently, also the ENDF/B-VII.1 and JENDL-4.0 ones)
are found to be significantly larger than those of the previous
recommendation [55]. In particular, at 30 keV, our cross section

015808-4

PHOTONEUTRON CROSS SECTIONS FOR NEODYMIUM . . .

105
ENDF/B-VII.1
JENDL-4.0
ROSFOND-2010
Present(E) [mb]

104

103

102
147

Nd(n, )148Nd

0.001

0.01

0.1

1

E [MeV]
FIG. 4. (Color online) Prediction of the 147 Nd(n,γ )148 Nd crosssection. The dotted, dashed, and dash-dotted curves correspond to
the JENDL-4.0 [54], ENDF/B-VII.1 [52], and ROSFOND-2010 [53]evaluations.

amounts to 880 ± 170 mb, to be compared with 544 ± 90 mb
recommended in Ref. [55] and theoretical values ranging
between 387 and 663 mb from various statistical model
calculations and compiled in the KADONIS library [56].
IV. APPLICATION TO s-PROCESS NUCLEOSYNTHESISIN AGB STARS

147< > [mb]104

given burning phases, namely, the core He-burning of massive
stars (heavier than 10M ) and the shell He-burning during
the thermal AGB instabilities (thermal pulses) of low- andintermediate-mass stars (<10M ) [1,58]. The core He-burningof solar-metallicity stars has proved its ability to produce
the lightest s elements (i.e., 70  A  90), but since 22 Ne
is a secondary source, the efficiency remains identical for
metal-poor stars. The astrophysical models underlying thethermal pulse scenario (believed to be responsible for the
production of the A > 90 s elements) remain quite uncertain
in many respects, in particular in the description of themixing mechanisms that could be at the origin of the neutron
production. AGB models including diffusive overshoot or
rotational effects suggest the partial mixing of protons (PMP)from the H-rich envelope into the C-rich layers during thethird dredge-up [59–61]. In low-mass AGB stars of typically
1 to 3M , this PMP model has been successful in explaining
the main and strong components of the s-process, including
the production of Nd and Sm isotopes. In more massive
AGB stars, such an s-process during the interpulse might beinhibited due to the high temperatures encountered at the baseof the convective envelope and the resulting combustion of
protons during the partial mixing [62]; the large temperatures
can however lead to a significant neutron irradiation within
the convective thermal pulse due to the activation of the22
Ne(α,n)25 Mg reaction [63].
Based on measured Maxwellian-averaged neutron capture
cross sections of the stable Nd nuclei, the production of
Nd and Sm isotopes by the s-process has already beenstudied in detail [8,42,43,64]. Our new estimation of the147
Nd(n,γ )148 Nd cross section may however affect the sprocess production of the sr nucleus 148 Nd and the s-only
148
Sm. To illustrate the impact of the newly determined MACS,

101
0.5

Nd(n, )148Nd

Present
Bao et al. (2000)
103

M=3M . ; Z=0.0001

0.4.

Surface overabundances X/X

Even though the observation of radioactive Tc in stellar envelopes [57] clearly proves that the s-process takes
place during the hydrostatic burning phases of a star, itremains difficult to explain the origin of the large neutron
concentrations required to produce s elements. Two nuclear
reactions are suggested as possible neutron sources, i.e.,13C(α,n)16 O and 22 Ne(α,n)25 Mg. These reactions could be
responsible for a large production of neutrons during the

PHYSICAL REVIEW C 91, 015808 (2015)

0.3

100

0.2
0.1
140

145

150

155

160

10-1

10-2
60

Present
Bao et al. (2000)
80

100

120

140

160

180

200

220

A
102
0

20

40

60

80

100

kT [keV]
FIG. 5. (Color online) Comparison between our newly determined 147 Nd(n,γ )148 Nd MACS with the values recommended inRef. [55].

FIG. 6. (Color online) Final surface abundances X for a 3M
AGB model star of metallicity Z = 0.0001 with respect to the solar
values X for all s-only nuclei and 148 Nd as a function of the mass
number A. The circles (including error bars) are obtained with thepresent 147 Nd(n,γ )148 Nd MACS and the diamonds with the values
given in Ref. [55]. The insert shows an enlargement of the 140 A  160 region.

015808-5

H.-T. NYHUS et al.

PHYSICAL REVIEW C 91, 015808 (2015)

nucleosynthesis calculations have been performed within the
PMP model [61] in 3M AGB model stars for three different
metallicities, namely, Z = Z = 0.0123, Z = 0.004, and Z =0.0001 [65]. Our upper value for the 147 Nd(n,γ )148 Nd crosssection, which is about twice as large as the one quoted
in the widely used compilation of Ref. [55], leads to alarger production of 148 Nd by 40% and a corresponding
reduction in 148 Sm production by about 10%. The final surface
overabundances for the low-metallicity Z = 0.0001 star are
illustrated in Fig. 6. In this specific case, if we use theupper limit of the cross section, we end up with an abundance ratio [148 Nd/148 Sm] = log[X(148 Nd)/X (148 Nd)] −log[X(148 Sm)/X (148 Sm)] = −0.24 (where X is the massfraction), while the previously used rate [55] gives −0.47. Inother words, in low-metallicity stars, 148 Nd can be relatively
produced with respect to the s-only nucleus 148 Sm, but also
production could be significantly greater with our new upper
limit, as seen in Fig. 6. In the case of the Z = 0.004 and Z =Z model stars, we find a significantly lower production of148
Nd with respect to 148 Sm, namely, [148 Nd/148 Sm] = −0.46
and −0.64, respectively, with our rate and −0.68 and −0.82,
respectively, with the low rate of Ref. [55].

interest. Based on an extensive analysis of five newly measured
photoneutron cross sections and the inverse radiative neutron
capture cross sections, the nuclear reaction ingredients havebeen constrained, leading to a final 147 Nd(n,γ )148 Nd crosssection about 60% larger than the unconstrained value adopted
in nucleosynthesis calculations. Our new rate determination
leads to an increase of 148 Nd production and a decrease of thes-only 148 Sm abundance by the s-process in AGB stars.
ACKNOWLEDGMENTS

The γ SF method has been applied to the Nd isotopic
chain in order to determine the radiative neutron capture
cross section of the unstable 147 Nd isotope of astrophysicalThis work was supported by the Japan Private School
Promotion Foundation and partly by the JSPS-FNRS bilateralprogram. We are grateful to M. Igashira of the Tokyo Instituteof Technology for making the 143,145,146 Nd samples available
to the present experiment. We thank Florin Rotaru of the
National Institute for Physics and Nuclear Engineering Horia
Hulubei for initiating us into GEANT4 coding and for fruitful
discussions. We acknowledge PRACE for awarding us accessto the resource CURIE based in France at TGCC-CEA. D. M.
Filipescu, O. Tesileanu and I. Gheorghe acknowledge financial
support from the Extreme Light Infrastructure Nuclear Physics(ELI-NP) Phase I, a project co-financed by the Romanian
Government and the European Union through the European
Regional Development Fund (425/12.12.2012, POS CCE, ID
1334 SMIS-CSNR 40741). H.-T. Nyhus and T. Renstrøm
acknowledge financial support from the Norwegian ResearchCouncil (NFR), Project No. 210007. S. Goriely acknowledges
financial support from the F.N.R.S.

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PHOTONEUTRON CROSS SECTIONS FOR NEODYMIUM . . .

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015808-7

PHYSICAL REVIEW C 92, 064323 (2015)

Photodisintegration of 9 Be through the 1/2+ state and cluster dipole resonance
H. Utsunomiya,1,2 S. Katayama,1 I. Gheorghe,3,4 S. Imai,1 H. Yamaguchi,2 D. Kahl,2 Y. Sakaguchi,2T. Shima,5 K. Takahisa,5 and S. Miyamoto6
1

Department of Physics, Konan University, Okamoto 8-9-1, Higashinada, Kobe 658-8501, Japan
Center for Nuclear Study, University of Tokyo, Hirosawa 2-1, Wako, Saitama 351-0198, Japan
3
ELI-NP, “Horia Hulubei” National Institute for Physics and Nuclear Engineering (IFIN-HH), 30 Reactorului,077125 Bucharest-Magurele, Romania
4
Faculty of Physics, University of Bucharest, RO-077125 Bucharest, Romania
5
Research Center for Nuclear Physics, Osaka University, Suita, Osaka 567-0047, Japan
6
Laboratory of Advanced Science and Technology for Industry, University of Hyogo, 3-1-2 Kouto, Kamigori, Ako-gun, Hyogo 678-1205, Japan(Received 5 November 2015; published 29 December 2015)2

Photodisintegration of 9 Be through the 1/2+ state near neutron threshold and cluster dipole resonance below
giant dipole resonance was measured with quasi-monochromatic γ -ray beams produced in the inverse Compton
scattering of laser photons. The cross section for the 1/2+ state is revisited, being consistent with the 2001 data.
The cross section for the cluster dipole resonance is consistent with the cluster dipole sum-rule which howeverdegenerates for the two-body (n- 8 Be) and three-body(n-α-α) configurations.
DOI: 10.1103/PhysRevC.92.064323

PACS number(s): 25.20.Lj, 24.30.Gd, 27.20.+n

I. INTRODUCTION
9Photodisintegration of Be has drawn a renewed attention
from the viewpoints of explosive nucleosynthesis of 9 Be
and nuclear structure of the Borromean system. The nucleosynthesis of 9 Be may proceed through α + α  8 Be and8Be(n, γ ) 9 Be reaction [1] in astrophysical sites like Type-II
supernovae [2] or neutron star mergers [3]. The explosivesynthesis of 9 Be followed by 9 Be(α,n) 12 C may dominate
over the triple α reaction to bridge the mass gaps at A = 5
and A = 8 [4]. Obviously, the 8 Be(n,γ ) 9 Be reaction cannot
be investigated in the experimental laboratory because 8 Be is
unstable. In contrast, the inverse photodisintegration of 9 Be
is experimentally feasible and straightforward. Previously two
experiments were performed to measure the photodisintegration cross section using quasi-monochromatic γ -ray beams
produced in the inverse Compton scattering of laser photons
with relativistic electrons [5,6]. The discrepancy between thetwo measurements is significant for the 1/2+ state near then- 8 Be threshold.
The big-bang nucleosynthesis of 9 Be may be catalyzed bya hypothetical long-lived negatively charged massive (100
GeV) leptonic particle, X− , through the two-step resonant
reaction (8 BeX− )atom + n → (9 Be 1 + X− )atom → 9 Be 3 − + X−
22[7]. A candidate for X− is the supersymmetric (SUSY)
counterpart of the tau lepton (τ ), i.e., the stau (τ̃ ) [8]. The
observational upper limit in old stars, 9 Be /H  2.1 × 10−13 ,may impose a strong constraint on the lifetime of X− . It
is however pointed out [9] that accurate information of theexcitation energy of 9 Be+1 as well as the charge radius of 8 Be
2
is required to calculate the reaction rate that is strongly affectedby the resonance position of (9 Be 1 + X− )atom with respect to the2(8 BeX− )atom + n threshold.
Besides its astrophysical significance, the 1/2+ state has
raised an important question about the nuclear structure of
9
Be in terms of resonant state [10–12] or virtual [13–15] state.
The threshold behavior of the 1/2+ state cross section may be
0556-2813/2015/92(6)/064323(8)attributed to a virtual state that is defined as a pole of the n- 8 Be
scattering matrix at the complex wave number k = −iκ (κ >0) as well as a resonant state at k = k1 − ik2 (k1 > k2 > 0).
An enhancement in photoneutron emission was reported
for 9 Be in the energy region of 5–17 MeV immediately below
the giant-dipole resonance (GDR) in the experiment withbremsstrahlung [16]. We hereby refer to the enhanced crosssection as cluster dipole resonance (CDR) as we discuss interms of the cluster dipole sum rule in Sec. IV. An experimental
confirmation of the cross section is desirable to investigate thenuclear structure of CDR in the Borromean nucleus with aweakly bound neutron.
In this paper, we present experimental data for photodisintegration of 9 Be through the 1/2+ state and CDR.
II. EXPERIMENTAL PROCEDURE

We investigated photodisintegration of 9 Be through the
1/2+ state and CDR at the NewSUBARU synchrotron radiation facility. Quasi-monochromatic γ -ray beams were produced by the Compton backscattering between laser photons
with 100% linear polarization and relativistic electrons in ahead-on collision geometry [17]. The laser Compton scattering(LCS) γ -ray beam produced in the head-on collision is alsolinearly polarized nearly 100%. We present here details of theexperiment with emphasis on the characteristics of the LCS
γ -ray beam and the neutron detection.
A. Gamma beam production and energy profile

The γ -ray production beam line BL01 is shown in Fig. 1.
Low- and high-energy γ -ray beams were produced using a
grating-fixed CW CO2 laser (λ = 10.5915 μm ± 3 Å anda Q-switch Nd:YVO4 INAZUMA laser (λ = 1064 nm),respectively. The nominal value of the electron beam energy
was changed from 974 to 954 MeV in the decelerate mode of
the storage ring and from 974 to 1121 MeV in the acceleration
mode for low-energy γ production, while it was changed from

064323-1©2015 American Physical Society

H. UTSUNOMIYA et al.

PHYSICAL REVIEW C 92, 064323 (2015)

FIG. 1. (Color online) The γ -ray production beam line at the NewSUBARU synchrotron radiation facility.

974 to 962 MeV for the high-energy γ production. The beamline has two collision points, P1 for the Nd:YVO4 laser andP2 for the CO2 laser, located at 18.5 m and 8.9 m from acollimator C2 mounted in the Hutch 1. We used a 1 mmdiameter C2 collimator to produce low-energy γ -ray beams
and a 2 mm-diameter C2 collimator to produce high-energy
beams. In addition to the C2 collimator, a 3 mm-diameterC1 collimator was mounted in the storage-ring vault. All
collimators are made of 10 cm-thick Pb.
Low-energy LCS γ -ray beams were measured with a highpurity Ge detector to determine the energy profile of the γ -raybeam, while high-energy γ -ray beams with a 3.5 in. × 4.0 in.
LaBr3 (Ce) detector. The Ge crystal of 64.3 mm diameter and60.1 mm length was irradiated 15 mm off the center to avoid
the central hole for the inner electrode and cooling rod.
Figure 2 shows an example of response function of the Ge
detector to a low-energy LCS γ -ray beam. The Ge detector
was calibrated with the standard γ -ray sources ( 133 Ba, 137 Cs,
and 60 Co including the sum peak). The full-energy peak ischaracterized by a high-energy edge and a low-energy tail.
The edge slightly slopes, reflecting the energy resolutionsof the electron beam (∼4 × 10−4 ) and the Ge detector. Theenergy spread of the tail reflects the kinematics of the Compton

backscattering between laser photons and relativistic electrons
into an aperture of the collimator. Monte Carlo simulations
with the GEANT4 code [18] were carried out to reproduce theresponse function. The electron beam emittance, the double
collimators, and the off-center irradiation of the Ge crystal
were incorporated into the simulation. The response function(solid line) was well reproduced by the simulation (dottedline). By turning off the interaction of γ rays with the detectormaterial (Ge) in the simulation code, we obtained an energy
spectrum of the LCS γ -ray beam produced. The spectrum isshown by the grey line in Fig. 2. The energy spread of thelow-energy γ -ray beams used for the study of the 1/2+ state
was 1.8–3.5% in full width at half-maximum (FWHM).
Figure 3 shows an example of response function of the
LaBr3 (Ce) detector to a high-energy LCS γ -ray beam. Theenergy calibration of the high-energy LCS γ -ray beams reliedon the absolute calibration of the electron beam energies withthe accuracy on the order of 10−5 [19]. The full-energy peakis visible for the 5.5 MeV γ -ray beam. Again the response
function was well reproduced by the simulation. The energy
spread of the high-energy γ -ray beams used for the study of
the CDR was 1.4–2.2% in FWHM.
3000

7000

Ee=962 MeV

6000

E =31 keV
(1.8% FWHM)CountsCounts

5000
4000

2500

E =562 MeV

2000

E =1.4% (FWHM)

e

1500
1000

3000
2000

500

1000

0
0

0
0

500

1000

1500

2000

1

2

3

4

5

6

7

E [MeV]E [keV]
FIG. 2. (Color online) An experimental response function (solidline) of the Ge detector to a low-energy LCS γ -ray beam producedwith the CO2 laser along with the simulated response function (dottedline) and energy distribution of the LCS γ -ray beam (grey line).

FIG. 3. (Color online) An experimental response function (solidline) of the LaBr3 (Ce) detector to a high-energy LCS γ -ray beam
produced with the Nd:YVO4 laser along with the simulated response
function (dotted line) and energy distribution of the LCS γ -ray beam
(grey line).

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PHYSICAL REVIEW C 92, 064323 (2015)

The intensity distribution of the LCS γ -ray beam at thetarget position was simulated with the GEANT4 code. With the
2 mm C2 collimator, the beam size on target was 2.3 mm indiameter in FWHM of the intensity distribution.

6

10

5

10

Counts/Channel

4B. Target
9

A 99% Be rod of 25 mm diameter and 40 mm length
was used as a target. A natural carbon rod of the same
dimension was also used to investigate the scattering effectof the LCS γ -ray beam [6]. No scattering effects were foundcompared with blank target runs. Heavy water (99.9%) in
an aluminum container with entrance and exit windows of
25.4 μm-thick Kapton foil was used as a D2 O target of 14 mm
diameter and 100 mm length. Photodisintegration of deuterium
was measured at the electron beam energy 1460 MeV for acrosscheck of the present absolute cross section measurement.
An empty target run confirmed a negligible effect of the Kapton
foils on photoneutron emission.

10

3

10
10

2

10
1.0

0

500

1000

1500

2000

ChannelFIG. 4. (Color online) Multiphoton and single-photon spectra of
the LCS γ -ray beam measured with the NaI(Tl) detector.

C. γ -ray flux

D. Neutron detection

A 8 in. × 12 in. NaI(Tl) detector with 100% detection
efficiency was used as a γ -ray flux monitor. The flux determination is straightforward for LCS γ -ray beams producedwith the CW CO2 laser. The γ rays were detected with the
NaI(Tl) detector at the count rate of 15–41 kcps. Energy spectra
were recorded with a multichannel analyzer with a conversion
time of ∼2.6 μs. The flux was determined by subtracting
background γ rays and correcting for a small amount of double
photon events.
The flux determination for pulsed LCS γ -ray beams
produced with the Q-switch Nd:YVO4 laser followed the
Poisson-fitting method [20,21]. The laser was operated at
20 kHz. Laser photons with a pulse width 60 ns collidewith relativistic electrons in the NewSUBARU storage ringat 500 MHz with a 20 ps pulse width. Although the numberof pairs of laser photons and electrons involved in thecollision during the 60 ns laser pulse (N) is large, thecollision probability per photon-electron pair (p) is small. As
a result, the number of collisions (n) is small with the average
number m = pN . Under this condition, the distribution of
the number of collision, Pm (n),n can be expressed by the
Poisson distribution, Pm (n) = mn e−m . Multiphoton spectra
generated by pulsed γ -ray beams measured with a NaI(Tl)were investigated at different γ -ray beam intensities andindeed characterized by the Poisson distribution [22]. Figure 4
shows a typical single- and multiphoton spectra. The numberof γ rays (Nγ ) is determined by Nγ = mNp with the average
number of γ rays per γ pulse and the number of γ pulses,
Np . The Np is equal to the number of total events of themultiphoton spectrum which is often referred to as pile-up
spectrum. Empirically, the average number of γ rays per pulse
m is given by the ratio of the average channel number ofthe multiphoton spectrum [CH ]av
p to that of the single-photon

Photoneutrons were detected with a 4π neutron detector
composed of 20 3 He proportional counters embedded in apolyethylene moderator in a triple-ring configuration. The
concentric Ring-1 (R1), Ring-2 (R2), and Ring-3 (R3) offour, eight, and eight 3 He counters are placed at the distancesof 38, 70, and 100 mm from the beam axis, respectively.
This detector is designed with the MCNP code [23] for ahighest total efficiency being more than 60% for neutrons
below 1 MeV. Figure 5 shows detection efficiencies of Ring1, Ring-2, and Ring-3 as well as the sum efficiency for
isotropically emitted neutrons. The efficiencies were calibrated
with a 252 Cf source at the National Metrology Institute ofJapan (NMIJ). The detector has long been used for (γ , n)cross section measurements for heavy nuclei (see [24,25][CH ]av
p[CH ]avs[22]. The uncertainty of the flux
spectrum [CH ]avs ,m =
determination comes from the energy linearity in the responseof the flux monitor detector to multiphotons. The uncertainty
was estimated to be ∼3% [22].

80
70
Total

Efficiency [%]

60
50
40

R1

30

R2

20
10
0.0
0.0

R3
1.0

2.0

3.0

4.0

5.0

En [MeV]
FIG. 5. (Color online) The detection efficiencies of the Ring-1,
Ring-2, and Ring-3 and the total efficiency for s-wave (solid line)
and p-wave (dotted lines) neutrons obtain by the GEANT4 simulation.
The efficiencies measured with a calibrated 252 Cf source are shownby the solid triangles and those simulated with the MCNP Monte Carlocode are shown by the open circles.

064323-3

H. UTSUNOMIYA et al.

PHYSICAL REVIEW C 92, 064323 (2015)

where Sn is the neutron threshold energy, Emax is the maximum
energy of the LCS γ -ray beam, nγ (Eγ ) gives the energy
distribution of the γ -ray beam normalized to unity and σ (Eγ ) is
the photoneutron cross section to be determined. Furthermore,
Nn represents the number of neutrons detected, Nt gives thenumber of target nuclei per unit area, Nγ is the number ofγ rays incident on target, n represents the neutron detection
efficiency, and finally ξ = (1 − eμt )/(μt) gives a correction
factor for a thick target measurement. The factor g represents
a fraction of the γ flux above Sn .
The monochromatic cross section results when the n(Eγ )in Eq. (1) is replaced by a δ function, δ(Eγ − E0 ):Ring Ratio

10

R2/R3
R1/R3
1.0
R1/R2
0.0

1.0

2.0

σ mon (E0 ) =3.0

En [MeV]
FIG. 6. The ring ratios of the present 4π neutron detector with
Ring-1, Ring-2, and Ring-3 of four, eight, and eight 3 He countersembedded in a polyethylene moderator.

for the latest measurements and references therein). The
detection efficiencies were recalibrated in advance to thepresent experiment using a 252 Cf source at a neutron emission
rate 2.27 × 104 s−1 with 2.2% uncertainty at the NMIJ. The
experimental calibration points were excellently reproduced.
There are two dominating modes of s-wave and p-wave
photoneutron emissions. Besides the isotropic emission of swave neutrons, the detection efficiencies were also simulated
for p-wave neutrons with the angular distribution Wpol (θ,φ) =3[sin2 θ (1 + cos 2φ)], where θ stands for the polar angle for
8π
photoneutron emission with respect to the beam direction (zaxis), while φ for the azimuthal angle with respect to the linear
polarization (x axis) of the γ -ray beam defined by a directionof the electric field. The results are shown in Fig. 5. One can seethat Ring-1, Ring-2, and Ring-3 summed over four, eight, andeight 3 He counters, respectively, have the same efficiencies as
for s- and p-wave neutrons. The angular distribution of p-wave
neutrons is largely smeared out in the polyethylene moderator.
Figure 6 shows ratios of the detection efficiencies of Ring-1,
Ring-2, and Ring-3 as a function of the neutron energy.
The ring-ratio technique [26] which takes advantage of theseunique energy dependences was used to determine the meanenergy of neutrons emitted in each γ -ray beam irradiation;
the neutron energies determined with the three ring ratios
were weight-averaged. The weighted average was in turn used
to determine the total detection efficiency of the 4π neutron
detector. The mean neutron energy changed from 16 keV to
200 keV in the photodisintegration of 9 Be through the 1/2+
state, while it changed from 1.15 MeV to 1.99 MeV in thephotodisintegration through CDR.

Nn.
Nt Nγ ξ n g

There are two methods for deconvoluting the integral of
Eq. (1) to obtain σ (Eγ ), the Taylor expansion method [24]and the least-squares method [27]. We summarize the Taylor
expansion method which has long been used in (γ , n) crosssection measurements for heavy nuclei (see [24] and references
therein).
A deconvolution can be done by expanding σ (Eγ ) in the
Taylor series at the average energy Eav :∞σ (Eγ ) =1  (n)σ (Eav )(Eγ − Eav )n .
n! n=0σ (Eav ) = σ mon (Eav ) − s2 (Eav ) − s3 (Eav ) − · · · ,
where
sn (Eav ) =
and
σ

(n)


d n σ (E) (Eav ) =.
dE n E=Eav

A. Crosscheck with the D(γ ,n) p cross section

Sn

(1)

(6)

Note that s1 is zero by the definition of Eav .
Since σ (i) (Eav ) cannot be calculated until σ (Eγ ) is determined, an iteration procedure must be employed. The iteration
begins with a best fit to the monochromatic cross section with
an appropriate function and ends with a reasonable conversion.
In the present data reduction, we used the Breit-Wigner
formula for the 1/2+ data and a Lorentzian function for a
specific fit to the CDR data. We approximate the best-fit
function with the third-order polynomial in small energy bins
to terminate the Taylor expansion at s3 in Eq. (4).
The systematic uncertainty is estimated to be 4.4% which
is a quadratic sum of 3% for the number of incident photons
and 3.2% for the neutron detection efficiency.

The experimental formula of photoneutron cross section is
given byNn,
Nt Nγ ξ n g(4)

 Emax1 (n)σ (Eav )nγ (Eγ )(Eγ − Eav )n dEγ (5)n!
Sn

IV. RESULTS AND DISCUSSIONSnγ (Eγ )σ (Eγ )dEγ =(3)

Putting Eq. (3) into Eq. (1), one obtains

III. DATA REDUCTION Emax(2)

The result of the present measurement of the D(γ ,n)preaction cross section is shown in Fig. 7. The present result
is in good agreement with the existing data [28–32] and the
JENDL evaluation [33].

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PHOTODISINTEGRATION OF 9 Be THROUGH THE 1/2 . . .

PHYSICAL REVIEW C 92, 064323 (2015)
0.50

5.0

D( ,n)p
3.0

0.40

n

E [MeV][mb]

JENDL/PD-2004

1.0
0.80
Birenbaum (1985)
Hara (2003)
Moreh (1989)
Bernabei (1988)
Ahrens ((1974)
Present

0.60
0.40

0.30
0.20
0.10
0.0
1.6

1.7

1.8

1.9

2.0

2.1

2.2

E [MeV]

0.20
0

5

10

15

20

FIG. 9. The mean neutron kinetic energies determined by the ringratio technique [26]. The two-body kinematics is shown by the solid
line.

Energy [MeV]
FIG. 7. The D(γ ,n) cross section. The present datum is shown by
the solid square.

The same LCS γ -ray beam was also used to measure thephotodisintegration cross section for 9 Be. The result is shownby the thick open cross in Fig. 8 in comparison with the 2001
data (filled circles) [5] and 2012 data (open circles) [6]. The
bremsstrahlung data (crosses) [16] are also shown in the figure.
The 2012 data are the monochromatic cross sections retrieved
from the EXFOR database [34]. We remark that the 2001 data
were published in such a way that cross sections are plotted at
the peak energies of the γ -ray beams with the horizontal error
bars representing energy spreads of the beams in FWHM.
B. 1/2+ state

The mean neutron energy, Enav , determined with the ringratio technique is shown in Fig. 9 as a function of theγ -ray energy. The mean neutron energies near the n- 8 Be
threshold are consistent with the kinematics of two-bodybreakup 9 Be → n + 8 Be, En = 89 (Eγ − Sn ). However, theEnav deviates from the two-body kinematics at the threeenergies above 1.8 MeV. The deviation indicates the onsetof three-body breakup, 9 Be → n + α + α, in this energy
region.
Figure 10 shows the present cross section for the 1/2+
state by the solid squares. The data were corrected for energy
spreads of the LCS γ -ray beam with the Taylor expansion
method. The monochromatic cross section is also shown by theopen circles in the figure. The present measurement between
the n- 8 Be threshold at 1.665 MeV and the n-α-α threshold at
1.573 MeV provided a vanishing cross section (9.3 × 10−5 ±0.016 mb) at 1.63 MeV.
The data measured from the n- 8 Be threshold to 1.78 MeV
were fitted with the Breit-Wigner (B-W) function with a focus
on the low-energy behavior of the cross section:
 2
γ n
c
σ (Eγ ) = π.
(7)Eγ (Eγ − ER )2 + (/2)2
1.6

2.5

Arnold (2012)

[mb]

9

1.2

1/2+

Be( ,n)1.0

Be( ,n)

[mb]

9

2.0

1.4

1.5

0.8
0.6

Utsunomiya (2001)

0.4

1.0

0.2
0.5
0.0
2.5

0.0
1.6

1.7

1.8

1.9

2.0

2.1

2.2

E [MeV]
3

3.5

4

4.5

5

E [MeV]
FIG. 8. The 9 Be(γ ,n) cross section. The present datum is shownby the thick open cross.

FIG. 10. The present 9 Be(γ ,n) cross section corrected for theenergy spread of the LCS γ -ray beam is shown by the solid squares
and the monochromatic cross section is shown by the open circles.
The solid line represents the Breit-Wigner fit to the cross section.

064323-5

H. UTSUNOMIYA et al.

PHYSICAL REVIEW C 92, 064323 (2015)of Ref. [6]) is shown in the figure. Note that the 2012 data
give a peak cross section (∼1.7 mb) that is much higher
than that (1.35 mb) of the present data. The data of theradioactive isotope measurements are rather consistent withthe present data, while the bremsstrahlung data exhibit a very
different threshold behavior. Averaged photoneutron crosssections extracted from the (e, e ) data [38,43] are also shownin the figure.
We remark that the B-W fit may not serve as evidence
that the 1/2+ state is a resonant state though the energy andwidth parameters resulting from the R-matrix analysis are also
consistent with the resonance nature of the 1/2+ state [12]. A
similar threshold behavior of the cross section may arise from avirtual state in the potential model of n- 8 Be scattering [13] andthe complex scaling method of describing the n-α-α system[15]. The authors were informed in private communication thatthe present cross section is reproduced by the complex scaling
method [44].

2.5
9

+

2.0

[mb]

Gibbons (1959)
John (1967)
Fujishiro (1982)
Goryachev (1992)
Burda (2010)
Arnold (2012)
Present

Be( ,n)
1/2

1.5

1.0

0.5

0.0
1.6

1.7

1.8

1.9

2.0

2.1

2.2

E [MeV]
FIG. 11. (Color online) The present 9 Be(γ ,n) cross section incomparison with the existing data (filled circles: Ref. [6], filled
diamonds: Ref. [42], inverted filled triangles: Ref. [40], open
triangles: Ref. [41], crosses: Ref. [16], open diamonds: Ref. [38]).

The γ width γ is related to the reduced transition probability
B(E1) ↓ [35] by
γ =

16π
α(c)−2 Eγ3 B(E1)↓.
9(8)The neutron width n for s-wave neutrons from the 1/2+ state
was taken [36] asn = 2 R (Eγ − Sn ).
(9)
The threshold cross section is well fitted with the B-Wfunction as shown by the solid line. The B-W fit, however, underestimates the experimental data measured above 1.8 MeV.
This underestimate may be associated with the onset of thethree-body breakup in this energy region as indicated by themean neutron energies.
The best-fit resonance parameters are listed in Table I, in
comparison with those of Refs. [5,6]. The present result is
consistent with the 2001 data [5]. It is to be noted that thedisagreement in B(E1) between the (γ , n) [5,37] and (e, e )[38,39] data was recently analyzed and resolved as a way ofintegration of the resonance [12].
The threshold behavior of the present cross section is shownin Fig. 11 in comparison with the existing data including thosetaken with radioactive isotopes [40–42] and bremsstrahlung[16]. The deconvoluted cross section of the 2012 data (Fig. 7

C. Cluster dipole resonanceA significant resonance was confirmed in the present
measurement in the energy region immediately below GDR as
shown in Fig. 12. The present data (filled squares) show evenmore enhanced cross sections than the bremsstrahlung data(crosses) at energies higher than 8 MeV. The cluster dipole
resonance has a significant strength compared to the observed
GDR. In the figure, the GDR data (open circles) are a sum of(γ , n), (γ , n + p), (γ , 2n), and (γ , 2n + p) cross sections ofRef. [45]. The 2001 data [5] (filled circles) are shown for the
5/2+ state. For the 1/2+ state, the present data as well as thedeconvoluted cross section of Ref. [6] (filled diamonds) andthe bremsstrahlung data of Ref. [16] (crosses) are shown.
The CDR strength was deduced by a global fit to thedata of GDR [45], CDR, and the 5/2+ state [5] with theleast-squares method. The Lorentzian and B-W functions
were used for the GDR and the 5/2+ state, respectively,
while the Gaussian function was used for CDR assumingthat its strength is localized in the low-energy tail of the
GDR. The best-fit function is shown by the dot-dashed line
in Fig. 12 along with its breakdown to the GDR, CDR, and5/2+ state by the dashed, solid, dotted lines, respectively. Theenergy-integrated strength of the CDR is 11.3 mb MeV.
We remark that the resonance strength depends on the
shape of the low-energy tail of the GDR which is estimatedby the Lorentzian function. The value (11.3 mb MeV) may
represent a lower limit because it is known that the Lorentzian
type of the γ -ray strength function (photoabsorption crosssection) significantly overestimates (n, γ ) cross sections for

TABLE I. Resonance parameters obtained in the Breit-Wiger fit to the (γ , n) cross section data for the 1/2+ state.
ER
(MeV)

n
(keV)

γ
(eV)

B(E1) ↓
(e2 fm2 )Ref.

1.748 ± 0.01
1.735 ± 0.003
1.731 ± 0.002
1.728 ± 0.001

283 ± 42225 ± 12213 ± 6214 ± 70.598 ± 0.004
0.568 ± 0.001
0.738 ± 0.002
0.595 ± 0.002

0.107 ± 0.007
0.104 ± 0.002
0.136 ± 0.002
0.111 ± 0.004

Utsunomiya et al. [5]Sumiyoshi et al. [37]Arnold et al. [6]Present

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PHOTODISINTEGRATION OF 9 Be THROUGH THE 1/2 . . .

PHYSICAL REVIEW C 92, 064323 (2015)

5
GDR

9

Be( ,n)4

Present[mb]

Kneissl (1975)
Goryachev (1992)
Utsunomiya (2001)
Arnold (2012)

3

CDR

2 1/2+
5/2+

1
0
2

4

6

8 10

30

E [MeV]
FIG. 12. (Color online) The 9 Be(γ ,n) cross section in the energy region from the n + 8 Be threshold to GDR (see text for details).

heavy nuclei [46–49]. The strength integrated over 4–16 MeV
without a contribution from the low-energy tail of the GDR is
14.2 mb MeV. Thus, the resonance strength is 11.3–14.2 mb
MeV.
Let us compare the resonance strength with the cluster
dipole sum rule [50–52] for the two-body (n- 8 Be) and threebody (n-α-α) systems:
σE1 (E)dE = 60

N Z  Ni Zi
−
.
A
Ai
i

(10)

The first term of Eq. (10) is the Thomas-Reiche-Kuhn (TRK)sum rule representing the E1 response of a nucleus in theabsence of exchange forces. After subtracting the intrinsic
contributions from the constituent clusters from the entire
response, the sum rule represents the E1 response arising from
relative motions between the constituents. The cluster dipole
sum rule gives 10% (13.3 mb MeV) of the TRK sum rule(133 mb MeV), irrespective of the two-body (n- 8 Be) or
three-body (n-α-α) systems. The present strength is consistent
with the cluster dipole sum rule, which however does notdistinguish whether a neutron oscillates in the n- 8 Be or n-α-αconfiguration. It is desirable to investigate the nature of thecluster dipole resonance both experimentally and theoretically.
The investigation requires a new experiment of n-α-α coincidences to measure correlations of a neutron against two α
particles. The authors are informed in private communicationthat a theoretical investigation is in progress based on theantisymmetrized molecular dynamics calculation [53].

V. CONCLUSIONSThe photodisintegration of 9 Be through the 1/2+ state andcluster dipole resonance was measured. The cross sectionof the 1/2+ state is consistent with the 2001 data and thedata of the radioactive isotope measurements. The observed
resonance strength is consistent with the cluster dipole sum
rule. However, the sum rule degenerates in the two-body(n- 8 Be) and three-body (n-α-α) systems. Consequently, thepresent result does not distinguish whether a neutron oscillates
in the two-body or three-body configuration. A new n-α-αcoincidence experiment is needed to investigate the configuration. A theoretical study is encouraged to investigate the natureof the 1/2+ state and the nuclear structure of the cluster dipole
resonance in 9 Be.
ACKNOWLEDGMENTS

We are indebted to Masayasu Kamimura of RIKEN
for drawing our attention to the stau-catalyzed big-bang
nucleosynthesis and Kiyoshi Kato of Hokkaido University
for discussions on resonant and virtual states. We thankAkinori Takemoto and Masashi Yamaguchi for their assistancein tuning the CO2 laser and the double collimators for
producing low-energy LCS γ -ray beams. This work was
supported by the Japan Private School Promotion Foundation.
I.G. acknowledges financial support from the Extreme Light
Infrastructure Nuclear Physics (ELI-NP) Phase I, a project
cofinanced by the Romanian Government and the European
Union through the European Regional Development Fund(425/12.12.2012, POS CCE, ID 1334 SMIS-CSNR 40741).

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