This is the accepted manuscript made available via CHORUS. The article has been
published as:

Spectroscopy of Pionic Atoms in ^{122}Sn(d,^{3}He)
Reaction and Angular Dependence of the Formation Cross
Sections
T. Nishi et al. (piAF Collaboration)
Phys. Rev. Lett. 120, 152505 — Published 13 April 2018
DOI: 10.1103/PhysRevLett.120.152505

Spectroscopy of pionic atoms in 122 Sn(d, 3 He) reaction and angular dependence of theformation cross sections
T. Nishi1,2 , K. Itahashi2 ,∗ G.P.A. Berg3 , H. Fujioka4 , N. Fukuda2 , N. Fukunishi2 , H. Geissel5 , R.S. Hayano1 ,S. Hirenzaki6 , K. Ichikawa1 , N. Ikeno7 , N. Inabe2 , S. Itoh1 , M. Iwasaki2 , D. Kameda2 , S. Kawase8,
T. Kubo2 , K. Kusaka2 , H. Matsubara8 , S. Michimasa8 , K. Miki1 , G. Mishima1 , H. Miya2 , H. Nagahiro6,
M. Nakamura2, S. Noji1 , K. Okochi1 , S. Ota8 , N. Sakamoto2 , K. Suzuki9 , H. Takeda2, Y.K. Tanaka1 ,K. Todoroki1 , K. Tsukada2 , T. Uesaka2 , Y.N. Watanabe1 , H. Weick5 , H. Yamakami4 , and K. Yoshida2
1

Department of Physics, School of Science, The University of Tokyo,
7-3-1 Hongo, Bunkyo-ku, 113-0033 Tokyo, Japan
2
Nishina Center for Accelerator-Based Science, RIKEN, 2-1 Hirosawa, Wako, 351-0198 Saitama, Japan3
Department of Physics and the Joint Institute for Nuclear Astrophysics Center for the Evolution of the Elements,
University of Notre Dame, Notre Dame, Indiana 46556, USA
4
Department of Physics, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-ku, Kyoto, 606-8502 Kyoto, Japan
5
GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstrasse 1, D-64291 Darmstadt, Germany
6
Department of Physics, Nara Women’s University,
Kita-Uoya Nishimachi, Nara, 630-8506 Nara, Japan
7
Department of Life and Environmental Agricultural Sciences, Faculty of Agriculture,
Tottori University, 4-101 Koyamacho-Minami, Tottori, 680-8551 Tottori, Japan
8
Center for Nuclear Study, The University of Tokyo,
2-1 Hirosawa, Wako, 351-0198 Saitama, Japan and9
Stefan Meyer Institute for Subatomic Physics, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria(piAF Collaboration)(Dated: February 28, 2018)
We observed the atomic 1s and 2p states of π − bound to 121 Sn nuclei as distinct peak structuresin the missing mass spectra of the 122 Sn(d, 3 He) nuclear reaction. A very intense deuteron beam anda spectrometer with a large angular acceptance let us achieve potential of discovery, which includes
capability of determining the angle-dependent cross sections with high statistics. The 2p state ina Sn nucleus was observed for the first time. The binding energies and widths of the pionic states
are determined and found to be consistent with previous experimental results of other Sn isotopes.
The spectrum is measured at finite reaction angles for the first time. The formation cross sections
at the reaction angles between 0 and 2◦ are determined. The observed reaction-angle dependence ofeach state is reproduced by theoretical calculations. However, the quantitative comparison with our
high-precision data reveals a significant discrepancy between the measured and calculated formation
cross sections of the pionic 1s state.

The spectroscopy of pionic atoms has contributed to
the fundamental knowledge of the non-trivial structureof the vacuum in terms of chiral symmetry and quantum chromodynamics (QCD) in the low energy region [1].
The spatial overlaps between the pionic orbitals and thecore nuclei peak near the half-density radii of the nuclei.
The pions are excellent probes for the study of medium
effects in the nuclear matter. An order parameter of thechiral symmetry [2–4], a quark condensate expectation
value hq̄qi, was deduced at the nuclear density in investigations on in-medium modification of an isovector
π-nucleon strong interaction through the wave function
renormalization [5–10].
The low energy pion-nucleus interaction is describedby a phenomenological optical potential. Parameter setsof the potential were obtained by fitting many known
pionic-atom and pion-nucleus-scattering data including
isotope shifts of pionic atoms with different neutron numbers [8–12]. Among these parameters is an s-wave isovector parameter b1 , which is closely related to the order parameter of the chiral symmetry breaking in the nuclear

medium hq̄qiρ [5]. Low-lying pionic orbitals are locatedin a close vicinity of the core nuclei for Z & 50 [13]. This
localized distribution is due to integration of the attractive Coulomb potential and the repulsive and absorptive
strong interaction potential. Determining the levels andwidths of the bound states provides quantum-mechanicalinformation that leads to constraints on the strong interaction. Previous experiments discovered methods of directly populating the low-lying orbitals, analyzed them
spectroscopically [14–16], and measured pionic states in
Pb and Sn nuclei. The ratio of hq̄qiρ to the in-vacuum
value hq̄qi0 was evaluated to be hq̄qiρ / hq̄qi0 ∼ 67% [6]based on the in-medium modification of the isovector interaction, which is in good agreement with chiral perturbation theories [17].
Measurements of the pionic atom formation cross sections at finite reaction angles provide unprecedented information. This contributes to a better understandingof the pionic-atom formation mechanisms and leads tohigher accuracy in deduction of the fundamental quantities. Experimental data at larger reaction angles open

2
new prospects for the identifications of the quantum
numbers corresponding to the structures observed in the
spectra. Previously one had merely to rely on the comparison between the measured and theoretical spectral
shapes [16]. Up to the present experiment, the formation
cross sections were measured only in very limited solid
angles around 0◦ . Meanwhile, theories predict reactionangle dependence mainly originating from the different
momentum transfers in the (d, 3 He) reactions [18]. Onlya small angular dependence is expected from the elementary π − production cross sections of the n(d, 3 He)π − reaction [19].
beamtargetBigRIPS

MWDC

dipoleF0
D1

10 m
scintillation
counterquadrupoles
F4

F1
D2

F2

F3

D3

D4 F5 D5

F6
D6

F7

FIG. 1. A schematic view of the experimental facility,
BigRIPS [20], and the detector setup. A deuteron beam impinged on a target located at the nominal target position F0.
The emitted 3 He particles were momentum-analyzed at thedispersive focal plane at F5 and the tracks were measured by
the MWDCs. The scintillation counters at F5 and F7 wereused for particle identification.

We conducted spectroscopic measurements of the missing mass of the 122 Sn(d, 3 He) nuclear reactions at the RI
Beam Factory RIBF, RIKEN [21] in October 2010. The
missing mass of the 122 Sn(d, 3 He) reaction near the pion
emission threshold was measured for the first time. The
experiment demonstrated the excellent performance of
RIBF applied in an experimental program of high precision spectroscopy with the primary beam. We employeda deuteron beam with a typical intensity of 2 × 1011 /s
accelerated by the cyclotron complex of AVF-RRC-SRC
and focused onto the target location of the BigRIPS inflight magnetic separator [20]. The beam was extracted
in micro bunches of frequency of 13.7 MHz and had ahigh duty factor. The beam energy has been determined to be Td = 498.9 ± 0.2 MeV by NMR measurements in BigRIPS. The horizontal beam emittance andintrinsic momentum spread have been estimated to be∼ 0.54×3.0 π mm·mrad (σ) and 0.04+0.01−0.02 %, respectively.
Figure 1 illustrates the schematic layout of the employed detectors and BigRIPS used as a spectrometer.
The acceptance aperture of ∼ 2◦ was utilized to covera reaction-angle range centered near 0◦ . The deuteronbeam impinged on a 1 mm wide strip target of 122 Sn
at F0 which was isotopically enriched to 95.8% and hada thickness of 12.5 ± 0.5 mg/cm2 . The achieved mean
luminosities of about 1031 cm−2 s−1 in the present experiment were much higher than those of previous experiments at GSI [6, 14–16] despite of the thinner target.
We expected direct formation of pionic atoms coupledwith neutron hole states in the nuclear reactions near
the recoil-free kinematical condition. Relevant neutron
hole states (excitation energies En (n′ j ′ l′ )) in the 121 Sn
nucleus are 2d3/2 (0.0 MeV), 3s1/2 (0.06034 MeV), 2d5/2(1.1212 MeV), and 2d5/2 (1.4035 MeV) [22].
The emitted 3 He particles were momentum analyzed
at F5 with a momentum dispersion of 60.64 ± 0.15
mm/%. We installed two sets of multi-wire drift chambers (MWDC) near the momentum dispersive focal planeat F5 and measured the tracks of the charged particles
with a tracking resolution of ∼ 40 µm (σ). The 3 He ionswere identified by the time-of-flight of ∼ 174 ns between
F5 and F7 measured by the scintillation counters. The
counters had a distance of about 23 m. We achieved
almost background-free 3 He spectra (< 0.1 % contamination). A typical trigger rate of the data acquisition
was 200/s due to the relatively narrow coincidence gate
between F5 and F7 detectors. The deadtime of the dataacquisition system has been estimated to achieve an efficiency of ∼ 93%.
The measured 3 He tracks have been used to determine
the 3 He kinetic energies, the positions, and the angles at
the target after detailed analyses and corrections of the
optical transfer coefficients up to the fifth order aberrations [23]. Hereafter measured 3 He emission angles aretreated as the reaction angle θ. The θ resolution has
been estimated to be ∼ 0.3◦ (σ). The mass of the reaction product, the pionic atom, has been determinedby the measured 3 He energy and θ. It has been related
to the excitation energy Eex relative to the ground-state
mass of 121 Sn (M (121 Sn)). The corresponding relation at0◦ is given by the equation Eex = [Mmm −M (121 Sn)]c2 =mπ− c2 − Bnl + En (n′ l′ j ′ ) where Mmm is the mass of thereaction product, Bnl is the binding energy of the pionin a state characterized by the principal (n) and angular(l) quantum numbers. mπ− = 139.571 MeV/c2 is the π −rest mass.
The 3 He kinetic energy has been calibrated by using
the two-body reaction of p(d, 3 He)π 0 . The target consists of a 100 ± 1 µm thick 2 mm wide polyethylene strip.
We performed a calibration measurement every two hours
during the production runs. The calibration spectra have
low-energy tails due to the large reaction angles. Therefore, we have examined the spectral response by Monte
Carlo simulations including effects of matter, spectrometer acceptance and detector performances. A fit has been
conducted to reproduce the entire spectral shape in theplane of the measured positions and angles and related
them to the 3 He energies. The systematic errors of theabsolute Eex values have been estimated to be +0.036−0.033 MeV(σ).
The p(d, 3 He)π 0 reaction has also been used to calibrate the effective beam intensity on the target. The
reaction cross section has been estimated to be 7.6 µb/sr
in the θ range of 0 – 0.5◦ based on an extrapolation of
the data at a slightly higher energy to ours [24]. For this3
we have used the measured beam energy dependence inRef. [25]. After applying an acceptance correction of thespectrometer evaluated by a Monte Carlo simulation, we
have estimated a systematic error for the absolute crosssection scale of 30%.
The experimental resolution has been estimated by
the quadratic sum of contributions from the incident
beam emittance and intrinsic momentum spread,the target thickness, and the optical aberrations of
the spectrometer. We have found a quadratic dependence of the resolution on Eex due to combined
effects of multiple scattering at a vacuum window
at F5 and higher-order optical-aberrations.
This
dependence
has
been
estimated
to
be
R(E
)
=
ex
p
2
+ (0.122 × (Eex − 139.799 MeV))2 (FWHM)
Rminwith the resolution minimum Rmin = 0.42 MeV, which
agrees with the measured spectral responses in thecalibration reaction of p(d, 3 He)π 0 .
40122Sn(d,3He)
0.0-2.0o1sπ2pπd2σ/(dΩ・dE) [μb/(sr・MeV)]

30

20

10
Fit region

0
5
0
15
10

(2d3/2)n-1(3s1/2)n-1505(2d5/2)n-1

0

128 130 132 134 136 138 140 142 144
Excitation Energy [MeV]
FIG. 2. (Top panel) Measured excitation spectrum of the122Sn(d, 3 He) reaction at the angular range of 0 < θ <◦2 . Three distinct peaks are observed in the region Eex =[134,139] MeV. The left and middle peaks are mainly originating from formation of pionic 1s and 2p states, respectively.
The right peak is partly contributed from the other pionicstates (2s, 3p, and 3s). The spectrum is fitted in the region
indicated. The fitting curve and contributions from the 1s
and the 2p states are presented by solid, dashed and dottedlines, respectively. (Bottom panel) Decomposition of the pionic 1s and 2p strengths into contributions from each neutron
hole state of 121 Sn as indicated. Note that fragmentation istaken into consideration for (2d5/2 )−1n .

Figure 2 (top panel) displays the measured excitation spectrum for nearly the full acceptance of the spectrometer. The abscissa is the excitation energy and theordinate is the double differential cross section of the122Sn(d, 3 He) reaction. The π − emission threshold is indicated by the vertical solid line at 139.571 MeV. On theleft side of the spectrum in the range of Eex < 134 MeV,a linear background is observed for nuclear excitation
without pion production. Above the emission thresholda continuum is observed due to quasi-free pion production.
Three prominent peaks are observed below the pion
emission threshold in the region of 134 MeV . Eex .
139 MeV. The leftmost peak is due to the formation of apionic 1s state mainly coupled with a neutron hole stateof (3s1/2 )−1
n . The middle peak contains contributions−1
from the configurations (1s)π (2d5/2 )−1
n , (2p)π (3s1/2 )n−1
and (2p)π (2d3/2 )n . The peak on the right side origi−1
nates mainly from the (2s)π (3s1/2 )−1n and (2p)π (2d5/2 )nconfigurations.
The spectrum has been fitted in an excitation energy region [128.0,138.0] MeV with calculated spectra
based on theoretical pionic atom formation cross sections in Ref. [26] folded by the experimental resolution
expressed by Gaussian functions. Pionic 1s, 2p, 2s, 3p,
and 3s states have been taken into considerations andother higher states as well as the quasi-free contributions
have been neglected. In the fit 8 parameters have been
used: the differential cross sections (dσ/dΩ) of pionic(nl) states I1s , I2p , the binding energies B1s , B2p , the 1s
width Γ1s , and a slope and an offset for the linear background. The 2p width has been fixed to a calculated
value of 0.109 MeV [18, 27] since it is much smaller thanthe experimental resolution. Since contributions fromthe other states 2s, 3p and 3s are small, their binding
energies and widths have been fixed to theoretical values and their relative cross section ratios I2s /I1s , I3s /I1s
and I3p /I2p to theoretical ratios [18, 27]. The resolution
minimum Rmin has also been used as a free parameter.
The fitted curve is presented with contributions fromthe pionic 1s and 2p states. The overall fit has a χ2 /n.d.fof 135.8/92. Figure 2 (bottom panel) shows the decomposition of the 1s and 2p formation cross sections into
different neutron hole states of 121 Sn as indicated. The
peak on the left is coupled with pionic 1s and the one on
the right with 2p.
We have evaluated the systematic errors attributed tothe deduced binding energies and width resulting fromi) absolute Eex scale error arising from the energy calibration, the uncertainty of the primary beam energy, theuncertainty of the target thickness and the ion-opticalproperties of the spectrometer, ii) the Eex dependenceof the resolution within evaluated errors, iii) the fitting
region and iv) 20% errors in the spectroscopic factorsof relevant neutron holes. The systematic errors of thebinding energies are mainly arising from the energy cali-

4bration and the dispersion of the spectrometer.
The binding energies and width are deduced to be40

B1s = 3.828 ± 0.013(stat.)+0.036−0.033 (syst.) MeV

30

Γ1s = 0.252 ± 0.054(stat.)+0.053−0.070 (syst.) MeV
B2p = 2.238 ± 0.015(stat.)+0.046−0.043 (syst.) MeV.

Sn(d,3He)
1.5-2.0o
1sπ

20
10
40
1.0-1.5o30
d2σ/(dΩ・dE) [μb/(sr・MeV)]

with the statistical and systematic errors. The achieved
resolution minimum of Rmin = 0.394+0.064−0.044 MeV is consistent with the estimation of 0.42 MeV described above.
B1s and B2p of a pionic Sn isotope are determined simultaneously for the first time. The deduced B1s , Γ1s
and B2p fairly well agree with the theoretical values
theo
B1s= 3.787 – 3.850 MeV, Γtheo= 0.306 – 0.324 MeV
1stheo
and B2p= 2.257 – 2.276 MeV [18, 27].
The measured spectrum has been decomposed into different θ ranges expecting the θ dependence of the formation cross sections [18, 26, 28]. Figure 3 shows theexcitation spectra for θ in the ranges of 1.5 – 2.0◦ , 1.0– 1.5◦ , 0.5 – 1.0◦ and 0 – 0.5◦ . The peak structures areclearly observed for each θ range. The peak positions
and widths are nearly constant for the different θ ranges,
which demonstrates the high quality of the measurement.
The decomposed spectra have been fitted to deduce θdependent cross sections for the pionic 1s and 2p states,
I1s (θ) and I2p (θ), with other parameters fixed to thosedetermined in the fitting procedure described above. The
linear background has been scaled by a parameter foreach angular range. The resulting fitting curves areshown together with curves for 1s and 2p contributions.
Figure 4 (top panel) depicts I1s (θ) (black) and I2p (θ)(grey). The abscissa is θ represented by the weighted
averages of the solid angles. The boxes show the statistical errors and the bars the systematic errors in addition. They have been studied in the same way as those
conducted for the binding energies and widths. An overall systematic error of 30% is attributed to the absolute
scale of the cross section. The dashed curves show theoretically calculated cross sections of the pionic 1s and 2p
states using phenomenological neutron wave functions ofKoura-type given in Ref. [29]. The solid curves show thesame but scaled with fitted factors of 0.17 and 0.79 forthe 1s and 2p states, respectively. We observe that thetheoretical θ dependences reproduce well the experimental data, which confirms the assignments of the angularmomenta of the states. In principle, this suggests thatthe theoretical models of finite momentum transfer [18]are valid. However, the absolute value of measured I1s (θ)
is much smaller than the theoretical calculation. Figure 4(bottom panel) shows the ratios of the I2p (θ) and I1s (θ).
The large discrepancies between the experimental data
and the theory suggest missing factors of the formation
cross sections which have to be independently applied tothe pionic states.
In conclusion, we have performed spectroscopy of pionic 121 Sn atoms and observed the 1s and 2p states as

2pπ

122

20
10
40

0.5-1.0o

30
20
10
40
0.0-0.5o30
20
10

Fit region

128 130 132 134 136 138 140 142
Excitation Energy [MeV]
FIG. 3. The measured excitation spectrum in Fig. 2 is decomposed into spectra with different θ ranges as indicated.
The overall fitting curves and the 1s and 2p components areshown by the solid, dashed and dotted lines, respectively.

prominent peak structures. For Sn, the 2p state is observed as a peak structure for the first time. We havedetermined the binding energies of the 1s and 2p states
and the width of the 1s state. The reaction-angle dependences of the pionic atom formation cross sections aremeasured and found to agree with the theoretical dependences, which supports the assignments of the quantumnumbers of the measured peak structures. We also findremarkable agreement with theoretically calculated 2p
formation cross sections over a wide range of reaction

5
Factory operated by RIKEN Nishina Center and CNS,
University of Tokyo. This work is partly supported by
MEXT Grants-in-Aid for Scientific Research on Innovative Areas (Grants No. JP22105517, No. JP24105712
and No. JP15H00844), JSPS Grants-in-Aid for Scientific Research (B) (Grant No. JP16340083), (A) (Grant
No. JP16H02197) and (C) (Grants No. JP20540273 and
No. JP24540274), Grant-in-Aid for JSPS Research Fellow (Grant No. 12J08538), the Bundesministerium für
Bildung und Forschung, and the National Science Foundation through Grant No. Phys-0758100, and the Joint
Institute for Nuclear Astrophysics through Grant No.
Phys-0822648 and PHY-1430152 (JINA Center for the
Evolution of the Elements).

Inl(θ) [μb/sr]

102
1sπ
10
2pπ

I2p(θ)/I1s(θ)

1
10
1

10-1
TheoryTheory (scaled)

10-2
0.0

1.0
θ [degree]

2.0

FIG. 4. (Top panel) Determined pionic-nl-state formation
cross sections Inl (θ) for different θ ranges. Statistical errors are shown by the boxes and systematic errors in addition by the bars. The deduced cross sections are comparedwith the theoretical calculations [18, 27]. (Bottom panel)I2p (θ)/I1s (θ). Systematic errors are canceled by taking theratios.

angles. However, the measured absolute cross sections of
the 1s state are smaller by a factor of ∼ 5. Note that theentire data were accumulated within 15 h, which is showing the potential of the facility RIBF for spectroscopy experiments. Continuous development is in progress aiming
at a better spectral resolution of ≤ 150 keV. The major
accomplishments in the present experiment will be succeeded by experiments with improved resolution, statistics and systematics errors to deduce π-nucleus isovector
scattering length b1 with better accuracy [30]. A newseries of experiments to study pionic atoms over a wide
range of nuclei is in preparation and will lead to a better
understanding of the fundamental structure of the QCD
vacuum based on measurements.
The authors thank Prof. Emeritus Dr. Toshimitsu Yamazaki for fruitful discussions and late Prof. Emeritus
Dr. Paul Kienle for his guidance in this study. The authors are grateful to the staffs of GSI for providing target materials and staffs of RIBF for stable operation of
the facility. This experiment was performed at RI Beam∗
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