RIKEN Accel. Prog. Rep. 50 (2017)

Ⅱ-4. Hadron Physics

Energy calibration using the p(d, 3 He)π 0 reactionin pionic atom spectroscopy at BigRIPS
T. Nishi,∗1 D.S. Ahn,∗1 G.P.A. Berg,∗1,∗2 M. Dozono,∗1 D. Etoh,∗1,∗3 H. Fujioka,∗1,∗4 N. Fukuda,∗1N. Fukunishi,∗1 H. Geissel,∗1,∗5 E. Haettner,∗1,∗5 T. Hashimoto,∗1 R.S. Hayano,∗6 S. Hirenzaki,∗1,∗7H. Horii,∗1,∗6 N. Ikeno,∗8 N. Inabe,∗1 K. Itahashi,∗1 M. Iwasaki,∗1 D. Kameda,∗1 S. Kawase,∗9 K. Kisamori,∗1,∗9Y. Kiyokawa,∗9 T. Kubo,∗1 K. Kusaka,∗1 M. Matsushita,∗9 S. Michimasa,∗9 G. Mishima,∗1,∗6 H. Miya,∗1D. Murai,∗1 H. Nagahiro,∗7 M. Niikura,∗1,∗6 S. Ota,∗9 N. Sakamoto,∗1 K. Sekiguchi,∗1,∗3 H. Suzuki,∗1K. Suzuki,∗1,∗10 M. Takaki,∗9 H. Takeda,∗1 Y.K. Tanaka,∗1,∗5 T. Uesaka,∗1 Y. Wada,∗1,∗3 Y.N. Watanabe,∗1,∗6∗1
∗1
∗1,∗5
∗1,∗4
H.
H.
Y.
and K.
K. Yoshida
Yoshida∗1H.Weick,
Weick,∗1,∗5H.Yamakami,
Yamakami,∗1,∗4Y. Yanagisawa,
Yanagisawa∗1andIn June 2014, we performed a missing-mass spectroscopy experiment on the 122,117 Sn(d,3 He) reaction
to measure the binding energies and widths of deeply
bound pionic states1) . In the experiment, excitation
spectra of 121,116 Sn near the π − emission thresholdwere obtained from the measurement of 3 He momenta,
which were magnetically analyzed using BigRIPS asa spectrometer. The momenta are determined fromtwo types of information: the central momentum andits deviation. The former is calibrated using the twobody reaction p(d, 3 He)π 0 with a polyethylene target.
The latter is determined precisely by position measurements at a dispersive focal plane. In this report, thedetails of the calibration are explained.
To precisely calibrate the central momentum in BigRIPS, we performed Monte-Carlo simulations andcompared them with experimentally obtained 3 He momenta and reaction angles. In the simulation, momenta and angles were obtained using the following
three steps.
(a) Emittance of the primary beam
The position, angle, and momentum spread of the primary deuteron beam were taken into account. The
measured emittance was 0.2 ×2.0π mm·mrad (horizontal/RMS) and 0.03% (RMS)3) . The momentum spreadis one of the main sources for the missing mass resolution.
(b) Two-body reaction at the target
The distribution of reaction angles of 3 He from thed(p, 3 He)π 0 reaction was taken from previous experimental data2) where the energy in the center-of-massframe was the same as in our experiment. The corresponding momenta are obtained from two-body kinematical calculation.

(c) Analysis with a transfer matrix
The momenta and reaction angles produced in steps(a) and (b) were converted to the positions and angles
at the focal plane using an experimentally measured
transfer matrix. In the conversion, the eﬀects of multiple scattering inside the target and in a 50 μm-thickstainless steel window located upstream of the focal
plane were also considered. The obtained positions
and angles are converted to the momenta and reaction
angles using the transfer matrix, as done for the experimental data. The obtained momentum deviations(represented as δ) and reaction angles in the simulation
were compared with those in the experiment. The simulation result reproduces the experimental data well,
as shown in Fig. 1. In the comparison, we calculated χ2
between two 2D histograms and determined the central momentum of BigRIPS by minimizing the χ2 .
As a result, we succeeded in suppressing the contribution from the energy calibration on the missing massprecision within 10 keV, which is negligibly small compared with other contributions such as the ambiguityof the primary beam energy. Thus, we established theenergy calibration method using the d(p, 3 He)π 0 reaction, which will improve the determination accuracy ofthe binding energy of the pionic atoms. The analysis
is ongoing.

∗1RIKEN, Nishina Center
JINA-CEE and Department of Physics, University of NotreDame∗3 Department of Physics, Tohoku University∗4 Department of Physics, Kyoto University∗5 GSI Helmholtzzentrum für Schwerionenforschung GmbH
∗6 Department of Physics, University of Tokyo∗7 Department of Physics, Nara Women’s University∗8 Department of Regional Environment, Tottori University∗9 CNS, University of Tokyo∗10 Stefan Meyer Institute, Austrian Academy of Sciences∗2- 120 -Fig. 1. δ - reaction angle plot from the p(d, 3 He)π 0 reaction.
(Left) Experimental data. (Right) Simulation result.

References
1) K. Itahashi et al., RIBF Proposal 054R1 (2013).
2) M. Betigeri et al., Nucl. Phys. A 690 473 (2001).
3) T. Nishi et al., RIKEN Accel. Prog. Rep. 48, 235 (2015).