INVESTIGATION OF THREE NUCLEON FORCE EFFECTS IN DEUTERON–PROTON BREAKUP REACTION ∗

Experiments devoted to study subtle ingredients of nuclear dynamics were carried out at KVI in Groningen with the use of the 1 H ( d, pp ) n breakup reaction at the deuteron beam energy of 80 MeV/nucleon. The aim of the work is to determine the breakup cross sections and confront them with the set of modern calculations which model forces acting between nu-cleons. Elastic scattering process was also measured for the purpose of the cross section normalization. This paper presents preliminary results of the data analysis including geometry cross check, energy calibration, particles identiﬁcation and sample distributions of the unnormalized breakup cross sections.


Introduction
Investigation of the three-nucleon system dynamics provides understanding of effective nucleon-nucleon (N N ) potential. Quantitatively, this can be done by comparing observables calculated with the use of the Faddeev equations with results of precise measurements. Modern realistic N N interaction models describe well systems composed of two nucleons, however they fail to reproduce data for three-nucleon (3N ) systems. Only N N calculations combined with additional ingredients of the dynamics like three nucleon force (3N F) [1], Culomb force [2] or relativistic component [3] are able to give proper description of the data. The two-and three-nucleon interactions can be also modeled within the coupled-channel (CC) framework by an explicit treatment of the ∆-isobar excitation. Alternatively, contribution of N N and 3N F to the dynamics may come from the Chiral Perturbation Theory. Here, the many-body interactions appear naturally at growing orders (non-vanishing 3N F at next-to-next-to leading order). Previous experimental data [4][5][6] reveal quite seizable 3N F and Coulomb effects, and confirmed its importance for understanding of the 3N system dynamics.

Experimental set-up
The experiment was performed with the use of the deuteron beam at the energy of 160 MeV provided by AGOR cyclotron at Kernfysisch Versneller Instituut in Groningen, The Netherlands. Charged products of elastic scattering and 1 H(d, pp)n breakup reaction were detected by BINA (Big Instrument for Nuclear Analysis) [5]. The detection system was developed to investigate the few-body system dynamics in almost 4π geometry. The backward part of the system (BALL) is built of 2 × 149 plastic scintillators working in a phosphich mode. This part covers a range of polar angles between 40 • and 165 • and the full range of azimuthal angles. The front part (WALL) consists of the Multi Wire Proportional Chamber (MWPC) and two layers of plastic scintillators which form a ∆E-E system. The scintillator stripes of both layers were mounted orthogonally creating 120 hodoscopes. The WALL part is used for detection of particles with the polar angles from 13 • to 40 • . The MWPC provides resolution of 0.4 • in polar and 0.6 • -2.0 • in azimuthal angles.

Analysis progress
Preliminary presorting was performed on the collected data. Parts of the data characterized with unstable beam current or problems in functioning of any system elements were carefully removed. The reaction channels were identified based on ∆E-E technique and sorted according to the relative azimuthal angle φ 12 = φ 1 −φ 2 of the two coincident particles. This condition allowed for identification of the two reaction channels: elastic scattering (φ 12 ∼ 180 • ) and breakup (particles which do not fulfill the restriction).

Elastic scattering
The elastic scattering is well suited for performing the detector calibration. To select this process, the particle identification was performed by setting gates on each ∆E-E spectrum (see Fig. 1). Then, the proton-deuteron Geant4 code were compared with signals from the detector for the given polar angle and the given hodoscope. Second step was to retrieve the initial kinetic energies of the nucleons, what was done with the use of the simulations as well. The relation between proton energy at the reaction point and the energy in the detector is presented in Fig. 3. The elastic events were also used for the geometry cross check and correction of beam-shift from the target center, allowing better reconstruction of the momenta of detected charged particles.

Breakup channel
The aim of the experiment is to obtain differential cross sections for the breakup reaction for various angular configurations defined by polar angles of the two protons (θ 1 , θ 2 ) and their relative azimuthal angle φ 12 . Kinematical spectra (kinetic energy of the first proton vs. kinetic energy of the coincident one) E 1 vs. E 2 for different breakup geometries were obtained (see Fig. 4). Events were projected onto the theoretical kinematical curve corresponding to the point-like, central geometry and counted for the given S value (arclength along the kinematical curve).
A number of the breakup coincidences was obtained as a function of the S and it corresponds to the unnormalized cross sections. The data needs to be corrected for efficiency of the detection system and normalized to the elastic events to obtain absolute values of the cross sections. This work is still in progress and so far shape of the obtained distributions can be qualitatively compared with the theoretical predictions, see Fig. 5.

Summary and outlook
The obtained precise experimental data in a wide phase space region can serve as a valid tool for verification of rigorous theoretical calculations which have been and are being developed. Collecting of such data will be continue. In the near future, series of experiments using the proton beam of energy in the range from 70 MeV to 230 MeV and BINA detector will be performed in the Cyclotron Center Bronowice in Kraków.
We acknowledge support by the Foundation for Polish Science -MPD program, co-financed by the European Union within the European Regional Development Fund, Małopolskie Centrum Przedsiębiorczości -Project "Doctus -Małopolski fundusz stypendialny dla doktorantów", the Polish 2013-2015 science founds as research Project No. 2012/05/E/ST2/02313 and funding from the Jagiellonian University within SET project -the project is co-financed by the European Union. This work was supported by the European Commission within the Seventh Framework Programme through IA-ENSAR (contract No. RII3-CT-2010-262010).