Investigations of Few-Nucleon System Dynamics in Medium Energy Domain

Precise and large set of cross sections, vector Ax , Ay and tensor Axx , Axy, Ayy analyzing powers for the 1 H(d, pp)n breakup reactions were measured at 100 and 130 MeV deuteron beam energies with the use of the SALAD and BINA detectors at KVI and Germanium Wall setup at FZ-Jülich. Results are compared with various theoretical approaches which model the three-nucleon (3N) system dynamics. The calculations are based on different two-nucleon (2N) potentials which can be combined with models of the three-nucleon force (3NF) and other pieces of the dynamics can also be included like the Coulomb interaction and relativistic effects. The cross sections data reveal seizable 3NF and Coulomb force influence. In case of analyzing powers very low sensitivity to the effects was found and the data are well describe by 2N models only. At 130 MeV for Axy serious disagreements appear when 3NF models are included into calculations. This work was partially supplemented by the Polish 2008–2010 science founds as a research Project No. N N202 174635, by the Polish 2009–2011 science founds as a research Project No. N N202 034836 and by funding from Jagiellonian University within SET project. The project is co-financed by the European Union. I. Ciepał (B) · A. Biegun · K. Bodek · J. Golak · G. Khatri · St. Kistryn · A. Magiera · W. Parol · R. Skibiński · R. Sworst · H. Witała · A. Wrońska · J. Zejma Institute of Physics, Jagiellonian University, Kraków 30059, Poland E-mail: izabela.ciepal@uj.edu.pl Tel.: +123-45-678910 Fax: +123-45-678910 B. Kłos · E. Stephan University of Silesia, Katowice 40007, Poland St. Kliczewski · A. Kozela · R. Siudak Institute of Nuclear Physics, Kraków 31342, Poland M. Eslami-Kalantari · A. Ramazani-Moghaddam-Arani · N. Kalantar-Nayestanaki · J. Messchendorp Kernfysisch Versneller Instituut, Groningen, 9747 AA, The Netherlands M. Eslami-Kalantari Faculty of Physics, Yazd University, Yazd, Iran A. Ramazani-Moghaddam-Arani Faculty of Physics, University of Kashan, Kashan, Iran Da. Kirillov · H. Machner · A. Nogga Forschungszentrum Jülich, Institut für Kernphysik, Jülich 52425, Germany 1302 I. Ciepał et al.


Introduction
One of the key issues of modern nuclear physics is investigation of forces acting between nucleons. Properties of 3N systems at medium energies are determined by pairwise nucleon-nucleon (NN) interaction, which is a dominant component. The interaction models are created based on the meson exchange theory or phenomenology. These so-called realistic NN potentials, like CD Bonn, Nijmegen or Argonne AV18 are able to predict observables for 2N systems with very high precision. To test thoroughly these models, environement with more than just two nucleons is needed. The simplest and nontrivial one is the 3N system, which can be studied in details with the use of the deuteron breakup reaction. The reaction with its 3N final state offers very simple and unique laboratory in which even very subtle dynamical effects like the 3NF, Coulomb force or relativistic component can be studied.
The theoretical predictions of observables are obtained by means of rigorous solution of Faddeev equations. Other than realistic NN potentials and supplementing them with 3NF models (TM99 3NF or Urbana IX 3NF), the 3N system dynamics can be described within the coupled-channels (CC) approach [1]. This method is based on explicit treatment of a single -isobar degrees of freedom, which generates also certain 3NF effects. Another alternative way comes from chiral perturbation theory (ChPT). Here, the nuclear potential is obtained in a way of a systematic expansion in terms of momentum variable, and the many-body interactions appear naturally at growing orders. The non-vanishing 3NF appars at the next-to-next-to-leading (NNLO) order [2,3], which is numerically fully developed. Within the CC formalism the Coulomb interaction was implemented into calculations for the first time [4]. Recently, a consistent theoretical treatment of phenomenological 3NF and Coulomb force has been achieved also for the AV18+UIX potential [5] that allows to investigate the role of both effects on the high level of accuracy. Moreover, the relativistic treatment of the breakup reaction in 3N system was developed for calculations using the NN potential [6] and this approach has been also extended for calculations includnig the 3NF [7].
To verify the model predictions the deuteron breakup reaction can be used as a valuable experimental tool. The final state of the reaction is complex enough to test different ingredients of few-nucleon system dynamics, appearing with varying strength in certain phase space regions.

Experimental Setup
The 1 H (d, pp)n breakup reactions were studied in different phase space regions with the use of three detection systems: the SALAD and BINA at KVI [8][9][10][11] and the Germanium Wall (GeWall) at FZ-Jülich [12]. Results of the analyzing powers were obtained with the use of the BINA and SALAD apparatuses at polarized deuteron beam energies of 100 and 130 MeV, respectively. The cross sections were measured using the SALAD and GeWall detectors at deuteron beam energy of 130 MeV. The BINA detector offered access to the almost full phase space, whereas the SALAD and GeWall setups covered only forward polar angles.
The SALAD detector consisted of a three-plane multi-wire proportional chamber (MWPC) and two layers of a segmented scintillator hodoscope: horizontal E and vertical stopping E detectors. The acceptance of the setup covered the region of the polar angles from 12 0 to 40 0 and the full range of the azimuthal angles. The liquid hydrogen target was placed inside the scattering chamber. BINA apparatus was constructed as an upgraded version of SALAD and possesed two main parts called Wall and Ball. Wall inherited most parts and features from SALAD, covering the same angular range and built of the same MWPC and modified E and E hodoscopes. The backward part is ball-shaped and consists of 149 phoswich detectors which cover polar angles between 40 0 and 160 0 . The Ball plays two roles: of particle detector and scattering chamber. In the measurements liquid targets L H 2 was used.
The GeWall setup at the Research Center in Jülich (FZJ) consisted of three high-purity semiconductor position sensitive germanium detectors. Two different types of the detectors were used: a thin transmission detector "Quirl" with an excellent spatial resolution used to determine the position and energy loss ( E detector) of the passing charged particles, and two thick energy detectors E1 and E2 with excellent energy resolutions. The angular acceptance of the apparatus was 5 0 − 14 0 for the polar and 2π for the azimuthal angles.

Results and Conclusions
New generation measurements of the 1 H (d, pp)n breakup reactions in a wide phase space region provided a very rich set of differential cross sections, vector A x , A y and tensor A x x , A xy , A yy analyzing powers.
The cross sections were obtained for about 80 [9] kinematical configurations, defined by the polar angles of the two outgoing protons, θ 1 , θ 2 , and their relative azimuthal angle ϕ 12 , for the energy of 65 MeV/nucleon with the use of the SALAD apparatus. Moreover, additional set of the cross sections for the same beam energy were obtained for 145 geometries with the GeWall detector [12]. The elastic scattering process was measured simultaneously in each experiment and the data were used for the breakup cross sections normalization. The obtained results allowed to trace different aspects of the system dynamics: 3NF effects and influence of the Coulomb force.
The data measured at KVI [13] reveal quite seizable 3NF effects and confirmed its importance for understanging of the three nucleon system dynamics. Inclusion of this additional force in the calculations leads generally to a better description of the cross sections.
In the kinematical region of small polar angles significant discrepancies between the measured and predicted cross sections were found [8]. The inconsistency was accounted for the Coulomb interaction. Recently, the Coulomb force was succesfully implemented into calculations within CC framework [4]. Adding the electromagnetic component into the models does not essentially change the quality of the data description at large relative energies, however at the small values the observed discrepancies are almost totaly removed [14]. The Coulomb force were studied in more details in dedicated experiment at FZJ [12], focused on a very narrow part of the phase space. Dependencies of χ 2 per degree of freedom (d.o.f.) as a function of the relative energy E rel and pair of the polar angles θ 1 , θ 2 of the two protons were studied, see Fig. 1. In the case of very small E rel (see Fig. 1, left panel) the Coulomb effects are extremaly high and only the predictions containing the Coulomb component are able to reproduce the data in a correct way. The obtained dependency of χ 2 on different combinations of θ 1 , θ 2 (see Fig. 1, right panel) shows that with increasing θ =| θ 1 − θ 2 | value the Coulomb effects play less important part in reproducing the experimental data. For high θ the Coulomb force influence is negligible.
The obtained results of the vector analyzing powers of the breakup reaction at 65 and 50 MeV/nucleon [11] are well reproduced by 2N calculations in the whole studied phase space. In case of the tensor analyzing powers certain discrepancies are observed. The theory predicts quite large effects of TM99 3NF, however there are configurations in which inclusion of the TM99 3NF lead to a worse agreement with the experimental data. Such discrepancies were found especially for A xy tensor analyzing power. This suggests an existence of some

Summary and Outlook
Precise and systematic studies of the breakup reaction in a large part of the phase space are very important for understanding of the interaction between nucleons in few-nucleon systems. Currently available theoretical approaches which try to model the interaction need very precise and large experimental database to be verified and further developed. Within these predictions different pieces of the dynamics can be studied separately and also their mutual interplay can be investigated. The obtained data in general confirmed the modern calculations, however there are still some problems with our understanding of the current models of the 3NF. Moreover, there is still strong need to have possibly complete theoretical treatments including all ingredients of the 3N system dynamics (3NF, Coulomb interaction, relativistic effects).
The future studies of the 3N system dynamics in the deuteron breakup reaction with the use of the WASA detector at FZJ are focused on investigation of the relativistic effects and the role of the 3NF at higher energies. Moreover, new scientific program concentrated on investigation of the few-nucleon systems dynamics at not too high energies was proposed to be carried out with the use of the BINA detector at the Cyclotron Center Bronowice in Cracow.
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