Role of the Total Isospin 3/2 Component in Three-Nucleon Reactions

Few-Body Systems, Oct 2016

We discuss the role of the three-nucleon isospin \(T=3/2\) amplitude in elastic neutron–deuteron scattering and in the deuteron breakup reaction. The contribution of this amplitude originates from charge-independence breaking of the nucleon–nucleon potential and is driven by the difference between neutron–neutron (proton–proton) and neutron–proton forces. We study the magnitude of that contribution to the elastic scattering and breakup observables, taking the locally regularized chiral N\(^4\)LO nucleon–nucleon potential supplemented by the chiral N\(^2\)LO three-nucleon force. For comparison we employ also the Av18 nucleon–nucleon potential combined with the Urbana IX three-nucleon force. We find that the isospin \(T=3/2\) component is important for the breakup reaction and the proper treatment of charge-independence breaking in this case requires the inclusion of the \(^1S_0\) state with isospin \(T=3/2\). For neutron–deuteron elastic scattering the \(T=3/2\) contributions are insignificant and charge-independence breaking can be accounted for by using the effective t-matrix generated with the so-called \(``2/3-1/3"\) rule.

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Role of the Total Isospin 3/2 Component in Three-Nucleon Reactions

Few-Body Syst Role of the Total Isospin 3/2 Component in Three-Nucleon Reactions H. Wita?a 0 1 2 3 4 J. Golak 0 1 2 3 4 R. Skibin? ski 0 1 2 3 4 K. Topolnicki 0 1 2 3 4 E. Epelbaum 0 1 2 3 4 K. Hebeler 0 1 2 3 4 H. Kamada 0 1 2 3 4 H. Krebs 0 1 2 3 4 U.-G. Mei?ner 0 1 2 3 4 A. Nogga 0 1 2 3 4 0 U.-G. Mei?ner Helmholtz-Institut fu?r Strahlenund Kernphysik and Bethe Center for Theoretical Physics, Universita?t Bonn , 53115 Bonn , Germany 1 H. Kamada Department of Physics, Faculty of Engineering, Kyushu Institute of Technology , Kitakyushu 804-8550 , Japan 2 A. Nogga Institut fu?r Kernphysik, Institute for Advanced Simulation and Ju?lich Center for Hadron Physics, Forschungszentrum Ju?lich , 52425 Ju?lich , Germany 3 U.-G. Mei?ner Institute for Advanced Simulation, Institut fu?r Kernphysik, Ju?lich Center for Hadron Physics, and JARA - High Performance Computing, Forschungszentrum Ju?lich , 52425 Ju?lich , Germany 4 K. Hebeler Institut fu?r Kernphysik, Technische Universita?t Darmstadt , 64289 Darmstadt , Germany We discuss the role of the three-nucleon isospin T = 3/2 amplitude in elastic neutron-deuteron scattering and in the deuteron breakup reaction. The contribution of this amplitude originates from chargeindependence breaking of the nucleon-nucleon potential and is driven by the difference between neutronneutron (proton-proton) and neutron-proton forces. We study the magnitude of that contribution to the elastic scattering and breakup observables, taking the locally regularized chiral N4LO nucleon-nucleon potential supplemented by the chiral N2LO three-nucleon force. For comparison we employ also the Av18 nucleonnucleon potential combined with the Urbana IX three-nucleon force. We find that the isospin T = 3/2 component is important for the breakup reaction and the proper treatment of charge-independence breaking in this case requires the inclusion of the 1 S0 state with isospin T = 3/2. For neutron-deuteron elastic scattering the T = 3/2 contributions are insignificant and charge-independence breaking can be accounted for by using the effective t-matrix generated with the so-called ?2/3 ? 1/3" rule. K. Hebeler Extreme Matter Institute EMMI, GSI Helmholtzzentrum f?r Schwerionenforschung GmbH, 64291 Darmstadt, Germany H. Kamada Department of Physics, Faculty of Engineering, Kyushu Institute of Technology, Kitakyushu 804-8550, Japan U.-G. Mei?ner Charge-independence breaking (CIB) is well established in the two-nucleon (2N) system in the 1 S0 state as evidenced by the values of the scattering lengths ?23.75 ? 0.01, ?17.3 ? 0.8, and ?18.5 ? 0.3 fm [ 1,2 ] for the neutron?proton (np), proton?proton (pp) (with the Coulomb force subtracted), and neutron?neutron (nn) systems, respectively. That knowledge of CIB is incorporated into modern, high precision NN potentials, as exemplified by the standard semi-phenomenological models: Av18 [3], CD Bonn [ 4 ], or NijmI and NijmII [ 5 ], as well as by the chiral NN forces [ 6?8 ]. Treating neutrons and protons as identical particles requires that nuclear systems are described not only in terms of the momentum and spin but also isospin states. The general classification of the isospin dependence of the NN force is given in [ 9 ]. The isospin violating 2N forces induce an admixture of the total isospin T = 3/2 state to the dominant T = 1/2 state in the three-nucleon (3N) system. The CIB of the NN interaction thus affects 3N observables. The detailed treatment of the 3N system with CIB NN forces in the case of distinguishable or identical particles was formulated and described in [ 10 ]. We extend the investigation done in [ 10 ] by including a three-nucleon force (3NF). In the calculations performed with the standard semi-phenomenological potentials we use the UrbanaIX (UIX) [ 11 ] 3NF, while the chiral N2LO 3N force [ 12 ] is used in addition to the recent and most accurate chiral NN interactions [ 13,14 ]. In this paper, based on such dynamics, we discuss the role of the amplitude with the total three-nucleon (3N) isospin T = 3/2 in elastic neutron?deuteron (nd) scattering and in the corresponding breakup reaction. In Sect. 2 we briefly describe the formalism of 3N continuum Faddeev calculations and the inclusion of CIB. The results are presented in Sect. 3. In Sect. 3.1 we discuss our results for elastic nd scattering and in Sect. 3.2 describe our findings for selected breakup configurations. We summarize and conclude in Sect. 4. 2 3N Scattering and Charge Independence Breaking Neutron?deuteron scattering with nucleons interacting through a NN interaction vN N and a 3NF V123, is described in terms of a breakup operator T satisfying the Faddeev-type integral equation [ 15?17 ] T |? = t P|? + (1 + t G0)V (1)(1 + P)|? + t P G0T |? + (1 + t G0)V (1)(1 + P)G0T |? . The two-nucleon t -matrix t is the solution of the Lippmann?Schwinger equation with the interaction vN N . V (1) is the part of a 3NF which is symmetric under the interchange o (...truncated)


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H. Witała, J. Golak, R. Skibiński, K. Topolnicki, E. Epelbaum, K. Hebeler, H. Kamada, H. Krebs, U.-G. Meißner, A. Nogga. Role of the Total Isospin 3/2 Component in Three-Nucleon Reactions, Few-Body Systems, 2016, pp. 1213-1225, Volume 57, Issue 12, DOI: 10.1007/s00601-016-1156-3