Abstract
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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Schori, O., Gabioud, B., Joseph, C., Perroud, J.P., Rüegger, D., Tran, M.T., Truöl, P., Winkelmann, E., Dahme, W.: Measurement of the neutron–neutron scattering length \(a_{nn}\) with the reaction \(\pi d \rightarrow nn\gamma \) in complete kinematics. Phys. Rev. C 35, 2252–2257 (1987)
de Téramond, G.F., Gabioud, B.: Charge asymmetry of the nuclear interaction and neutron–neutron scattering parameters. Phys. Rev. C 36, 691–701 (1987)
Wiringa, R.B., Stoks, V.G.J., Schiavilla, R.: Accurate nucleon–nucleon potential with charge-independence breaking. Phys. Rev. C 51, 38–51 (1995)
Machleidt, R., Sammarruca, F., Song, Y.: Nonlocal nature of the nuclear force and its impact on nuclear structure. Phys. Rev. C 53, R1483–1487 (1996)
Stoks, V.G.J., Klomp, R.A.M., Terheggen, C.P.F., de Swart, J.J.: Construction of high-quality NN potential models. Phys. Rev. C 49, 2950–2963 (1994)
Epelbaum, E.: Few nucleon forces and systems in chiral effective field theory. Prog. Part. Nuclear Phys. 57, 654–741 (2006)
Epelbaum, E., Hammer, H.W., Meißner, U.-G.: Modern theory of nuclear forces. Rev. Mod. Phys. 81, 1773–1825 (2009)
Machleidt, R., Entem, D.R.: Chiral effective field theory and nuclear forces. Phys. Rep. 503, 1–75 (2011)
Henley, E.M., Miller, G.A.: in Mesons and Nuclei, Rho M. and Brown G. E., eds. (North-Holland, Amsterdam 1979). Vol. I p. 405
Witała, H., Glöckle, W., Kamada, H.: Charge-independence breaking in the three-nucleon system. Phys. Rev. C 43, 1619–1629 (1991)
Pudliner, B.S., Pandharipande, V.R., Carlson, J.: Pieper, Steven C., Wiringa, R.B.: Quantum Monte Carlo calculations of nuclei with \(A < 7\). Phys. Rev. C 56, 1720–1750 (1997)
Epelbaum, E., Nogga, A., Glöckle, W., Kamada, H., Meißner, Ulf-G, Witała, H.: Three-nucleon forces from chiral effective field theory. Phys. Rev. C 66, 064001–064017 (2002)
Epelbaum, E., Krebs, H., Meißner, U.-G.: Improved chiral nucleon–nucleon potential up to next-to-next-to-next-to-leading order. Eur. Phys. J. A 51, 53–81 (2015)
Epelbaum, E., Krebs, H., Meißner, U.-G.: Precision nucleon–nucleon potential at fifth order in the chiral expansion. Phys. Rev. Lett. 115, 122301-1-5 (2015)
Witała, H., Cornelius, T., Glöckle, W.: Elastic scattering and break-up processes in the n–d system. Few Body Syst. 3, 123–134 (1988)
Glöckle, W., Witała, H., Hüber, D., Kamada, H., Golak, J.: The three-nucleon continuum: achievements, challenges and applications. Phys. Rep. 274, 107–285 (1996)
Hüber, D., Kamada, H., Witała, H., Glöckle, W.: How to include a three-nucleon force into Faddeev equations for the 3N continuum: a new form. Acta Phys. Pol. B 28, 1677–1685 (1997)
Epelbaum, E., Meißner, U.-G., Palomar, J.E.: Isospin dependence of the three-nucleon force. Phys. Rev. C 71, 024001-1-11 (2005)
Binder, S., et al.: Few-nucleon systems with state-of-the-art chiral nucleon–nucleon forces. Phys. Rev. C 93, 044002–044006 (2016)
Hebeler, K., Krebs, H., Epelbaum, E., Golak, J., Skibiński, R.: Efficient calculation of chiral three-nucleon forces up to N\(^3\)LO for ab initio studies. Phys. Rev. C 91, 044001–044009 (2015)
Witała, H., Glöckle, W., Golak, J., Nogga, A., Kamada, H., Skibiński, R., Kuroś-Żołnierczuk, J.: Nd elastic scattering as a tool to probe properties of 3N forces. Phys. Rev. C 63, 024007–024012 (2001)
Maeda, Y., et al.: Differential cross section and analyzing power measurements for \(\overrightarrow{n}d\) elastic scattering at 248 MeV. Phys. Rev. C 76, 014004–13 (2007)
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This article belongs to the special issue “30th anniversary of Few-Body Systems”.
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Witała, H., Golak, J., Skibiński, R. et al. Role of the Total Isospin 3/2 Component in Three-Nucleon Reactions . Few-Body Syst 57, 1213–1225 (2016). https://doi.org/10.1007/s00601-016-1156-3
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DOI: https://doi.org/10.1007/s00601-016-1156-3