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 N4LO nucleon-nucleon potential supplemented by the chiral N2LO 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 1S0 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.
Highlights
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, proton–proton, and neutron–neutron systems, respectively
We investigated the importance of the scattering amplitude components with the total 3N isospin T = 3/2 in two 3N reactions
The inclusion of these components is required to account for CIB effects of the NN interaction
Summary
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. Th√eir magnitude is driven by the strength of the CIB as given by the difference of the corresponding t-matrices In such a case, the magnitude of CIB decides about the importance of the pqβ|T |φ contributions, and the isospin T = 3/2 3NF matrix elements, which participate in generating the pqβ|T |φ amplitudes. The magnitude of CIB decides about the importance of the pqβ|T |φ contributions, and the isospin T = 3/2 3NF matrix elements, which participate in generating the pqβ|T |φ amplitudes It is the set of equations Eq (7) which we solve when we differentiate between nn and np interactions and include both T = 1/2 and T = 3/2 3NF matrix elements.
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