Three-nucleon system: Irreducible and reducible contributions of the three-nucleon force

Abstract

The three-nucleon bound and scattering equations are solved in momentum space for a coupled-channels Hamiltonian. The Hamiltonian couples the purely nucleonic sector of Hilbert space with a sector in which one nucleon is excited to a isobar. The interaction consists of irreducible two-baryon and irreducible three-baryon potentials. The calculation keeps only the purely nucleonic one among the irreducible three-baryon potentials. The coupled-channels two-baryon potential yields additional reducible contributions to the three-nucleon force. The Coulomb interaction between the two protons is included using the method of screening and renormalization. Three-nucleon force effects on the bound-state energies and on observables of elastic nucleon-deuteron scattering and breakup are studied. PACS number(s): 21.30.−x, 21.45.−v, 24.70.+s, 25.10.+s I. MOTIVATIONThe notion of the three-nucleon (3N) force is not a uniquely defined concept for the theoretical description of nuclear phenomena. The 3N force arises in the hadronic picture of nuclear systems, a model developed by theoreticians for calculational convenience. The 3N force is therefore also model dependent and experimentally not measurable.The microscopic degrees of freedom underlying nuclear phenomena are the quarks and gluons of quantum chromodynamics (QCD). However, a direct description of nuclear phenomena in terms of those microscopic degrees of freedom is not available yet; instead, the effective description in terms of quark-gluon clusters, i.e., in terms of hadrons and their interactions among each other and with electroweak probes is a common conceptual and often quantitatively successful approach to nuclear phenomena at low and moderate energies which we also adopt. At low energies, rigid nucleons appear to make up nuclei in bound and scattering states; after all, nuclear bound states have masses which are almost multiples of the one of a single nucleon. At energies above the pion-(π ) production threshold, the isobar and the π meson become additional active degrees of freedom. The interactions between the hadronic constituents of nuclear systems depend on the chosen degrees of freedom, i.e., on the energy range of applicability; they are mediated by exchanged mesons. The dynamics is usually assumed to be controlled by a field theory for the effective hadronic degrees of freedom, originally by a phenomenological field theory with a zoo of mesons [1]. At present, the favorably employed one is the chiral effective field theory (χ EFT) [2-4], which respects the chiral symmetries of QCD and works with the nucleon and π as degrees of freedom, sometimes extended by the inclusion of the isobar [5,6].However, for practical calculations of nuclear systems, the dynamics is chosen to follow quantum mechanics. The forces between the hadrons, arising from field-theoretic processes, have therefore to be cast into the form of Hermitian potentials. That dynamic simplification is achieved by freezing some of the field-theoretic degrees of freedom. The quantum-mechanical kin...

Influence of target deformation and deuteron breakup in (d,p) transfer reactions

“…In this section we apply the aforementioned formalism to the 10 Be(d, p) 11 Be reaction at various deuteron energies. For our calculations, we follow a prescription as close as possible to that of [12], using CH89 parametrization [15] for the potentials V n 10 Be and V p 10 Be , evaluated at a neutron energy of E d /2 and a proton energy corresponding to the exit energy of the proton.…”

“…This is not possible in the standard formulations of the aforementioned CCBA and ADWA methods, which tend to emphasize one of the two mechanisms. An exception is provided by the Faddeev formalism, which has been recently extended to include collective excitations of the fragments (globally referred to as core excitations) [10,11]. The core excitation effect was found to affect the calculated transfer cross sections beyond the expected scaling of the cross section due to the corresponding spectroscopic factors.…”

“…The core excitation effect was found to affect the calculated transfer cross sections beyond the expected scaling of the cross section due to the corresponding spectroscopic factors. The problem has been further investigated in a recent work [12] for the 10 Be(d,p) 11 Be case, and the effect was found to strongly depend on the deuteron incident energy as well as on the separation energy of the residual nucleus.…”

“…This extended CDCC wave function is used within a CCBA-like framework to calculate the A(d, p)B stripping cross sections. The formalism will be applied to the reaction 10 Be(d,p) 11 Be, at different deuteron energies, and the results compared with those from Ref. [12].…”

“…In Sec. III, the formalism is applied to the reaction 10 Be(d,p) 11 Be, comparing with the same observables studied in Ref. [12] with the Faddeev formalism, and with emphasis on the 11 Be reaction, highlighting the different paths considered in this work.…”