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Register a new userToward a Spin- and Parity-Independent Nucleon-Nucleon Potential
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Authors
J.-M. Sparenberg
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A supersymmetric inversion method is applied to the singlet $^1S_0$ and $^1P_1$ neutron-proton elastic phase shifts. The resulting central potential has a one-pion-exchange (OPE) long-range behavior and a parity-independent short-range part; it fits inverted data well. Adding a regularized OPE tensor term also allows the reproduction of the triplet $^3P_0$, $^3P_1$ and $^3S_1$ phase shifts as well as of the deuteron binding energy. The potential is thus also spin-independent (except for the OPE part) and contains no spin-orbit term. These important simplifications of the neutron-proton interaction are shown to be possible only if the potential possesses Pauli forbidden bound states, as proposed in the Moscow nucleon-nucleon model.
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The discrete energy-eigenvalues of two nucleons interacting with a finite-range nuclear force and confined to a harmonic potential are used to numerically reconstruct the free-space scattering phase shifts. The extracted phase shifts are compared to those obtained from the exact continuum scattering solution and agree within the uncertainties of the calculations. Our results suggest that it might be possible to determine the amplitudes for the scattering of complex systems, such as n-d, n-t or n-alpha, from the energy-eigenvalues confined to finite volumes using ab-initio bound-state techniques.
In the rest frame of a many-body system, used in the calculation of its static and scattering properties, the center of mass of a two-body subsystem is allowed to drift. We show, in a model independent way, that drift corrections to the nucleon-nucleon potential are relatively large and arise from both one- and two-pion exchange processes. As far as chiral symmetry is concerned, corrections to these processes begin respectively at $cO(q^2)$ and $cO(q^4)$. The two-pion exchange interaction also yields a new spin structure, that promotes the presence of $P$ waves in trinuclei and is associated with profile functions which do not coincide with neither central nor spin-orbit ones. In principle, the new spin terms should be smaller than the $cO(q^3)$ spin-orbit components. However, in the isospin even channel, a large contribution reverts this expectation and gives rise to the prediction of important drift effects.
Two-pion exchange parity-violating nucleon-nucleon interactions from recent effective field theories and earlier fully covariant approaches are investigated. The potentials are compared with the idea to obtain better insight on the role of low-energy constants appearing in the effective field theory approach and the convergence of this one in terms of a perturbative series. The results are illustrated by considering the longitudinal asymmetry of polarized protons scattering off protons, $vec{p}+p -> p+p$, and the asymmetry of the photon emission in radiative capture of polarized neutrons by protons, $vec{n}+p -> d+gamma$.
Background: Elastic scattering is probably the main event in the interactions of nucleons with nuclei. Even if this process has been extensively studied in the last years, a consistent description, i.e. starting from microscopic two- and many-body forces connected by the same symmetries and principles, is still under development. Purpose: In this work we study the domain of applicability of microscopic two-body chiral potentials in the construction of an optical potential. Methods: We basically follow the KMT approach to build a microscopic complex optical potential and then we perform some test calculations on 16O at different energies. Results: Our conclusion is that a particular set of potentials with a Lippmann-Schwinger cutoff at relatively high energies (above 500 MeV) has the best performances reproducing the scattering observables. Conclusions: Our work shows that building an optical potential within Chiral Perturbation Theory is a promising approach to the description of elastic proton scattering, in particular, in view of the future inclusion of many-body forces that naturally arise in such framework.
Several experimental investigations have observed parity violation in nuclear systems-a consequence of the weak force between quarks. We apply the $1/N_c$ expansion of QCD to the P-violating T-conserving component of the nucleon-nucleon (NN) potential. We show there are two leading-order operators, both of which affect $vec{p}p$ scattering at order $N_c$. We find an additional four operators at $O(N_c^0 sin^2 theta_W)$ and six at $O(1/N_c)$. Pion exchange in the PV NN force is suppressed by $1/N_c$ and $sin^2 theta_W$, providing a quantitative explanation for its non-observation up to this time. The large-$N_c$ hierarchy of other PV NN force mechanisms is consistent with estimates of the couplings in phenomenological models. The PV observed in $vec{p}p$ scattering data is compatible with natural values for the strong and weak coupling constants: there is no evidence of fine tuning.
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