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Register a new userAn inversion procedure for coupled-channel scattering: determining the deuteron-nucleus tensor interaction
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We present a practical $S$-matrix to potential inversion procedure for coupled-channel scattering. The inversion technique developed is applied to non-diagonal $S^J_{ll}$ for spin one projectiles, yielding a tensor interaction $T_{rm R}$, and is also applicable to spin-1/2 plus spin-1/2 scattering. The method is a generalization of the iterative-perturbative, IP, method. It is tested and evaluated and we investigate the degree of uniqueness of the potential, particularly for cases where there is insufficient information to define the potential uniquely. We examine the potentials which result when the $S$-matrix is generated from a $T_{rm P}$ interaction. We also develop the generalisation, using established procedures, of IP $S$-matrix-to-potential inversion to direct observable-to-potential inversion. This `direct inversion procedure is demonstrated to be an efficient method for finding a multi-component potential including a $T_{rm R}$ interaction fitting multi-energy $sigma$, ${rm i}T_{11}$, $T_{20}$, $T_{21}$ and $T_{22}$ data for the scattering of spin-1 nuclei from spin-zero target. It is applicable to other channel spin 1 cases.
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We analyze $^{16}$O-$^{16}$O and $^{12}$C-$^{12}$C scattering with the microscopic coupled-channels method and investigate the coupled-channels and three-nucleon-force (3NF) effects on elastic and inelastic cross sections. In the microscopic coupled-channels calculation, the Melbourne g-matrix interaction modified according to the chiral 3NF effects is used. It is found that the coupled-channels and 3NF effects additively change both the elastic and inelastic cross sections. As a result, the coupled-channels calculation including the 3NF effects significantly improves the agreement between the theoretical results and the experimental data. The incident-energy dependence of the coupled-channels and 3NF effects is also discussed.
The Continuum Discretized Coupled Channels (CDCC) method is a well established theory for direct nuclear reactions which includes breakup to all orders. Alternatively, the 3-body problem can be solved exactly within the Faddeev formalism which explicitly includes breakup and transfer channels to all orders. With the aim to understand how CDCC compares with the exact 3-body Faddeev formulation, we study deuteron induced reactions on: i) $^{10}$Be at $E_{rm d}= 21.4, 40.9 ; {rm and} ; 71$ MeV; ii) $^{12}$C at $E_{rm d} = 12 ; {rm and} ; 56$ MeV; and iii) $^{48}$Ca at $E_{rm d} = 56$ MeV. We calculate elastic, transfer and breakup cross sections. Overall, the discrepancies found for elastic scattering are small with the exception of very backward angles. For transfer cross sections at low energy $sim$10 MeV/u, CDCC is in good agreement with the Faddeev-type results and the discrepancy increases with beam energy. On the contrary, breakup observables obtained with CDCC are in good agreement with Faddeev-type results for all but the lower energies considered here.
We outline a machine learning strategy for determining the effective interaction in the condensed phases of matter using scattering. Via a case study of colloidal suspensions, we showed that the effective potential can be probabilistically inferred from the scattering spectra without any restriction imposed by model assumptions. Comparisons to existing parametric approaches demonstrate the superior performance of this method in accuracy, efficiency, and applicability. This method can effectively enable quantification of interaction in highly correlated systems using scattering and diffraction experiments.
A second-order supersymmetric transformation is presented, for the two-channel Schrodinger equation with equal thresholds. It adds a Breit-Wigner term to the mixing parameter, without modifying the eigenphase shifts, and modifies the potential matrix analytically. The iteration of a few such transformations allows a precise fit of realistic mixing parameters in terms of a Pade expansion of both the scattering matrix and the effective-range function. The method is applied to build an exactly-solvable potential for the neutron-proton $^3S_1$-$^3D_1$ case.
We consider the charged-current quasielastic scattering of muon neutrinos on an Oxygen 16 target, described within a relativistic shell model and, for comparison, the relativistic Fermi gas. Final state interactions are described in the distorted wave impulse approximation, using both a relativistic mean field potential and a relativistic optical potential, with and without imaginary part. We present results for inclusive cross sections at fixed neutrino energies in the range $E_ u =$ 200 MeV - 1 GeV, showing that final state interaction effects can remain sizable even at large energies.
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