Nucleon-nucleon potentials from inversion

Abstract

Quantum inversion theory has been applied to theSchrodinger operator and is used to obtain NN potentials to partial wave phase shifts. We solved the Gelfand-Levitan and Marchenko fundamental inversion equations and determined from the output-kernels the energy independent and local r-space potentials. The results are based on phase shift data from experimental and theoretical sources where a point charge Coulomb reference potential was added for pp data. Potentials are given for the single channel ' S o , ' P I , ID,, I F 3 , 'Po, 3P1, 3D,, 'F, and the coupled channel 3SD,, )PF, configuration. For a comparison of inversion and mesonic potentials also the half-off-shell K-matrices and deuteron bound state wave functions were calculated.

Nucleon-nucleon potentials and their test with bremsstrahlung

“…Our potential selection coxnprises inversion potentials based on phase-shift analyses by Amdt-FA91 [23] and Nijmegen-II [6,10] and phase shifts from the Bonn-B potential [4]. The Nijmegen phases have a y2 1, the lowest claimed so far in a phase-shift analysis.…”

“…Discrepancies of these potentials in breakup Faddeev calculations and few-body and nuclear-matter binding energies systematically show that something is missing in these potentials [12 -14]. It is generally agreed upon that local potentials always underbind triton by 800 + 150 keV [10,12] whereas Bonn-B misses the experimental binding energy of 8.45 MeV only by 250 keV [4]. This is a significant result in favor of a significant nonlocality in nucleon-nucleon potentials.…”

Eigenphase preserving two-channel SUSY transformations

“…Here, we omit the second term in (7) since it becomes negligible at large distances with respect to the first term. Thus, solution u(k, r) may be obtained as…”

“…quite difficult to generalize. Using the Marchenko equation, the results of Newton and Fulton were nevertheless reproduced and improved by von Geramb et al [7]. A review of the present state of the art in the inverse scattering methods may be found in [8]- [11].…”

Nucleon-nucleon potentials in comparison: Physics or polemics?

“…However, for reasons of fairness, we like to stress that our sub-selection is essentially accidental, and that there are many other, equally representative examples for each stage of the development of theoretical nuclear potentials. In particular, we mention the potential by Tourreil, Rouben, and Sprung [7], the Argonne V 14 potential [8], and the more recent models developed at Bochum [9], Williamsburg [10], and Hamburg [11].…”