Convergence of 2-Body Effective Range Expansions for $nd$ Quartet Scattering - Nuclear TheoryReport as inadecuate




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Abstract: We examine the convergence properties of the 2-nucleon Effective RangeExpansion as used in Effective Theories ET-ERE-s for 3-nucleon calculations.We accomplish this by accounting for the 2-body dynamics with a simple rank-1separable 2-body potential where the finite range effects can be incorporatedsystematically in both the 2- and 3-body problems. We make our initialcomparisons in the simple context of the $^3S 1$ 2-nucleon channel and the$^4S {3-2}$ 3-nucleon channel. We find that convergence problems for some ofthe 3-nucleon scattering amplitudes using the ET-ERE can be traced to its pooraccount of finite range effects that soften the momentum dependence of thedeuteron propagator in the Faddeev kernel. In contrast, our simple separablepotential with dipole form factors works very well in all cases considered.



Author: J.R. Shepard, J.A. McNeil

Source: https://arxiv.org/







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