Abstract
Ab initio calculations in Nuclear physics for atomic nuclei require a specific knowledge of the interactions among their constituents, protons and neutrons. In particular, NN interactions can be constrained down to scale resolutions of ∆r ∼ 0.6fm from the study of phase shifts below the pion production threshold. However, this allows for ambiguities and uncertainties which have an impact on finite nuclei, nuclear- and neutron-matter properties. On the other hand the nuclear many body problem is intrinsically difficult and the computational cost increases with numerical precision and number of nucleons. However, is is unclear what the physical precision should be for these calculations. In this contribution we review much of the work done in Granada to encompass both the uncertainties stemming from the NN scattering database in light nuclei such as triton and alpha particle and the numerical precision required by the solution method.
Highlights
One of the main goals in Theoretical Nuclear Physics for many years has been to achieve a sufficiently accurate ab initio solution of the Nuclear Many Body Problem from a reductionist perspective
To provide some historical perspective, we show in the upper left panel the averaged phase shifts, i.e., the absolute errors for np partial wave phase shifts due to the different potentials fitting scattering data with χ2/dof ∼ 1 [15,16,17,18,19] as a function of the LAB energy, namely (CD Bonn) [78], Nijmegen (Nijm-I and Nijm-II) [15], Argonne AV18 [17], Reid (Reid93) [79], and the covariant spectator model [19]
Power expansions in momentum space of effective interactions were introduced by Moshinsky [134] and Skyrme [135] to provide significant simplifications to the nuclear many body problem in comparison with the ab initio approach, in which it is customary to employ phenomenological interactions fitted to NN scattering data to solve the nuclear many body problem
Summary
One of the main goals in Theoretical Nuclear Physics for many years has been to achieve a sufficiently accurate ab initio solution of the Nuclear Many Body Problem from a reductionist perspective. This applies in particular to the a priori accuracy of the solution of the nuclear many body problem, which may eventually be relaxed as to facilitate calculations not addressed before This may occur at a high price; it is not unthinkable that any realistic attempt to quantify the theoretical uncertainties may end up with a lack of predictive power on the side of the theory. Given the formidable computational effort needed to implement accurately many body calculations—even for light nuclei—an a priori determination of the errors induced from input data would very helpful This would set an useful accuracy goal and a limit beyond which all refinements in the numerics would not improve the theoretical accuracy of the output. This provides a motivation to quantify the accuracy needed to solve the many body problem
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