The Garvey-Kelson relations (GKRs) are algebraic expressions originally developed to predict nuclear masses. In this paper we show that the GKRs provide a fruitful framework for the prediction of other physical observables that also display a slowly varying dynamics. Based on this concept, we extend the GKRs to the study of nuclear charge radii. The GKRs are tested on 455 out of the approximately 800 nuclei whose charge radius is experimentally known. We find a rms deviation of 0.01fm between the GK predictions and the experimental values. Predictions are provided for 116 nuclei whose charge radius is presently unknown.

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Garvey-Kelson Relations for Nuclear Charge Radii

Several methods have been developed to calculate and predict nuclear masses over the last 70 years. The accuracy of the present state‐of‐the‐art nuclear mass models is impressive, because these quantities can be calculated with an average 0.05 % precision. However this precision level is still insufficient to deal with nuclear reactions of astrophysical interest, especially r‐process ones. Different approaches exist to calculate nuclear masses, ranging from the simple Bethe‐Weizsacker Liquid Drop Formula (LDM) to the sophisticated Finite Range Droplet Model calculations or the microscopic Hartree‐Fock‐Bogoliuvob techniques from first principles, using Skyrme or Gogny parametrizations of the nucleon‐nucleon interaction. Here we suggest a new method to calculate this fundamental property of the atomic nucleus, using a completely phenomenological point of view. Our method is based in the analysis of the differences between measured masses and LDM predictions, which contains information related to those ingredients not taken into account in the LDM formula, such as shell closures, nuclear deformations and residual nuclear interactions. The differences are arranged in a two dimensional plot which can be viewed as an incomplete image of the full chart of nuclides, equivalent to a product of the full image and a binary mask. In order to remove the distortions produced by this mask we employ an algorithm, well known in astronomy, used to remove artificial effects present in the astrophysical images collected through telescopes. This algorithm is called the CLEAN method. It is one of a number of methods which exists to deconvolve undesirable effects in images and to extrapolate or reconstruct missing parts in them. By using the CLEAN method we can fit measured masses with an r.m.s error of less than 100 keV. We have performed several checks and concluded that its utilization must be carried out carefully in order to obtain reliable results in the zone of unknown masses between the driplines. We also outline potential applications of the present approach.

J. C. López

Papers

Calculation of nuclear masses using image reconstruction techniques