Standardization of charge density distributions and relation to experimental data

Standardization of charge density distributions and relation to experimental data 

A reliable comparison of different charge density distributions, and therefore a careful analysis of differences in various ph3reical effects due to a change in the nuclear charge density, is only possible if two requirements are met. Firstly, the charge density distributions must be standardized in some way, so that they become comparable in a well defined sense. Secondly, a relation to a particular nuclide or to a full sequence of nuclides must be established. 

Both requirements can be fulfilled quite easily in the following way. Different charge density distributions models can be standardized to a particular value of the moment function M p) for some fixed p. We follow the usual choice p = 2, which gives the rms radius, Eq. (44), to standardize our nuclear models. 

In those cases where particular selected nuclides (with their proton numbers Z and neutron numbers N) are to be modelled, their corresponding experimental rms radii a(Z, N) can be imposed on every suitable nuclear charge density distribution model (for experimental values of rms radii see, e.g., [7,35]). If, on the other hand, one is interested in studying trends depending on the nuclear mass number A or on the atomic number Z, an expression for the rms radius a as a function of these numbers is required. 

A simple relation between any length parameter and the nuclear mass number A follows directly from geometrical considerations and the assumption of constant nuclear (mass) density ( liquid drop model or homogeneous model ), e.g. for the rms radius 

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