Analytic parametrization of 4He charge form factor.

Abstract

An N/D method of analytic representation for form factors, recently found successful for the deuteron, is used to analyze all the available data on the $^{4}\mathrm{He}$ charge form factor and obtain useful information. The nearest anomalous cut positions in the t plane relevant for this analysis are calculated using possible exchanges at the photon-helium vertex. In contrast to the deuteron case, all familiar and simple intermediate states yield anomalous cut positions above the three-pion cut. Although including the contributions of the three-pion cut in the D function and the five-pion cut in the N function yields a reasonable fit except around the second maximum, the best fit is obtained using the anomalous cut at ${t}_{a}$=0.247 ${\mathrm{GeV}}^{2}$ instead of the five-pion cut. An exponential weight function, necessary for optimized polynomial expansion in Laguerre polynomials in the N function, seems to be essential in reducing the ${\ensuremath{\chi}}^{2}$ value as in the case of the deuteron. The dip in the form-factor data is parametrized in terms of a zero of the N function and the formula predicts a second zero and a third maximum which can be verified in future experiments. The existing data favor an asymptotic behavior of the type exp[-const(lnt${)}^{2}$](lnt${)}^{4}$/t $^{2}$ and the formula extrapolates smoothly into the timelike region. A plot of charge density against nuclear radius shows a central depression and the root-mean-square and half-density radii of the distribution are computed.