Effects of nuclear deformation on the form factor for direct dark matter detection

TL;DR

This paper investigates how nuclear deformation from spherical to elliptical shapes affects the form factor in direct dark matter detection, concluding that small deformations have negligible impact due to random nuclear orientations.

Contribution

It introduces an analysis of nuclear deformation effects on the form factor, extending previous models that assumed spherical nuclei.

Findings

Small ellipticity does not significantly alter the form factor.

Random nuclear orientations at room temperature negate deformation effects.

Deformation effects can be neglected for practical dark matter detection analyses.

Abstract

For direct dark matter detections, to extract useful information about the fundamental interaction from data, it is crucial to properly determine the nuclear form factor. The form factor for spin-independent cross section of collisions between dark matter particle and nucleus is thoroughly studied by many authors. When the analysis was carried out, the nuclei are always supposed to be spherically symmetric. In this work, we investigate the effects of deformation of nuclei from a spherical shape to an elliptical shape on the form factor. Our results indicate that as long as the ellipticity is not too large, such effects cannot cause any substantial effects, especially as the nuclei are randomly orientated in a room temperature circumstance one can completely neglect them.