# Super-shell structures and pairing in ultracold trapped Fermi gases

## TL;DR

This paper investigates super-shell structures and pairing phenomena in ultracold trapped Fermi gases, combining analytical and numerical methods to understand their energy levels and pairing gaps under various trapping potentials.

## Contribution

It provides an analytical approach to super-shell structures and pairing gaps in ultracold Fermi gases, extending previous Hartree-Fock results with periodic orbit and WKB calculations.

## Key findings

- Super-shell structures are analytically characterized.
- Level densities influence pairing gaps.
- Super-shell effects are predicted for attractive interactions.

## Abstract

We calculate level densities and pairing gaps for an ultracold dilute gas of fermionic atoms in harmonic traps under the influence of mean field and anharmonic quartic trap potentials. Super-shell structures, which were found in Hartree-Fock calculations, are calculated analytically within periodic orbit theory as well as from WKB calculations. For attractive interactions, the underlying level densities are crucial for pairing and super-shell structures in gaps are predicted.