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Super-shell structure in harmonically trapped fermionic gases and its semi-classical interpretation

M. Ogren·Y. Yu·S. Aberg·S. M. Reimann·M. Brack
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Abstract

It was recently shown in self-consistent Hartree-Fock calculations that a harmonically trapped dilute gas of fermionic atoms with a repulsive two-body interaction exhibits a pronounced {\it super-shell} structure: the shell fillings due to the spherical harmonic trapping potential are modulated by a beat mode. This changes the ``magic numbers'' occurring between the beat nodes by half a period. The length and amplitude of the beating mode depends on the strength of the interaction. We give a qualitative interpretation of the beat structure in terms of a semiclassical trace formula that uniformly describes the symmetry breaking U(3) $\to$ SO(3) in a 3D harmonic oscillator potential perturbed by an anharmonic term $\propto r^4$ with arbitrary strength. We show that at low Fermi energies (or particle numbers), the beating gross-shell structure of this system is dominated solely by the two-fold degenerate circular and (diametrically) pendulating orbits.

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M. Ogren, Y. Yu, S. Aberg, S. M. Reimann, M. Brack. 2006-12-28. Super-shell structure in harmonically trapped fermionic gases and its semi-classical interpretation. https://doi.org/10.1088/0031-8949%2F2006%2Ft125%2F008

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