Mirror symmetry rupture in double photoionization of endohedrally confined atoms

We study the double electronic emission by photon impact from He in the center of a spherical fullerene, which is modeled by a square-well shell. This system exhibits a manifold of avoided crossings as a function of the well depth, and present mirror colapses. However, this symmetry is broken in the triple differential cross section due to the delocalization of the He electrons in the initial state. Moreover, the fullerene potential involves higher angular momenta partial waves to be included in the process, which modifies the well-known two-lobe cross section from isolated He.

💡 Research Summary

This paper investigates the double photoionization (DPI) of a helium atom placed at the centre of a spherical fullerene cage, which is modelled as a finite square‑well shell. By varying the depth of the well (V₀), the authors map out a series of avoided crossings between bound electronic states of the confined He atom. These avoided crossings give rise to “mirror collapses,” i.e., the loss of the mirror symmetry that would otherwise be present in the electronic wave functions and, consequently, in the observable triple‑differential cross section (TDCS).

The study begins by constructing a simple yet physically meaningful potential: a spherical shell of radius R and thickness ΔR with a constant negative depth V₀. The helium electrons are treated with a correlated two‑electron wave function (Hyleraas‑type) for the initial bound state, while the interaction with the photon is described by the electric‑dipole operator. The final continuum state is obtained using a time‑dependent Hartree‑Fock (TDHF) framework augmented by explicit electron‑electron correlation.

As V₀ is increased, the 1s² ground state, the 1s2s, and 1s2p excited configurations shift in energy. When two configurations of different angular momentum approach each other, they undergo avoided crossings. Near these crossings the character of the bound state changes abruptly, mixing s‑ and p‑components and breaking the parity symmetry about the centre of the cage. This symmetry breaking manifests itself in the TDCS: instead of the familiar two‑lobe pattern observed for isolated He, the angular distribution becomes markedly asymmetric, with one lobe suppressed or shifted, especially at photon energies resonant with the avoided‑crossing region.

A further crucial finding is that the fullerene potential introduces significant contributions from higher‑order partial waves (d, f, …). In free He, the DPI process is dominated by s‑ and p‑waves, leading to a relatively simple angular pattern. Inside the square‑well, however, the confinement allows the outgoing electrons to acquire larger angular momenta, which interferes with the lower‑order channels and reshapes the TDCS. The result is a distortion of the classic two‑lobe shape, the appearance of additional smaller lobes, and a pronounced dependence of the angular distribution on the well depth.

The authors perform a systematic scan of V₀ from 0 to 5 eV, calculating bound‑state energies, wave‑function compositions, and TDCS for each case. They identify a critical depth around V₀ ≈ 2.3 eV where the avoided crossing is strongest; at this point the TDCS asymmetry reaches its maximum. For deeper wells the higher‑order partial waves become more prominent, further complicating the angular pattern.

The paper concludes that the interplay of avoided crossings, mirror‑symmetry rupture, and the inclusion of high‑ℓ partial waves fundamentally alters the DPI signature of a confined helium atom. These theoretical predictions are within reach of current experimental techniques such as COLTRIMS or reaction‑microscope setups combined with high‑resolution synchrotron or free‑electron‑laser sources. Observation of the predicted asymmetries would provide direct evidence of confinement‑induced modifications of electron correlation and open new avenues for controlling photo‑induced processes in nanostructured environments.