Two-dimensional scission-branch conjecture for the liquid-drop model

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Let χ\chi be the fissility parameter and let χ3≈0.428\chi_3\approx0.428 be the two-dimensional analogue of the Businaro–Gallone point. A scission point is a transition state on the separate branch described in the paper; for χ>χ3\chi>\chi_3 it resembles a lemniscate. Scission-branch conjecture. Each scission point is a transition state for χ>χ3\chi>\chi_3. For χ<χ3\chi<\chi_3, the scission point becomes unstable against mass-asymmetric perturbations, but the branch continues to arbitrarily small χ\chi, and the scission point on this branch converges to two touching disks as χ→0\chi\to0. This is a numerical conjecture about the two-dimensional asymptotic branch; the supplied text gives no proof or resolution.

References

Primary source

Zirui Xu and Qiang Du, “Bifurcation and fission in the liquid drop model: a phase-field approach”, arXiv:2302.14449 (2023).

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