Abstract
Irrotational flow of a spherical thin liquid layer surrounding a rigid core is described using the defocusing nonlinear Schr\"odinger equation. Accordingly, azimuthal moving nonlinear waves are modeled by periodic dark solitons expressed by elliptic functions. In the quantum regime the algebraic Bethe ansatz is used in order to capture the energy levels of such motions, which we expect to be relevant for the dynamics of the nuclear clusters in deformed heavy nuclei surface modeled by quantum liquid drops. In order to validate the model we match our theoretical energy spectra with experimental results on energy, angular momentum, and parity for $\ensuremath{\alpha}$-particle clustering nuclei.
Highlights
Solitons are stable localized wave packets that can propagate a long distance in dispersive media without changing their shapes
One can ask what is the role of dark solitons and how their dynamics is seen in the quantum regime
In this paper we have developed an asymptotic description of azimuthal envelope solitons on spherical liquid layers as solutions of defocusing nonlinear Schrödinger equation
Summary
Solitons are stable localized wave packets that can propagate a long distance in dispersive media without changing their shapes. Nonlinear models with soliton solutions offer possible explanations for the emergence of such rotons as coherent states in nuclear systems [45], in α-particles’ collision with medium-heavy nuclei [46,47,48], in nuclear fission [49], and in cnoidal excitations of Fermi-PastaUlam rings [50]. These results suggest that some dynamical systems can have collective localized stable excitations in compact or bounded geometries. In the last section we match our theoretical energy spectra with experimental results on energy, angular momentum, and parity for α-particle clustering nuclei for atomic masses ranging from 20 to 212
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