# Bose-Einstein condensation of dilute alpha clusters above four $\alpha$ threshold in $^{16}$O in field theoretical superfluid cluster model

## TL;DR

This paper demonstrates the Bose-Einstein condensation of alpha clusters in $^{16}$O using a field-theoretical superfluid model, successfully reproducing experimental energy levels and revealing the underlying symmetry-breaking mechanisms.

## Contribution

It introduces a novel field-theoretical superfluid cluster model that explains the alpha cluster states in $^{16}$O as Bose-Einstein condensates, aligning well with experimental data.

## Key findings

- Reproduces experimental energy levels of $^{16}$O.
- Identifies low-energy states as Nambu-Goldstone modes.
- Shows robustness of alpha cluster structures above threshold.

## Abstract

Observed well-developed $\alpha$ cluster states in $^{16}$O, located above the four $\alpha$ threshold, are investigated from the viewpoint of Bose-Einstein condensation of $\alpha$ clusters by using a field-theoretical superfluid cluster model in which the order parameter is defined. The experimental energy levels are reproduced well for the first time by calculation. In particular, the observed 16.7 MeV $0_7^+$ and 18.8 MeV $0_8^+$ states with low-excitation energies from the threshold are found to be understood as a manifestation of the states of the Nambu-Goldstone zero-mode operators, associated with the spontaneous symmetry breaking of the global phase, which is caused by the Bose-Einstein condensation of the vacuum 15.1 MeV $0^+_6$ state with a dilute well-developed $\alpha$ cluster structure just above the threshold. This gives evidence of the existence of the Bose-Einstein condensate of $\alpha$ clusters in $^{16}$O. It is found that the emergence of the energy level structure with a well-developed $\alpha$ cluster structure above the threshold is robust, almost independently of the condensation rate of $\alpha$ clusters under significant condensation rate. The finding of the mechanism why the level structure that is similar to $^{12}$C emerges above the four $\alpha$ threshold in $^{16}$O reinforces the concept of Bose-Einstein condensation of $\alpha$ clusters in addition to $^{12}$C.