Effective field theory of Bose-Einstein condensation of $\alpha$ clusters and Nambu-Goldstone-Higgs states in ${}^{12}$C

Abstract

An effective field theory of $\alpha$ cluster condensation is formulated as a spontaneously broken symmetry in quantum field theory to understand the raison d'etre and nature of the Hoyle and $\alpha$ cluster states in ${}^{12}$C. The Nambu--Goldstone and Higgs mode operators in infinite systems are replaced with a pair of canonical operators whose Hamiltonian gives rise to discrete energy states in addition to the Bogoliubov--de Gennes excited states. The calculations reproduce well the experimental spectrum of the $\alpha$ cluster states. The existence of the Nambu--Goldstone--Higgs states is demonstrated and crucial. The $\gamma$ decay transitions are also obtained.

8 pages, 8 figures

References in corpus (8)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
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• Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability
• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
• Splitting Instability of a Multiply Charged Vortex in a Bose-Einstein Condensate
• Hoyle band and $\alpha$ condensation in ${}^{12}\mathrm{C}$
• Quantum Field Theoretical Description of Unstable Behavior of Trapped Bose-Einstein Condensates with Complex Eigenvalues of Bogoliubov-de Gennes Equations

Cited by in corpus (7)

• Status of Alpha-Particle Condensate Structure of the Hoyle State
• Alpha particle clusters and their condensation in nuclear systems
• Bose-Einstein condensation of alpha clusters and new soft mode in 12C--52Fe 4N nuclei in field theoretical superfluid cluster model
• Supersolidity of the $\alpha$ cluster structure in the nucleus ${}^{12}$C
• Thermal and quantum fluctuations of confined Bose-Einstein condensate beyond the Bogoliubov approximation
• Supersolidity of $\alpha$ cluster structure in ${}^{40}$Ca
• Bose-Einstein condensation of five $\alpha$ clusters in ${}^{20}$Ne and supersolidity