Dilute Multi Alpha Cluster States in Nuclei

Abstract

Dilute multi $\alpha$ cluster condensed states with spherical and axially deformed shapes are studied with the Gross-Pitaevskii equation and Hill-Wheeler equation, where the $\alpha$ cluster is treated as a structureless boson. Applications to self-conjugate $4N$ nuclei show that the dilute $N\alpha$ states of ${}^{12}$C to ${}^{40}$Ca with $J^{\pi }=0^{+}$ appear in the energy region from threshold up to about 20 MeV, and the critical number of $\alpha$ bosons that the dilute $N\alpha$ system can sustain as a self-bound nucleus is estimated roughly to be $N_{cr}\sim 10$. We discuss the characteristics of the dilute $N\alpha$ states with emphasis on the $N$ dependence of their energies and rms radii.

44 pages, 8 figures

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• Theory of Bose-Einstein condensation in trapped gases
• Alpha cluster condensation in 12C and 16O
• Four-particle condensate in strongly coupled fermion systems
• Description of 8Be as Deformed Gas-like Two-Alpha-Paricle States
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Cited by in corpus (66)

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• Status of Alpha-Particle Condensate Structure of the Hoyle State
• Negative parity states of ${}^{11}$B and ${}^{11}$C and the similarity with $^{12}C
• Resonance states in 12C and alpha-particle condensation
• Evidence for $\alpha$-particle condensation in nuclei from the Hoyle state deexcitation
• Evidence for an alpha cluster condensed state in 16O(alpha,alpha') at 400 MeV
• Nonlocalized cluster dynamics and nuclear molecular structure
• Microscopic study of 4-alpha-particle condensation with proper treatment of resonances
• $\alpha$-particle condensate states in ${}^{16}$O
• Density-induced suppression of the alpha-particle condensate in nuclear matter and the structure of alpha cluster states in nuclei
• $\alpha +\alpha +t$ cluster structures and Hoyle-analogue states in ${}^{11}$B
• Alpha cluster structures and monopole excitations in ${}^{13}$C
• Experimental investigation of $\alpha$-condensation in light nuclei
• Candidates for the 5$\alpha$ condensed state in ${}^{20}$Ne
• Spectral convexity for attractive SU(2N) fermions
• Boson-Fermion pairing in a Boson-Fermion environment
• Container evolution for cluster structures in ${}^{16}\mathrm{O}$
• Cluster states and monopole transitions in ${}^{16}$O
• Nuclear Alpha-Particle Condensates
• Searching for states analogous to the 12C Hoyle state in heavier nuclei using the thick target inverse kinematics technique
• Alpha Clustering from the Quartet Model
• Monopole excitation of the Hoyle state and linear-chain state in 12C
• Three-alpha-cluster structure of the 0^+ states in ^{12}C and the effective alpha-alpha interactions
• Alpha-cluster Condensations in Nuclei and Experimental Approaches for their Studies
• Hoyle-analogue state in 13C studied with Antisymmetrized Molecular Dynamics
• Real-time evolution method and its application to 3$\alpha$ cluster system
• Container structure of alpha alpha Lambda clusters in ${}_{\Lambda }^9$Be
• Non-statistical decay and $\alpha$-correlations in the ${}^{12}$C+${}^{12}$C fusion-evaporation reaction at 95 MeV
• Gas-like state of $\alpha$ clusters around ${}^{16}$O core in ${}^{24}$Mg
• Monopole oscillations in light nuclei with a molecular dynamics approach
• Thermal properties of light nuclei from ${}^{12}$C+${}^{12}$C fusion-evaporation reactions
• Multi-cluster dynamics in ${}_{\Lambda }^{13}\mathrm{C}$ and analogy to clustering in ${}^{12}\mathrm{C}$
• Signals of Bose Einstein condensation and Fermi quenching in the decay of hot nuclear systems
• Alpha-particle condensation: a nuclear quantum phase transition
• Nuclear alpha-particle condensates: Definitions, occurrence conditions, and consequences
• Alpha matter on a lattice
• A new possibility for light-quark Dark Matter
• Open Problems in $\alpha$ Particle Condensation
• Bose-Einstein condensation of alpha clusters and new soft mode in 12C--52Fe 4N nuclei in field theoretical superfluid cluster model
• Unstable states in dissociation of relativistic nuclei. Recent findings and prospects of researches
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• Effective field theory of Bose-Einstein condensation of $\alpha$ clusters and Nambu-Goldstone-Higgs states in ${}^{12}$C
• Resonant and Scattering States in the $\alpha +\alpha$ System from the Non-Localized Cluster Model
• Internal One-Particle Density Matrix for Bose-Einstein Condensates with Finite Number of Particles in a Harmonic Potential
• Mirror symmetry breaking in He isotopes and their mirror nuclei
• Three triton states in 9Li
• Cluster-Daughter Overlap as a New Probe of Alpha-Cluster Formation in Medium-Mass and Heavy Even-Even Nuclei
• Correlation in formation of ${}^8$Be nuclei and $\alpha$-particles in fragmentation of relativistic nuclei
• Search for the 6$\alpha$ condensed state in ${}^{24}$Mg using the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ scattering
• The Hoyle Family: The search for alpha-condensate states in light nuclei
• Present status of nuclear cluster physics and experimental perspectives
• Recent Experimental Results on Nuclear Cluster Physics
• 2alpha+t cluster feature of $3/2_3^{-}$ state in ${}^{11}$B
• Repulsive Four-Body Interactions of $\alpha$ Particles and Quasi-Stable Nuclear $\alpha$-Particle Condensates in Heavy Self-Conjugate Nuclei
• ${}^{10}$B+$\alpha$ states with chain-like structures in ${}^{14}$N
• Production of $\alpha$-particle condensate states in heavy-ion collisions
• Search for $\alpha$ condensed states in ${}^{13}$C using $\alpha$ inelastic scattering
• Theory for Quartet Condensation in Fermi Systems with Applications to Nuclei and Nuclear Matter
• Signature of a possible $\alpha$-cluster state in $N=Z$ doubly-magic ${}^{56}$Ni
• Impact of pion tensor force on alpha clustering in ${}^{20}$Ne
• Bose-Einstein condensation of five $\alpha$ clusters in ${}^{20}$Ne and supersolidity
• Temperature of the hot $\alpha$-source: a guidance to probe the Bose-Einstein condensation of $\alpha$ clusters in the heavy-ion collision
• Two-Center Gaussian potential well for studying light nucleus in cluster structure
• Six-$\alpha$ cluster Bose-Einstein condensation and supersolid ${}^{12}$C($0_2^{+})$+${}^{12}$C($0_2^{+})$ molecular structure in ${}^{24}$Mg