Correlated-Gaussian approach to linear-chain states -Case of four $\alpha$-particles-

Abstract

We show that correlated Gaussians with good angular momentum and parity provide flexible basis functions for specific elongated shape. As its application we study linear-chain states of four-alpha particles in variation-after-projection calculations in which all the matrix elements are evaluated analytically. We find possible chain states for $J=0^{+}$, $2^{+}$, $4^{+}$ and perhaps $6^{+}$ with the bandhead energy being about 33 MeV from the ground state of ${}^{16}$O. No chain states with $J\ge 8$ are found. The nature of the rotational sequence of the chain states is clarified in contrast to a rigid-body rotation. The quadrupole deformation parameters estimated from the chain states increase from 0.59 to 1.07 for $2^{+}$ to $6^{+}$. This work suggests undeveloped fields for the correlated Gaussians beyond those problems which have hitherto been solved successfully.

arXiv comment13 pages, 6 figures, accepted for publication in Phys. Rev. C

References in corpus (20)

• Quantum Monte Carlo calculations of A=8 nuclei
• Precise solution of few-body problems with stochastic variational method on correlated Gaussian basis
• Ab initio no-core full configuration calculations of light nuclei
• Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics
• Ab initio approach to s-shell hypernuclei 3H_Lambda, 4H_Lambda, 4He_Lambda and 5He_Lambda with a Lambda N-Sigma N interaction
• Rod-shaped Nuclei at Extreme Spin and Isospin
• Ab initio coupled-cluster study of 16-O
• Cluster structures of excited states in ${}^{14}$C
• Linear chain structure of four-$\alpha$ clusters in ${}^{16}$O
• Second bound state of the positronium molecule and biexcitons
• One-dimensional $\alpha$ condensation of $\alpha$-linear-chain states in ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$
• New representation of orbital motion with arbitrary angular momenta
• Experimental investigation of a linear-chain structure in the nucleus 14C
• Beyond mean-field description of the low-lying spectrum of 16O
• Ab initio study of the photoabsorption of ${}^4$He
• Be-$\alpha$ correlations in the linear-chain structure of C isotopes
• Searching for 4$\alpha$ linear-chain structure in excited states of ${}^{16}$O with a covariant density functional theory
• Correlated-basis description of $\alpha$-cluster and delocalized $0^{+}$ states in ${}^{16}$O
• Electric dipole response of ${}^6$He: Halo-neutron and core excitations
• Examination of the stability of a rod-shaped structure in ${}^{24}$Mg

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• 4$\alpha$ linear-chain state produced by ${}^9$Be+${}^9$Be collision