Alpha particle clusters and their condensation in nuclear systems

Abstract

In this article we review the present status of α clustering in nuclear systems. An important aspect is first of all condensation in nuclear matter. Like for pairing, quartetting in matter is at the root of similar phenomena in finite nuclei. Cluster approaches for finite nuclei are shortly recapitulated in historical order. The α container model as recently been proposed by Tohsaki-Horiuchi-Schuck-Röpke (THSR) will be outlined and the ensuing condensate aspect of the Hoyle state at 7.65 MeV in 12 C investigated in some detail. A special case will be made with respect to the very accurate reproduction of the inelastic form factor from the ground to Hoyle state with the THSR description. The extended volume will be deduced. New developments concerning excitations of the Hoyle state will be discussed. After 15 years since the proposal of the α condensation concept a critical assessment of this idea will be given. Alpha gas states in other nuclei like 16 O and 13 C will be considered. An important aspect are experimental evidences, present and future ones.The THSR wave function can also describe configurations of one α particle on top of a doubly magic core. The cases of 20 Ne and 212 Po will be investigated.

16O within the Semimicroscopic Algebraic Cluster Model and the importance of the Pauli Exclusion Principle

“…(3,0), (4,1), (1,4), (5,2), (6,3) 4 (0,2), (1,3), (4,0) 2 , (3,2) 2 , (2,4), (5,1) 3 , (4,3), (3,5), (6,2) 2 , (7,3) Table 1. Model space of the 4-α-particle system, for up to 4 ω excitations and only including states with the "most antisymmetric" irrep in UST (4).…”

Ab initio Calculations of the Isotopic Dependence of Nuclear Clustering

“…Unfortunately in many cases this dramatically increases the amount of computer memory and computing time needed in calculations of heavier nuclei. Nevertheless there is promising work in progress using the symmetry-adapted no-core shell model [15], antisymmetrized molecular dynamics [16], fermionic molecular dynamics [17], the alpha-container model [18], Monte Carlo shell model [19], and Green's function Monte Carlo [20].Lattice calculations using chiral effective field theory and auxiliary-field Monte Carlo methods have probed alpha clustering in the 12 C and 16 O systems [21][22][23][24]. However these lattice simulations have encountered severe Monte Carlo sign oscillations in cases where the number of protons Z and number of neutrons N are different.…”

The Hoyle Family: The Search for Alpha-Condensate States in Light Nuclei

“…In an extended THSR approach [71], where different Gaussian width parameters are permitted, meaning that two of the three α-particles can be closer than to the third α-particle, a whole spectrum of states in 12 C can be generated. The calculated E2 transition strengths indicate a rotational pattern.…”

“…The γ decay could then be inferred by measuring the decay of the Hoyle state into three α-particles in the TPC. However, using the B(E2) values published in reference [71] a minuscule branching ratio γ / α ≈ 10 −8 is calculated, making this measurement impractical at present.…”