On formation of the $^{12}$C(0$^+_2$) and $^{12}$C(3$^-$) states in relativistic dissociation of light nuclei

TL;DR

This study investigates near-threshold α-cluster states, notably $^{12}$C$(0^+_2)$ (Hoyle state) and $^{12}$C$(3^-)$, in the relativistic dissociation of light nuclei $^{12}$C → 3$α$ and $^{16}$O → 4$α$ at 3.65 GeV per nucleon using nuclear emulsion. The authors reconstruct the invariant mass of α-particle ensembles, expressed as $Q$, from emission angles under momentum-per-nucleon conservation, to identify these states without direct decay-vertex measurements. For $^{12}$C → 3$α$, they find a near-threshold $^{12}$C$(0^+_2)$ signal ($Q_{3α} ≈ 0.42$ MeV) and a broader $^{12}$C$(3^-)$ contribution (Rayleigh with $σ ≈ 2.4$ MeV), with approximately 43%, 9%, and 19% of events attributed to $^8$Be$(0^+)$, $^{12}$C$(0^+_2)$, and $^{12}$C$(3^-)$, respectively. In $^{16}$O → 4$α$, after background suppression, the $^{12}$C$(3^-)$ channel is evident with mean $Q_{3α}$ near 2.5 MeV, yielding fractions of about 23% for $^{12}$C$(0^+_2)$α, 32% for $^{12}$C$(3^-)$α, and 6% for 2×$^8$Be$(0^+)$, with a ratio of 1.4 between the $^{12}$C$(3^-)$α and $^{12}$C$(0^+_2)$α channels. Overall, the work demonstrates the prominence of near-threshold α-excitations in relativistic dissociation and validates invariant-mass reconstruction as a tool to study such states.

Abstract

The formation of the excited states $^{12}$C(0$^+_2$) and $^{12}$C(3$^-$) is investigated in the dissociation of $^{12}$C $\to$ 3$α$ and $^{16}$O $\to$ 4$α$ at the energy of 3.65 GeV per nucleon in the nuclear emulsion. The identification becomes possible by reconstructing the invariant mass from measurements of emission angles in the approximation of conservation of momentum per nucleon of the parent nucleus. The contribution of the decays $^{12}$C(0$^+_2$) and $^{12}$C(3$^-$) to the dissociation $^{12}$C $\to$ 3$α$ is 11 and 19%, and in $^{16}$O $\to$ 4$α$ it is - 20 and 30%, correspondingly.

Figures (3)

• Figure 1: Distribution over $Q_{3\alpha}$ in the events: $^{12}$C $\to$$^8$Be(0$^+$)$\alpha$ (dots) and $^{16}$O $\to$$^8$Be(0$^+$)2$\alpha$ (solid); normalized to the number of events.
• Figure 2: Distribution over $Q_{3\alpha}$ and $Q_{4\alpha}$ (insert) in the events: $^{16}$O $\to$ 2$^8$Be(0$^+$).
• Figure 3: Distribution over $Q_{3\alpha}$ in the events: $^{12}$C $\to$$^8$Be(0$^+$)$\alpha$ (dots) and $^{16}$O $\to$$^8$Be(0$^+$)2$\alpha$ (solid) excluding the events with 2$^8$Be(0$^+$) and $^{12}$C(0$^+_2$).