Rotational excitation of the Hoyle state in ¹²C

Abstract

Abstract.12 C is synthesised in stars by fusion of three α particles. This process occurs through a resonance in the 12 C nucleus, famously known as the Hoyle state. In this state, the 12 C nucleus exists as a cluster of α particles. The state is the band-head for a rotational band with the 2 + rotational excitation predicted in the energy region 9 -11 MeV. This rotational excitation can affect the triple-α process reaction rate by more than an order of magnitude at high temperatures (10 9 K). Depending on the energy of the resonance, the knowledge of the state can also help determine the structure of the Hoyle state. In the work presented here, the state of interest is populated by beta decay of radioactive 12 N ion beam delivered by the IGISOL facility at JYFL, Jyväskylä. IntroductionThe 12 C nucleus has a cluster structure in the Hoyle state, which is a 0 + resonance just above the triple-α threshold. With the non-spherical structure of the state, 12 C has a rotational band built upon this state. A recent measurement by Zimmerman et al.[1], along with the other observations [2][3][4][5] suggest that the first excitation of this band, the 2 + state, is to be found in 9 -11 MeV energy region. The second and higher lying member of this rotational band, 4 + has been found experimentally [6], but the 2 + excitation has proven difficult to study because of the the presence of a broad 0 + resonance at 10.3 MeV [4,7].At higher temperature in stars (10 9 K), this rotational excitation state becomes relevant to the triple-α process, affecting the reaction rate. In addition to its importance in determining the 12 C production rate, the state is also important when considering the structure. With the energy of this first rotational excitation known, the determined moment of inertia can settle the debate on the structure of the 12 C nucleus in the Hoyle state as different theoretical models predict different arrangements of the cluster in the Hoyle state [8].The experiment was performed at JYFL, Jyväskylä, Finland. The IGISOL (Ion-Guide Isotope Separator OnLine) facility delivered a beam of the radioisotope 12 N which β decays to 12 C, populating the states of interest. Due to the selection rules of β decay, this method gives

Radiative Width of the Hoyle State from γ -Ray Spectroscopy

“…The number of random events has been evaluated using the accidental coincidences of the 4.44 MeV γ ray with itself, indicated as "4.44/4.44". The number of such events in the various TDC gates were 131 (12), 157(13), 134 (12), 63 (8), which gives a subtraction factor of 1.15 (11), a value consistent with the one obtained from the proton spectra. To deduce the final γγ coincidence spectra, the scaling factor of 1.061(12) was adopted.…”

“…The existence of the state was confirmed in the same year from the analysis of the α spectrum from the 14 Nðd; αÞ 12 C reaction [5]. The Hoyle state is α unbound and the dominant decay process (> 99.94%) is through the emission of an α particle, leading to the very short-lived isotope 8 Be, which then disintegrates into two α particles. Stable carbon will only be produced either if the Hoyle state decays directly to the ground state via an electric monopole (E0) transition or by a cascade of two electric quadrupole (E2) transitions.…”

“…The discussion includes nuclear clustering, a spacial arrangement of the three α particle clusters of which the state is believed to be composed, and discussion on a new form of nuclear matter, in analogy with the Bose-Einstein condensates. The characterization of the 2 þ and 4 þ states on top of the 7.65 MeV 0 þ state, forming the Hoyle band [8], together with much improved ab initio calculations [9] are important steps forward.…”

“…Using the above N p ð2 þ 1 Þ rates the scaling factor was obtained as 8251ð91Þ=f½7697ð88Þ þ 7914ð89Þ− 54ð9Þ=2g ¼ 1.061ð12Þ. The N p ð0 þ Þ rates in the same TDC gates were 249(16), 158(13), 197 (14), and 66 (8), respectively. This gives N 7.65 020 ¼ 212ð22Þ counts.…”

The radiative width of the Hoyle state from $γ$-ray spectroscopy

“…The discussion includes nuclear clustering, a spacial arrangement of the three α particle clusters of which the state is believed to be composed, and discussion on a new form of nuclear matter, in analogy with the Bose-Einstein condensates. The characterization of the 2 + and 4 + states on top of the 7.65 MeV 0 + state, forming the Hoyle band [9], together with much improved ab initio calculations [10] are important steps forward.…”