Fig. 1: The experimental setup used at the HI\u01b4S facility at the TUNL at Duke University1, showing the 1 GeV electrons colliding with the Free Electron Laser photons (red) to produce the gamma-beam (blue). The photo-dissociation of the oxygen in the CO2 gas yield the a + 12C ions with tracks shown in the upper left corner, recorded by the CCD camera and Photo Multiplier Tube. Figure reproduction from1 with permission from Springer Nature. Open Access Creative Commons license, creativecommons.org\/ licenses\/by\/4.0\/<\/figcaption><\/figure>\nStellar helium burning<\/h3>\n The iron core balances the enormous gravitational pressure due to a quantum mechanical repulsion of the electrons (fermions) in the iron core. This quantum mechanical counter pressure can no longer sustain the pressure of self-gravity when the core reaches 1.4 solar masses (the Chandrasekhar limit), and the star collapses under its own gravity, leading to a Type II supernova explosion that leaves behind a black hole or a neutron star. During stellar helium burning, carbon is formed by the so-called \u2018triple-alpha process\u2019 and oxygen is formed by the further fusion of carbon with an alpha-particle (the nucleus of the helium atom).<\/p>\n
Thus, both carbon and oxygen are formed in stellar helium burning. The ratio of carbon to oxygen (C\/O) at the end of helium burning is critically dependent on the rate of fusion of carbon with an alpha-particle. However, accurately quantifying this rate has eluded researchers for the last four decades since it was declared by Willie Fowler in his 1984 Nobel speech as a problem of \u201cparamount importance\u201d in nuclear astrophysics. Critically, the C\/O ratio at the end of stellar helium burning determines whether the Type II supernova leaves behind a neutron star (for C\/O >1) or a black hole (for C\/O < 1).<\/p>\n
The fusion of carbon with an alpha-particle to form oxygen is impossible to measure experimentally at the most efficient stellar burning energy of 300 keV (the Gamow Window), because the rate is too low. Instead, measurements are made above 1.5 MeV and extrapolated to astrophysical energies. Accurate extrapolation requires an understanding of the angular momentum of the alpha-particle and 12<\/sup>C system, namely the relative strengths of the \u0196 = 1 and \u0196 = 2 partial waves, and their interference. This is achieved by measuring the angles of the outgoing particles from the reaction. A prediction for the interference of the \u0196 = 1 and \u0196 = 2 partial waves is calculable from quantum theory. However, so far, no dataset has exhibited clear agreement with this prediction. Surprisingly, this contradiction with an elementary prediction of quantum mechanics has largely been ignored, even though it may point out to poorly understood systematic uncertainties within existing data.<\/p>\nFig. 2: Storage ring and optical cavity of the VEGA gamma-beam system being constructed by Lyncean Technologies at the ELI-NP facility in Magurele, Romania. Figure courtesy of Lyncean Technologies, Inc<\/figcaption><\/figure>\nMeasuring the time-reversed process<\/h3>\n We investigated the fusion of 12<\/sup>C with an alpha-particle using a completely different experimental setup. Up to now, all measurements mimicked the stellar fusion of carbon with an alpha-particle to form oxygen with the detection of the emitted gamma-radiation or oxygen by-product. We instead measured the time-reversed process: the photo-dissociation of oxygen to form carbon and an alpha-particle. Quantum mechanics allows us to deduce the direct process from the time reversed one using the principle of detailed balance. The time-reversed photodissociation process has a reaction rate that is larger by approximately a factor 50. This measurement required high energy (8-10 MeV) gamma-particles that were made available at the High Intensity \u01b4amma Source (HI\u01b4S) at the TUNL in Duke University. In Fig. 1, we show the HI\u01b4S setup, taken from R Smith, M Gai, S R Stern, D K Schweitzer, and M W Ahmed, Nature Communications1<\/sup>. A new variable energy gamma (VEGA) system is now under construction at the Extreme Light Infrastructure \u2013 Nuclear Physics (ELI-NP) facility of the EU in Romania. In Fig. 2, we show the VEGA system that is anticipated to deliver better energy resolution (0.5%) than available at the HI\u01b4S (3%) and higher intensity. The two gamma-beam systems use the Compton back-scattering of low energy (optical) laser-photons with approximately 1 GeV electrons circulating in the ring, as shown in Figs. 1 and 2.<\/p>\nOne additional advantage of measuring the time-reversed photo-dissociation process is that we can use oxygen-rich gas as both the target and detector materials. The use of a time projection chamber (TPC) detector as an active target TPC (AT-TPC) is a new concept in low energy nuclear physics; with our UConn-HI\u01b4S optical readout TPC (O-TPC) detector, shown in Fig. 11<\/sup>, among the first to be employed.<\/p>\nAn AT-TPC allows measurements with vanishingly small background, a major advantage over measurements using germanium gamma-detectors that are plagued by beam related and detector related intrinsic backgrounds. Furthermore, using an AT-TPC detector, one measures the entire angular distribution (0-180\u00b0) in one detector with an unprecedented angular resolution (2\u00b0). A measurement using one detector is preferable to the use of an array of separate gamma detectors, that are sensitive to variations in angular coverage and efficiency.<\/p>\nFig. 3: Professors W Dominik and Z Janas calibrating the Warsaw TPC at the IFJ in Krakow, in preparation for measurements at the HI\u01b4S and ELI-NP. Picture courtesy of Moshe Gai<\/figcaption><\/figure>\nWe also measured the angle integrated total reaction cross section and our measurement is in perfect agreement1<\/sup>\u00a0 with previous measurements. The agreement of the angle integrated cross section serves to \u2018benchmark\u2019 our method and encourage further measurements at lower energies that can be reliably extrapolated to stellar conditions. For that purpose we collaborated with the Warsaw group who constructed an electronic readout TPC that is far superior to the O-TPC employed by us at the HI\u01b4S. In Fig. 3, we show the Warsaw TPC calibrated at the IFJ in Krakow, Poland, with 13 MeV gamma-rays from the 15<\/sup>N + p \uf067 16<\/sup>O + \u01b4 reaction. This TPC will be initially used at the HI\u01b4S and then at the ELI-NP to continue our measurements to energies as low as 1 MeV. Our initial successful measurement at the HI\u01b4S1<\/sup> allow us to envisage a rich future research programme at the HI\u01b4S in the USA and the ELI-NP in Romania. This material is based on work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, grants DE-FG02-94ER40870, and the UK Science and Technology Facilities Council.<\/p>\n