Study of the 6.05 MeV cascade transition in
Introduction
After stellar hydrogen burning, the core of a star is transformed mainly to 4He. Without the core energy production, the center contracts, and the core temperature, , rises. Meanwhile the outer layers of the star expand and the star develops into the Red Giant phase. At the nuclear energy production, due to the synthesis of three α particles to carbon (triple-α process), becomes large enough to sustain the temperature of the core. As a consequence, the contraction stops and the helium burning phase is started. In the first stage of stellar helium burning – since the 12C abundance is very low – the only active process is the triple-α reaction, while later after build up of a significant abundance of carbon the reaction is the dominating process. The cross section of the reaction at the relevant Gamow energy – – determines the helium burning time scale and, together with the convection mechanism, the abundances of carbon and oxygen at the end of helium burning. The carbon abundance at that stage has important consequences for the subsequent evolution of various astrophysical scenarios, e.g. a direct influence on type II Supernova (SN) nucleosynthesis [1], [2], [3], [4], [5], the maximum luminosity and kinetic energy of type I SN [6], and the cooling sequence of CO white dwarfs [7], [8], [9]. Thus, an experimental determination of the cross section in the relevant energy region in the order of 10% or better will improve our understanding of the convection processes and remains an important ingredient for the understanding of stellar evolution.
The cross section of the reaction () is dominated by E1 and E2 capture processes into the 16O ground state, where the two multipoles appear to be of similar importance at stellar energies. This energy region is not accessible with present experimental techniques and an extrapolation to is necessary. The cross section at low energies is typically expressed in terms of the astrophysical S factor [10] defined for this reaction as: where E is in keV. Since the capture cross sections of the E1 and E2 multipoles have different energy dependencies, one must have an independent and precise information on the energy dependence of each multipole cross section.
A series of direct experiments with γ-ray detector arrays (e.g. [11], [12], [13], [14], [15]) were carried out in the past years to constrain the ground state transitions. Additional information can be derived from measurements of the ()-elastic scattering [16], the β-delayed α-decay of 16N [17], [18], [19], and the total cross section with a recoil separator [20].
In addition to the ground state contributions, cascade transitions have to be considered whereas much less data are available. The cascade transitions can proceed through a number of 16O excited states and in particular transitions to the () and 7.12 MeV () have been observed in the past [21], [22].
A more detailed discussion of the various contributions is given for example in the review of Buchmann and Barnes [23] where a total S factor of is recommended with an uncertainty range of 25 to 35%.
Recently, the importance of the state at in 16O was emphasized [24]. This excited 0+ state decays exclusively by e+e− transition (E0) to the 0+ ground state and only the primary γ-ray line can be observed. This component was measured with the DRAGON recoil separator at TRIUMF, Canada, in the energy2 region to 5.42 MeV with a high efficiency BGO γ-ray array in coincidence with the observed recoils. The data have been analyzed with an R-matrix calculation and extrapolated to the astrophysical energy region, . This value is an additional contribution to the given in [23] and, thus, a non-negligible part of the total S factor at helium burning temperatures. Therefore, this cascade transition deserves a further investigation in order to prove its importance for stellar evolution.
The DRAGON experiment [24] spanned a rather large energy interval and is, due to the coincidence condition, one of the first reliable γ-ray measurements above in . In general data at high energies are important for reliable R-matrix extrapolations to astrophysical energies, but the only existing direct γ-ray measurement at such energies so far was published in 1964 [25] where a quoted absolute uncertainty of a factor 2 prevents any definite conclusion. However, the DRAGON measurement [24] suffered from low 12C beam intensities, the moderate energy resolution of the BGO crystals, and the limited acceptance of the separator preventing an independent normalization to the ground state transition. Some of these issues could be overcome in the measurement reported here.
Section snippets
Experimental setup
The experiment was carried out at the ERNA (European Recoil Separator for Nuclear Astrophysics) recoil separator at the Dynamitron – Tandem Laboratory of the Ruhr-Universität Bochum, Germany. A 12C beam intensity of typically 5 pμA in the 3+ or 4+ charge state was used in the energy range to 4.5 MeV. Details of the experimental setup are as reported previously [26], [27], [28]. Briefly, a ion beam emerging from the tandem accelerator was focused by a quadrupole doublet, filtered by a
Data analysis
The trigger of the acquisition system was based on the signal from the end-detector. Therefore, only γ-ray events in coincidence with recoil-like signals have been acquired. The selection of the appropriate region for the 16O recoils set further strong constraints on the identification of γ-ray events from the reaction. The background from accidental coincidences between γ-rays and recoil events in this region was estimated from γ-ray-recoil coincidences of the 12C
R-matrix analysis of the 6.05 MeV transition
The 6.05 MeV S factor data have been analyzed in the R-matrix formalism. The corresponding R-matrix code was developed specifically for an analysis of the reaction and is based on an alternative parametrization [39] of the original R-matrix theory [40]. The code can use physical resonance parameters [39] and is suited to fit simultaneously the direct γ-ray data, the 16N β-delayed α decay, and the () elastic scattering, respectively. The details on the code and further results
Summary
In conclusion, the 6.05 MeV cascade transition in was studied with the ERNA recoil separator by means of γ-ray-recoil coincidences, delivering background-free γ-ray spectra in the energy region above . This energy region gives strong constraints on the extrapolation of the astrophysical S factor for this transition and an R-matrix analysis of the present data yielded an upper limit of . The large value found previously [24] is excluded by the
Acknowledgements
The authors thank C. Rolfs and H.-P. Trautvetter for fruitful discussions. This work was supported by DFG (Ro429/35) and INFN.
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Present address: RUBION, Ruhr-Universität Bochum, D-44780 Bochum, Germany.