New approach to determining radiative capture reaction rates at astrophysical energies

Abstract

Radiative capture reactions play a crucial role in stellar nucleosynthesis but have proved challenging to determine experimentally. In particular, the large uncertainty (∼100%) in the measured rate of the 12 C(α, γ) 16 O reaction is the largest source of uncertainty in any stellar evolution model. With development of new high current energy-recovery linear accelerators (ERLs) and high density gas targets, measurement of the 16 O(e, e α) 12 C reaction close to threshold using detailed balance opens up a new approach to determine the 12 C(α, γ) 16 O reaction rate with significantly increased precision (<20%). We present the formalism to relate photo-and electro-disintegration reactions and consider the design of an optimal experiment to deliver increased precision. Once the new ERLs come online, an experiment to validate the new approach we propose should be carried out. This new approach has broad applicability to radiative capture reactions in astrophysics. multipole decompositions of the response functions up to C3/E3 are given in the Appendix. † In most of this work we use natural units where = c = 1, although later, when writing expressions for the cross sections, we include them to make the units explicit.

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“…In the randomizations, we multiplied the individual pseudodata uncertainties as taken from Ref. [7,17] by the square root of the ratio of the original best fit S factor values, defined by the fit values in Table I, to the original measured uncertainties, given by the CTAG experiments. We further multiplied these uncertainties by the square root of the E 1 and E 2 reduced chi square values, the Birge factor [18], for the E 1 and E 2 fits, respectively.…”

“…Proposed OSGA experiments [8][9][10]31,32] as well as the OSEEA experiment [7] are expected to have several orders of magnitude improvement in integrated luminosity over previous experiments and should provide data at the lowest practical values of energy. We take our best R-matrix fits to the E 1 and E 2 CTAG S-factor data as the most probable description of the projected MIT data [7]. We then randomly varied the OSEEA S E 1 and S E 2 -factor pseudodata based on their projected uncertainties [7] according to a Gaussian probability distribution about the best fit S E 1 -and S E 2 -factor values.…”

“…This is achieved by starting with a reasonable R-matrix fit that can be used as a basis for comparison to fits with and without projected OSEEA data. In particular, we consider a proposed MIT experiment [7] in order to assess the possible role of new measurements in reducing the overall uncertainty in the cross section. In this work the E 1 and E 2 12 C(α, γ ) 16 O ground state cross sections can be extracted [7] from measurements of the OSEEA.…”

“…In particular, we consider a proposed MIT experiment [7] in order to assess the possible role of new measurements in reducing the overall uncertainty in the cross section. In this work the E 1 and E 2 12 C(α, γ ) 16 O ground state cross sections can be extracted [7] from measurements of the OSEEA. A detailed R-matrix analysis of the 12 C(α, γ ) 16 O (CTAG) reaction and an excellent review of the subject are given in Ref.…”

“…We performed extrapolations to 300 keV in order to study the impact of potential new data. Efforts aimed at improving the data and extrapolation are under way [7][8][9][10][11][12][13][14][15] at a number of laboratories worldwide. The new inverse reaction 16 O(γ , α) 12 C (OSGA) experiments [8][9][10]15] as well as the forthcoming OSEEA reaction [7] bring different sets of systematic errors than previous experiments and thus provide an additional check on systematics.…”