A “hybrid” R-matrix-optical model parametrization of the 12C(α, γ)16O cross section

doi:10.1016/0375-9474(74)90715-5

Nuclear Physics A

Volume 220, Issue 2, 25 February 1974, Pages 221-232

https://doi.org/10.1016/0375-9474(74)90715-5 Get rights and content

Abstract

The ¹²C(α,γ)¹⁶O cross section at astrophysical energies has been determined from existing ¹²C(α, α)¹²C and ¹²C(α,γ)¹⁶O data by means of a “hybrid” R-matrix - optical model method; we obtain an S-factor of 0.08 _−0.04^+0.05 MeV·b at E_c.m = 300 keV. The El γ-ray width of the 9.59 MeV state has been determined to be 23 ± 3 meV.

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Measurement and DWBA analysis of the 12C(6Li, d)16O α-transfer reaction cross sections at 48.2 MeV. R-matrix analysis of 12C(α, γ)16O direct capture reaction data
2007, Nuclear Physics A
The angular distributions for low lying states of ¹⁶O produced in the ¹²C(⁶Li, d)¹⁶O α-transfer reaction at $E_{{}^{6}{Li}} (lab) = 48.2 MeV$ have been measured using a high energy resolution position sensitive detection system. The measured cross section data have been analyzed by the FRDWBA theory with a particular emphasis put on the states of astrophysical interest mainly the $1^{-}$ (7.12 MeV) state. Extracted values of nuclear level parameters (excitation energy, $E_{x}$ , line width, $Γ_{c . m .}$ , α-spectroscopic factor, $S_{α}$ , and reduced α-width, $γ_{α}^{2}$ or $θ_{α}^{2}$ ) are reported and discussed in comparison to previous ones. The used binding potential corresponds to a long nuclear interaction range (up to a channel radius $a = 7.7 fm$ ), suggesting that the channel radius $a = 6.5 fm$ is likely suitable for the calculations of reduced α-widths near the nuclear surface. However, given that previous DWBA results are available for comparison only near the channel radius $a = 5.5 fm$ , calculations have been carried out here for both three preceding a values. Formal values, $0.0036 ⩽ θ_{α}^{2} (7.12) ⩽ 0.152$ and $0.019 ⩽ θ_{α}^{2} (6.92) ⩽ 0.096$ of the reduced α-widths ( $a = 6.5 fm$ ) of the $1^{-}$ (7.12 MeV) and $2^{+}$ (6.92 MeV) states have thus been derived. Furthermore, the R-matrix analysis of various data sets of importance to the ¹²C( $α, γ$ )¹⁶O direct capture reaction has been carried out, leading to the range of values for the $1^{-}$ (7.12 MeV) state, $0.0096 ⩽ θ_{α}^{2} (7.12) ⩽ 0.0166$ , which is consistent with the preceding DWBA interval, and to a result for the E1 component of the reaction astrophysical factor, $S_{E 1} (0.3) = {80.6}_{−16}^{+17} keV b$ , very consistent with most constrained values previously reported in the literature.
The 12C(α, γ)16O reaction at astrophysical energies
2001, Nuclear Physics A
Nuclear astrophysics with secondary (Radioactive) beams
1993, Progress in Particle and Nuclear Physics
It is shown that the use of secondary beams allows for measurement of small cross sections of importance for nuclear astrophysics. In all cases discussed the measurements performed in the laboratory are for the time reversed process, which give rise to a larger yield and increased sensitivity. We examine the $^{14} C (α,γ)^{18} O$ reaction, vis-a-vis nonstandard big bang nucleosynthesis, the $^{12} C (α,γ)^{16} O$ reaction, of importance for helium burning (in massive stars), and the $^{7} Be (p,γ)^{8} B$ reaction, of importance for the ⁸B solar neutrino problem.
Is it possible to observe an isoscalar E1-multipole in 6Liγ{down harpoon left}αd reactions?
1990, Physics Letters B
Radiative capture of deuterons by α-particles $(αd→^{6} Liγ)$ and the inverse reactions are considered in the framework of the potential cluster model. Special attention is paid to corrections to the E1 multipole in the long wave approximation which can compete with the dominant E2 multipole. It is shown that these corrections could already be detected in the experimental data on the angular distributions of photons. The asymmetry of the deuteron angular distributions in polarized γ-quanta disintegration could be another quantity where the E1 transition could be exhibited. Among many corrections, the one which is due to the mass difference between the α-particle and two times the deuteron mass is the most important.
The scattering of alpha particles from 12C and the 12C(α, γ)16O stellar reaction rate
1987, Nuclear Physics, Section A
The elastic scattering of alpha particles from ¹²C has been investigated for 35 angles in the range θ_lab = 22° to 163° and for 51 energies at E_α = 1.0 to 6.6 MeV. The extracted phase shifts for l = 0 to 6 partial waves have been parametrized in terms of the multilevel R-matrix formalism. Information on the deduced parameters of states in ¹⁶O is reported. The data reveal reduced α-particle widths for the 6.92 and 7.12 MeV subthreshold states consistent with recent work. The implications for the stellar reaction rate of $^{12} C (α, γ)^{16} O$ are discussed.
The 12C(α, γ)16O cross section at stellar energies
1987, Nuclear Physics, Section A
The capture reaction ¹²C(α, γ)¹⁶O has been investigated at E = 0.94 to 2.84 MeV with the use of an intense α beam and implanted ¹²C targets of high isotopic purity. The studies involved NaI(Tl) crystals and, for the first time, germanium detectors. The measurement of absolute cross sections, γ-ray angular distributions and excitation functions is reported. A cross section of 48 pb is found at E = 0.94 MeV. The data provide information on the E1 and E2 capture amplitudes involved in the transition to the ground state as well as to excited states. The S-factor at stellar energies has been determined by means of theoretical fits. The results verify the previous report of a substantial higher S-value compared to the value recommended in 1975. The present uncertainty in the S-value as well as possible improvements are discussed. This S-value is of crucial importance to nuclear astrophysics.

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^☆: Supported in part by the National Science Foundation [GP-28027].

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Nuclear Physics A

Abstract

References (22)

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Cited by (42)

Measurement and DWBA analysis of the <sup>12</sup>C(<sup>6</sup>Li, d)<sup>16</sup>O α-transfer reaction cross sections at 48.2 MeV. R-matrix analysis of <sup>12</sup>C(α, γ)<sup>16</sup>O direct capture reaction data

The <sup>12</sup>C(α, γ)<sup>16</sup>O reaction at astrophysical energies

Nuclear astrophysics with secondary (Radioactive) beams

Is it possible to observe an isoscalar E1-multipole in <sup>6</sup>Liγ{down harpoon left}αd reactions?

The scattering of alpha particles from <sup>12</sup>C and the <sup>12</sup>C(α, γ)<sup>16</sup>O stellar reaction rate

The <sup>12</sup>C(α, γ)<sup>16</sup>O cross section at stellar energies

A “hybrid” R-matrix-optical model parametrization of the 12C(α, γ)16O cross section☆

Abstract

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Nucl. Phys.

Phys. Rev.

Nucl. Phys.

Phys. Rev. Lett.

Phys. Rev.

Austral. J. Phys.

A “hybrid” R-matrix-optical model parametrization of the ¹²C(α, γ)¹⁶O cross section☆