The scattering of alpha particles from C12

doi:10.1016/0029-5582(62)90242-0

Nuclear Physics

Volume 37, August–September 1962, Pages 1-22

https://doi.org/10.1016/0029-5582(62)90242-0 Get rights and content

Abstract

The elastic scattering of alpha particles from C¹² has been experimentally studied in the energy range 2.5 to 4.8 MeV using a recently constructed precision small volume gas scattering chamber. Excitation functions have been measured at the centre-of-mass angles 70° 7′, 90° 0′, 99° 15′, 109° 54′, 125° 16′, 140° 16′, 149° 27′ and 166° 35′, and angular distributions have been measured at 2.820, 3.377, 3.989 and 4.640 MeV. These data have been parameterized in terms of nuclear scattering phase shifts and the phase shifts have been analysed using the single level dispersion theory. Three states in O¹⁶ were observed: a 1^- state at 9.552 MeV in O¹⁶, a 2⁺ state at 9.815 MeV in O¹⁶ and a 4⁺ state at 10.329 MeV in O¹⁶. These states were found to have centre-of-mass reduced widths of 608, 1.07 and 195 keV, respectively, with corresponding ratios to the Wigner limit of 85%, 0.15% and 27%.

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Provided that SigmaCalc-2012 describes the angular dependence correctly, then the standard deviation σ = 10.3% is the real uncertainty of a cross-section measurement. This uncertainty is considerably larger than stated in most publications: Berti et al. [10] states an accuracy of 2.5%, Somatri et al. [22] 5%, Feng et al. [21] 2–3%, Plaga et al. [16] 3–4% and Miller Jones et al. [23] 2.6%. Jiang et al. [24,26] gives an uncertainty of 4%, while his data deviate by about 50% from all other data [25] and were excluded as outliers.
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This approach also allows intuitive reading of excitation curves as depth profiles broadened by straggling and resonance width. However, for the 12C(α,α)12C in particular, the excitation curve approach brings poorer depth information because the nuclear reaction resonance shape is asymmetric and broader (Г = 33 keV) [5] than detector resolution (Г = 15 keV) and because excitation curves probe only the energy loss along the inwards path, whereas spectral analyses (either RBS or simulated NRA) probe projectile energy losses in both inwards and outwards paths. In this article, we present a data handling procedure that unites advantages of both C detection methods – NRA sensitivity and RBS intuitive spectrum reading – while keeping the depth information extractable from spectrum analysis.
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Helium elastic scattering from carbon for 30° to 150° in the energy region from 2 to 4.8 MeV
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The differential cross-sections for elastic scattering of $^{4}$ He ions by carbon atoms were measured at scattering angles of 30°, 45°, 60°, 135° and 150° in the energy range from 2 to 4.8 MeV. Up to now mostly data for angles larger than 150° were published in the literature. A thick carbon target with a thin evaporated Cu layer on the surface was used for the measurement. The number of impinging projectiles was obtained from the He ions scattered by the Cu layer assuming Rutherford cross-sections. The carbon scattering cross-sections were then obtained from comparison of measured He energy spectra with the simulated ones. Above 2 MeV all evaluated cross-sections become non-Rutherford. Deviations from Rutherford cross-sections are about 50% for 30° scattering angle and amount up to a factor 30 for 150° scattering angle. The measured experimental cross-sections were compared with the calculated theoretical cross-sections and already published data. Satisfactory agreement was obtained for all measured scattering angles and energies.
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^†: Now at Sandia Corporation, Albuquerque, New Mexico.

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Nuclear Physics

Abstract

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