Eur. Phys. J. A (2013) 49: 46
https://doi.org/10.1140/epja/i2013-13046-3

Regular Article - Experimental Physics

Radius of ¹²C in the excited 2 ₂ ⁺ Hoyle state

¹⁹⁸⁷⁶ RRC Kurchatov Institute, 123182, Moscow, Russia
²⁹⁸⁷⁶ Universidad Autónoma del Estado de México, C.P. 50000, Toluca, Mexico
³⁹⁸⁷⁶ Lomonosov Moscow State University, Moscow, Russia

^* e-mail: tbl@uaemex.mx

Received: 27 February 2013
Revised: 14 March 2013
Accepted: 18 March 2013
Published online: 17 April 2013

Abstract

The differential cross sections of the inelastic α + ¹²C scattering leading to the excitation of the short-lived 2 ₂ ⁺ (E _x = 9.84 or 9.6 MeV) state in ¹²C have been analysed within a modified diffraction model. We determined the diffraction radii of ¹²C in this excited state at E _α = 386 and 240 MeV and compared them with the diffraction radius for the 0 ₂ ⁺ (E _x = 7.65 MeV) Hoyle state. We found that the rms radii for the 2 ₂ ⁺ state is 〈R(2 ₂ ⁺ )〉 = 3.07 ± 0.13fm, which agrees well with the rms radius of the 0 ₂ ⁺ , 7.65 MeV Hoyle state and is a factor of 1.3 larger than the rms radius for the ground state of ¹²C. The similarity between the rms radii of the 0 ₂ ⁺ and 2 ₂ ⁺ states provides a strong argument in favor of a hypothesis that the 2 ₂ ⁺ state is the first member of a rotational band based on the 0 ₂ ⁺ Hoyle state.