$0_{^+} $ states of the $^{12}$C nucleus: Faddeev calculation in configurations space

ORAL

Abstract

The $\alpha $-cluster model and Faddeev equations in configuration space are applied to study the $^{12}$C nucleus. The model includes the Ali-Bodmer nuclear potential [1], attractive three-body potential, and takes into account the Coulomb interaction. An s-wave model [2] is adapted and parameters of the three-body potential are chosen to describe the first two 0$_{^+} $ levels of $^{12}$C. The value of the range parameter of the potential is adjusted to reproduce the position of diffraction minimum for the elastic form factor of $^{12}$C. The model assumes a strong distortion of the charge density of $\alpha $ clusters inside the $^{12}$C nucleus. It was found that the most probable configuration of the $\alpha $-clusters in the 0$_1^+$ state corresponds to an equilateral triangle with sides as large as 3.5 fm and in the 0$_2^+ $ state to a linear chain with the values of 2.9 fm and 13.1 fm for each link. Having calculated low-lying levels of $^{12}$C, we found that the contributions of higher partial waves of nuclear interaction to the energy of 3$\alpha $-system are unnaturally large and some states turn to be overbound. Upon applying the method [3] based on the Pade approximants we've got a satisfactory description the 0$_3^+ $ and 0$_4^+ $ states [4]. Additional $0^+$ broad resonance obtained in [3] was not found. 1. S. Ali, A. R. Bodmer, Nucl. Phys. 80, 99 (1966). 2. Z. Papp, et al. Few-Body Systems 30, 31 (2001). 3. C. Kurokawa and K. Kato, Phys. Rev. C76, 021301-1 (2005). 4. http://www.tunl.duke.edu/nucldata/.

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Authors

  • Branislav Vlahovic

    North Carolina Central University

  • R.F. Kelly

    SVT Associates, Department of Material Science and Engineering, Department of Chemistry, University of Florida, Florida International University, WebAssign, North Carolina State University, Broughton High School, Dept.~of Chemistry, Univ.~of Florida, Dept.~of Physics, Univ.~of Florida, National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32306, USA, Center for Superconductivity Research, Dept. of Physics, University of Maryland, College Park, MD, 20742, USA, Dept. of Physics, University of Florida, 32611, USA, Experimentalphysik VI, Center for Electronic Correlations and Magnetism, Institute of Physics, Augsburg, Germany, Physics \& Astronomy, UNC-CH, Chapel Hill, NC, University of North Carolina, Auburn University, University of Virginia, Tech. Univ. Eindhoven, University of Florida, Los Alamos National Labs, University of New Mexico, Advanced Materials Research Institute, University of New Orleans, New Orleans, LA, Department of Physics, University of Florida, UF, NHMFL, FSU / NHMFL, FSU, University of Arkansas, Dept. of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA, Dept. of Physics, University of Florida, Gainesville, FL 32611-8440, USA, Dept. Chemistry Florida State Univeristy, University of Brewen, Tohoku University, Okayama University, Dept of Chemistry, Florida State University, Dept. of Chemistry, Florida State University, National High Magnetic Field Laboratory, Tallahassee, FL, Laboratoire Lois Neel, Grenoble, France, Dept. of Chemistry, Texas A\&M University, Tsinghua Univ., INEL, JINR, Vanderbilt Univ./LBNL, Vanderbilt Univ., SVT Associates, Inc., Department of Chemical Engineering, University of Florida, Department of Materials Science and Engineering, University of Florida, Department of Electrical Engineering, National Central University, Taiwan, University of Miami, North Carolina Central University, University of Missouri Rolla, AB Millimetre, France, Thomas Keating Ltd., UK, Dept. of Physics, Univ. of Florida, Department of Material Science and Engineering University of Florida, Department of Chemistry University of Florida, Department of Chemical Eng. University of Florida, Naval Research Lab, Washington, DC, University of Rajshahi, LENIN All Russian Electrotechnical Institute, Moscow, Russia, Independent Researcher, Argentina

  • Vladimir Suslov