Total reaction cross section for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:mn>12</mml:mn></mml:mrow><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow></mml:math>+<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:mrow><mml:mprescript

Treu, W.; Fröhlich, H.; Galster, W.; Dück, P.; Voit, H.

doi:10.1103/physrevc.22.2462

Cited by 49 publications

(34 citation statements)

References 13 publications

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“…where b m 0 b 2 0 ͞2h 2 is a system-independent constant equal to 0.0086 MeV 21 . This linear behavior of the potential with the energy has been particularly observed in a nucleus scattering [18] and the experimentally extracted slope is in agreement with the theoretical b value.…”

Section: Fig 2 the Same Asmentioning

confidence: 99%

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Nonlocal Description of the Nucleus-Nucleus Interaction

et al. 1997

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A parameter-free nonlocal double-folding-inspired interaction is proposed for the nucleus-nucleus systems. Excellent reproductions of elastic scattering differential cross section data were obtained for several systems over a wide range of bombarding energies. Our results should be of value in the description of the scattering of other many-body systems. [S0031-9007(97)05269-1] PACS numbers: 21.30. Fe, 25.70.Bc The mean field interaction between complex quantum many-body systems (nucleus-nucleus, cluster-cluster, etc.) is still an open question in current physics research. The study of this matter is a fundamental step in the understanding of many-body dynamics. In the nucleus-nucleus case, significant progress has been achieved concerning this question during the last decade [1], as a consequence of the measurement of accurate and extensive elastic scattering data at intermediate energies. Nuclear rainbow scattering, first observed in a systems [2][3][4] and later in light heavy ions [5][6][7], probes the nucleus-nucleus potential not only at the surface region but also at smaller distances, and ambiguities in the real part of the potentials have been removed. The resulting phenomenological interactions have significant dependence upon the bombarding energies. Some theoretical models have been developed to account for this energy dependence through realistic mean field potentials. Nowadays, the most successful models seem to be those based on the DDM3Y interaction [8][9][10] which is an improvement of the originally energyindependent double-folding potential [11]. But, in order to fit the data, the density-and energy-dependent DDM3Y potential needs a renormalization factor which besides being system dependent [1,12] is still slightly energy dependent [1].In this Letter we show, by an extensive description of elastic scattering data using an optical integro-differential equation, that the dependence on the bombarding energy of the real bare potential is mostly due to the intrinsically nonlocal nature of the effective one-body interaction. The real bare potential (by bare we mean the average, mean field, interaction with no coupled channels effects) is constructed using the folding model. It contains no adjustable parameters and is energy independent. The absorptive part is taken to be a three parameters WoodsSaxon interaction. We also supply a simple approach to obtain the local-equivalent energy-dependent potential.Before we set the stage for the analysis of elastic scattering data, we first describe our theoretical model.When dealing with nonlocal interactions, one is required to solve the integro-differential equationwhere, on physical grounds [13], the kernel function is taken to be symmetric: U͑ R, R 0 ͒ U͑ R 0 , R͒. We take for U͑ R, R 0 ͒ the following form motivated by the physics problem at handIn our analysis, the Coulomb interaction, V C ͑R͒, was obtained using an expression for the double sharp cutoff folded potential [14] and the local energy-dependent imaginary potential, W ͑R, E͒, was taken t...

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Section: Fig 2 the Same Asmentioning

confidence: 99%

“…The data are from Refs. [5,[21][22][23][24]. The solid lines correspond to nonlocal optical model calculations using an energyindependent and parameter-free real potential (see text).…”

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confidence: 99%

Nonlocal Description of the Nucleus-Nucleus Interaction

et al. 1997

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“…This is illustrated in Fig.2, where we compare the fusion probabilities computed with definitions (8) Our main goal is to investigate the 12 C+ 12 C fusion cross section. However, we first assess the accuracy of the model with elastic cross sections, which are well known experimentally at energies close to the Coulomb barrier [23]. The elastic cross sections are computed from the scattering matrices by using standard formulae [16].…”

Section: -P4mentioning

confidence: 99%

“…The present folding model is first applied to 12 C+ 12 C elastic scattering at energies around the Coulomb barrier, where experimental data are available [23]. These data can be used to assess the reliability of the model, and hence of the fusion cross sections.…”

Section: Elastic Scattering and Fusionmentioning

confidence: 99%

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Role of the Hoyle state in the¹²C+¹²C fusion at low energies

Descouvemont

Assunção

2014

EPJ Web of Conferences

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Abstract.The 12 C+ 12 C fusion reaction is investigated in a multichannel folding model, using the density-dependent DDM3Y nucleon-nucleon interaction. The 12 C(0states are included, and their densities are taken from a microscopic cluster calculation. Absorption to fusion channels is simulated by a short-range imaginary potential and the model does not contain any fitting parameter. We compute elastic and fusion cross sections simultaneously. The role of 12 C+ 12 C inelastic channels and, in particular, of the 12 C(02 ) channel involving the Hoyle state is important even at low energies.

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