Elastic and inelastic scattering of 12C ions at intermediate energies

Hostachy, J-Y.; Buénerd, M.; Chauvin, J.; Lebrun, D.; Martin, P.; Lugol, J.C.; Papineau, L.; Roussel, Pierre; Alamanos, N.; Arvieux, J.; Cerruti, C.

doi:10.1016/0375-9474(88)90514-3

Cited by 76 publications

(29 citation statements)

References 36 publications

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“…III C. Once b max is determined, the nuclear-Coulomb interference effect is fully taken into account, which is one of the advantages of the Glauber formalism. Figure 10 plots the Rutherford ratio of 208 Pb+ 12 C scattering at the incident energy of 200 MeV where experimental data are available [69], and at the incident energy of 1000 MeV. The calculation reproduces the data very well up to 3 degrees.…”

Section: E Comparison With Experimental Datasupporting

confidence: 56%

Extracting nuclear sizes of medium to heavy nuclei from total reaction cross sections

et al. 2016

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Background: Proton and neutron radii are fundamental quantities of atomic nuclei. To study the sizes of short-lived unstable nuclei, there is a need for an alternative to electron scattering. Purpose: The recent paper by Horiuchi et al. [Phys. Rev. C 89, 011601(R) (2014)] proposed a possible way of extracting the matter and neutron-skin thickness of light-to medium-mass nuclei using total reaction cross section, σ R . The analysis is extended to medium to heavy nuclei up to lead isotopes with due attention to Coulomb breakup contributions as well as density distributions improved by paring correlation. Methods:We formulate a quantitative calculation of σ R based on the Glauber model including the Coulomb breakup. To substantiate the treatment of the Coulomb breakup, we also evaluate the Coulomb breakup cross section due to the electric dipole field in a canonical-basis-time-dependent-Hartree-Fock-Bogoliubov theory in the three-dimensional coordinate space. Results: We analyze σ R 's of 103 nuclei with Z = 20, 28, 40, 50, 70, and 82 incident on light targets, 1,2 H, 4 He, and 12 C. Three kinds of Skyrme interactions are tested to generate those wave functions. To discuss possible uncertainty due to the Coulomb breakup, we examine its dependence on the target, the incident energy, and the Skyrme interaction. The proton is a most promising target for extracting the nuclear sizes as the Coulomb excitation can safely be neglected. We find that the so-called reaction radius, a R = √ σ R /π, for the proton target is very well approximated by a linear function of two variables, the matter radius and the skin thickness, in which three constants depend only on the incident energy. We quantify the accuracy of σ R measurements needed to extract the nuclear sizes. Conclusions:The proton is the best target because, once the incident energy is set, its a R is very accurately determined by only the matter radius and neutron-skin thickness. If σ R 's at different incident energies are measured, one can determine both the proton and neutron radii for unstable nuclei as well. The total reaction cross sections calculated in this paper are given as Supplemental Material for the sake of future measurements.

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Section: E Comparison With Experimental Datasupporting

confidence: 56%

Extracting nuclear sizes of medium to heavy nuclei from total reaction cross sections

et al. 2016

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“…Elastic scattering angular distributions for the system 12 C 1 12 C at intermediate energies were analyzed in Ref. [12]. It was shown that the region of radial sensitivity, where the optical potential is probed, is r Ӎ 4 fm.…”

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confidence: 99%

“…(6) and the potential values in the probed radial region, which were unambiguously determined from the elastic data analyses of Refs. [7,12,[14][15][16]. In Fig.…”

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Pauli Nonlocality in Heavy-Ion Rainbow Scattering: A Further Test of the Folding Model

et al. 1997

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Nonlocal interactions are an intrinsically quantum phenomenon. In this work we point out that, in the context of heavy ions, such interactions can be studied through the refractive elastic scattering of these systems at intermediate energies. We show that most of the observed energy dependence of the local equivalent bare potential arises from the exchange nonlocality. The nonlocality parameter extracted from the data was found to be very close to the one obtained from folding models. The effective mass of the colliding, heavy-ion, system was found to be close to the nucleon effective mass in nuclear matter. [S0031-9007(97)02958-X] PACS numbers: 25.70. Bc, 21.30.Fe, 21.65. + f, Of fundamental importance in nuclear physics are the effects arising from the Fermi nature of the nucleons. When calculating interaction potentials between nuclei, these effects translate into a nonlocality. This Pauli nonlocality has been discussed in the context of the nucleon-nucleus scattering [1,2]. A fully microscopic calculation of the nucleus-nucleus interaction is quite complicated and one relies here on procedures such as the resonating-group method [3]. Other methods rely on relating the nucleusnucleus nonlocality to that of the nucleon-nucleus one using folding procedure [4]. However, the prediction of Jackson and Johnson [4], namely, the nonlocality range in the nucleus-nucleus systems, is smaller than that in the nucleon-nucleus one by about the inverse of the reduced mass in the former, was never really subjected to tests. In this Letter we supply such a test through a careful analysis of the elastic scattering of the systems 12 C 1 12 C and 16 O 1 12 C at intermediate energies.Before we set the stage for our analysis of exchange effects in the ion-ion interaction, we first say a few words about this interaction. The effective, one-body interaction that determines the elastic scattering between two nuclei can be written in a schematic way asThe first term, V bare ͑r, r 0 ͒, is usually called the bare interaction. It represents the ground state expectation value of the interaction operator, which contains as basic input the average effective nucleon-nucleon force (G matrix). The nonlocality here is solely due to the Pauli exclusion principle and in what follows we refer to it as the Pauli nonlocality. The second term contains the contribution arising from virtual transitions to intermediate states i (inelastic channels, transfer channels, etc). The corresponding nonlocality arises almost entirely from the polarizations that ensue in the heavy-ion system owing to the propagation in the intermediate channels. This is exemplified by the channel Green's function G ͑1͒ i ͑r, r 0 ; E͒, which contains an explicit energy dependence. This latter contribution is called the Feshbach term and thus we refer to its nonlocality as the Feshbach nonlocality. When confronting theory with experiment one usually relies on a one-body optical model with a local potential. This brings into light immediately the issue of extracting from Eq. (1) a l...

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“…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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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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Elastic and inelastic scattering of 12C ions at intermediate energies

Cited by 76 publications

References 36 publications

Extracting nuclear sizes of medium to heavy nuclei from total reaction cross sections

Extracting nuclear sizes of medium to heavy nuclei from total reaction cross sections

Pauli Nonlocality in Heavy-Ion Rainbow Scattering: A Further Test of the Folding Model

Nonlocal Description of the Nucleus-Nucleus Interaction

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