Energy dependence of the nucleus–nucleus interaction in the 9Be + 12C system and the 9Be reorientation
Introduction
The nucleus–nucleus interaction as a complicated many-body problem is still far from being fully understood. A systematic analysis of experimental data within different theoretical models leads us to the solution of this problem. The well-known theoretical analyses of heavy ion data within the optical model (OM), folding models, coupled channels (CC) and coupled reaction channels (CRC) models provide a lot of useful information about common properties of the nucleus–nucleus interaction, its dependence on the kinetic energy and structure of nuclei. In practice, however, it was found that the parameters of the nucleus–nucleus interaction, determined within some of these models in fitting procedures, have large ambiguities. This often takes place for the OM potential parameters, if the energy range or type of data used in the fitting procedures are limited. We hope that a complex analysis of elastic and inelastic scattering and transfers reaction data within the CRC model in the broad energy range allows for the essential narrowing of the ambiguities of OM potential parameters. These parameters are in general energy-dependent. Many articles in the past were devoted to the study of this dependence (see Refs. [1], [2] and references therein). Recently, interest in the energy dependence of OM potential parameters has increased due to the observation of the threshold anomalies in the elastic scattering of heavy ions (see Refs. [3], [4], [5], [6], [7], [8] and references therein). It was found that this dependence may differ for the interaction of different heavy ions and is tightly bound with their nuclear structure. Therefore the study of the energy dependence for the nuclear interaction of different heavy ions is still of great interest.
This article is devoted to the study of the energy dependence of the OM potential for the 9Be + 12C interaction in a rather broad range of energy Ecm=5.14–90.46 MeV [9], [10], [11], [12], [13], [14], [15], [16], [17]. The CRC model was used in the analysis of the data. The elastic and inelastic scattering, spin reorientation of 9Be and transfer reactions were included in the coupled channel scheme to narrow down the ambiguities in the determination of the OM potential. The energy-dependent OM potential for this interaction, determined in the CRC analysis, can be useful for the study of common properties of the nucleus–nucleus interaction and also for the study of the 9Be(12C,X) reactions, which can be effectively used for the investigation of the nucleus–nucleus interaction for unstable nuclei.
In this article we present new experimental data of elastic scattering of 12C ions on the 9Be nuclei measured with the help of the Kiev U-240 cyclotron at the beam energy 65 MeV in a broad angular range and the data of the inelastic scattering for the transitions to the 1.68 MeV (1/2+) and 2.429 MeV (5/2−) excited states of the 9Be nucleus. The latter data were used in the present article for the determination of deformation parameters. These data together with other sets of experimental data in the broad energy interval Ecm=5.14–90.46 MeV [9], [10], [11], [12], [13], [14], [15], [16], [17] were analyzed within the optical model and CRC methods. The energy dependence of optical potential parameters obtained in the fitting procedure was analyzed with the analytic forms of the Woods–Saxon type using the dispersion relation between the real and imaginary parts of the optical potential.
The present paper is organized as follows. In Section 2 we present the experimental procedure and experimental data for the angular distributions of elastic and inelastic scattering at Elab(12C) = 65 MeV. The results of analysis of all available experimental data at Ecm=5.14–90.46 MeV are presented in Section 3. The energy dependence of the OM potential parameters found in the analysis is discussed in Section 4. A summary and conclusions close our paper.
Section snippets
Experimental procedure
The angular distributions of elastic and inelastic scattering of 12C ions by the 9Be nuclei were measured using the Kiev U-240 cyclotron at the beam energy 65 MeV in the angular range θcm=23.4°−155°. The spread of the beam energy on the target was ∼0.6%. The 9Be target was prepared on a thin nickel foil (∼300μg/cm2). The 9Be layer was equal ∼ 300 μg/cm2. Two ΔE–E spectrometers with ΔE (40 μm) and E (1 mm) silicon detectors and standard electronics were used in the experiment. Two-dimensional E×
Optical model analysis
The Woods–Saxon optical potentialand Coulomb potential of the uniformly charged spherewere used in the OM calculations. Here Ri=ri(AP1/3+AT1/3) (i=V,W,C), AP and AT are the masses of the projectile and target respectively, , μ=APAT/(AP+AT) and k is the wave vector.
Six parameters of the potential (see Eq. (1)) were fitted with code SPI-GENOA [18] to describe the experimental data [9], [10], [11], [12], [13],
Summary and conclusions
The angular distributions of the 9Be(12C,12C) elastic and inelastic scattering for the transitions to the ground state of the 12C nucleus and to the ground and 1.68 MeV (1/2+), 2.429 MeV (5/2−) excited states of the 9Be nucleus were measured at the energy Elab(12C)=65 MeV in a broad angular range.
The data were analyzed within the optical and coupled reaction channels (CRC) models. The optical model (OM) potential of the Woods–Saxon shape with the volume imaginary part was used. The elastic and
Acknowledgements
This work was supported in part by the Polish State Committee for Scientific Research and the Ukrainian State Committee of Science and Technology.
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