Improved six-parameter alpha-nucleus optical potentials

doi:10.1016/0370-2693(75)90187-2

Physics Letters B

Volume 55, Issue 1, 20 January 1975, Pages 59-62

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Abstract

We report on two phenomenological six-parameter forms for the alpha-nucleus optical potential which give significantly improved fits to intermediate energy elastic scattering data, reducing $χ^{2} F$ in most instances by a factor of about three, and in several instances giving $χ^{2} F$ of the order of unity.

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G.F. Burdzik et al.
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Cited by (73)

Energy density functional for α+12C elastic scattering
2023, Nuclear Physics A
Citation Excerpt :
From a semi-classical viewpoint, it results from the interference of the far-side scattering trajectories at the same scattering angle. The nuclear rainbow scattering is first observed in the α-particle's elastic scattering measurements on different targets at intermediate energies [1–4]. This kind of scattering reflects the transparency of the nuclear potential (weak absorption process).
In this work, the α-particle elastic scattering from ¹²C is studied using three different ¹²C densities based on the cluster model. This work aims to extend our previous analysis of α+¹²C system to study the energy dependence of the real double folded (DF) potential deduced from the energy density functional (EDF) α-cluster model over a wide energy range. In addition, The EDF α-cluster model is compared with other cluster models to see how reliable is this cluster model for ¹²C nucleus. The two α-cluster models used for comparison are based on the antisymmetrized molecular dynamics (AMD) and a cubic approximation of the nuclear equation of state (liquid drop type density-LD) models. The ¹²C densities based on these cluster models are used in the double folding procedure to obtain α+¹²C real part of the optical model potential (OMP). The imaginary part of the OMP is considered in conventional Wood-Saxon (WS) form. The obtained elastic scattering results show the reliability of the EDF α-cluster model in reproducing the experimental data on equal footing with the other two considered cluster models. Thus the EDF is reliable for studying the ground state α-cluster of the light $4 m α$ -conjugate nuclei.
α-particle elastic scattering from 12C, 16O, 24Mg, and 28Si
2017, Nuclear Physics A
Citation Excerpt :
For the system α + 28Si, the calculated cross sections based on our calculated potential are presented in Fig. 7 with the corresponding best fitting parameters in Table 6. The experimental data for this system are taken from Ref. [20] for the energy 104 MeV, Ref. [25] for energy 166 MeV, Ref. [32] for 120 MeV and Ref. [33] for 240 MeV. General lock shows that the calculated elastic scattering is in a good agreement with experimental data.
The elastic scattering of α-particle is analyzed in terms of the optical model over the energy 104–172.2 MeV for ¹²C, 48.7–146 MeV for ¹⁶O, 50–119 MeV for ²⁴Mg, and 104, 166, 120 and 240 MeV for ²⁸Si. We generate the real part of the optical model potential using the single folding model. In the single folding procedure, the ground state density of the target is folded with an effective density dependent α-nucleon interaction. For the imaginary part, the usual Woods–Saxon form is used. The parameters of the effective density dependent α-nucleon interaction are determined by fitting the experimental data of elastic scattering. The effective interaction's parameters are optimized using the $χ^{2}$ criterion. We reasonably reproduce the elastic scattering cross sections for all studied systems. The obtained results reflect the success of our obtained α-nucleon effective interaction.
On temperature dependence of the optical potential for alpha-particles at low energies
2006, Nuclear Physics A
Within the double folding formalism of the α-nucleus optical potential, used previously for a semi-microscopic analysis of the α-particle elastic scattering on $A \sim 100$ nuclei at energies below 32 MeV, effects due to changes of the nuclear density at a finite temperature are considered. Parameterizations of the double-folding (DF) real potential as well as of a regional phenomenological potential have been used in the study of the $(n, α)$ reaction cross sections for the target nuclei ^92,95,98,100Mo. Taking into account the microscopic DF potentials based on nuclear density distributions, we are able to fully describe the excitation functions of the $(n, α)$ reactions. It is shown that the temperature dependence of the nuclear density distribution function can be an important aspect that has to be included in statistical model calculations even for a nuclear temperature smaller than 2 MeV.
Potentials for the α-40,44,48Ca elastic scattering
2005, Nuclear Physics A
The differential cross sections for the elastic scattering of α particles by ^40,44,48Ca, over a wide range of incident energies, have been analyzed using a deep as well as shallow non-monotonic optical potential and compared with those using a squared Woods–Saxon (SWS) potential. The shallow non-monotonic potential exhibits a volume integral for the real part, characteristic of a molecular potential. The parameters of the SWS potential have also been obtained for α–⁴⁸Ca scattering. The parameters of the shallow non-monotonic potential calculated from the energy-density-formalism provide a satisfactory description of the elastic scattering data. The non-monotonic potentials, both deep and shallow, are found to yield consistently a lower value of the radius parameter of the real potential for ⁴⁸Ca than that for ⁴⁰Ca, in conformity with the observed magnitudes of the root-mean-square radii for the two nuclei. Both the potentials indicate that the semi-magic ⁴⁴Ca behaves differently from the doubly-magic ^40,48Ca, in agreement with the findings from the folding potentials. The dispersion effect arising from the causality principle has been investigated for the shallow non-monotonic α–⁴⁰Ca potential and is found to play a rather minor role in describing the elastic scattering data.
Cluster structure of 40,44,48Ca
2003, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
The α elastic scattering on “non-alpha cluster” nuclei $^{44,48} Ca$ as well as their “alpha cluster” isotope $^{40} Ca$ has been successfully described by a potential derived from a single-folding model, in which the most of the nucleons in a nucleus exist in α-like clusters and the rest, in an unclustered nucleonic configuration. The folding potential does not need any renormalization factor over broad ranges of incident energies. The number of nucleons existing in the α-like clusters in the three Ca-isotopes has been found to be same and deduced as 34.
The interaction between light heavy-ions and what it tells us
1997, Physics Report
Significant progress has been achieved during the last decade in our knowledge and understanding of the optical potential between two light heavy-ions. This has mostly been a consequence of the measurement of accurate and extensive elastic differential cross sections. Some of these data, covering over eight orders of magnitude in cross section, extend to sufficiently large scattering angles that they show remarkable refractive effects which remind one of features of the scattering of alpha particles by nuclei that have been known since the work of Goldberg some twenty years ago. Refractive effects, particularly nuclear rainbows, are evident in $^{12} C +^{12} C$ and $^{16} O +^{16} O$ angular distributions at bombarding energies between 6 and 100 MeV per nucleon. Their angular location and cross section have led to the determination of the gross features of the local optical potentials and in many cases have removed ambiguities in the depths of the real parts of the potentials. The resulting phenomenological potentials are strongly attractive (“deep”), with relatively weak absorption, and depend upon the bombarding energy. The optical model potential for such heavy-ions is no longer simply a way to parameterize scattering data (or perhaps just one of many ways). Ambiguities have been resolved, and a good understanding of the theoretical basis of its features has been attained. The folding model is central to this understanding, coupled with increased insight into the nature of realistic effective nucleon-nucleon interactions. This Report reviews the experimental evidence, its interpretation, and what we have learnt from it. Much of the interpretation becomes especially transparent when couched in the language of semiclassical scattering theory. We summarize this language, as well as the basic features of the theory of the optical model.

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Physics Letters B

Abstract

References (6)

Phys. Rev.

Bull. Am. Phys. Soc.

Phys. Rev. Lett.

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On temperature dependence of the optical potential for alpha-particles at low energies

Potentials for the α-<sup>40,44,48</sup>Ca elastic scattering

Cluster structure of <sup>40,44,48</sup>Ca

The interaction between light heavy-ions and what it tells us