Model for compound nucleus formation in various heavy-ion systems

V. Yu. Denisov

Phys. Rev. C 109, 014607 – Published 8 January 2024

Abstract

The statistical model for the calculation of the compound nucleus formation cross section and the probability of compound nucleus formation in heavy-ion collisions is discussed in detail. Light, heavy, and superheavy nucleus-nucleus systems are considered in this model in the framework of one approach. It is shown that the compound nucleus is formed in competition between passing through the compound-nucleus formation barrier and the quasielastic barrier. The compound-nucleus formation barrier is the barrier separating the system of contacting incident nuclei and the spherical or nearly spherical compound nucleus. The quasielastic barrier is the barrier between the contacting and well-separated deformed ions, which are the same as the incident ions. It is shown that the compound nucleus formation cross section is suppressed when the quasielastic barrier is lower than the compound nucleus formation barrier. The critical value of angular momentum, which limits the compound nucleus formation cross-section values for light and medium-mass ion-ion systems at above-barrier collision energies, is discussed in the model. The suppression of the compound nucleus formation cross section even at small partial waves for very heavy ion-ion systems is obtained in the model. The values of the capture and compound nucleus formation cross sections calculated for various light, heavy, and superheavy nucleus-nucleus systems as well as the probability of the compound nucleus formation for superheavy nuclei agree well with the available experimental data.

Received 27 September 2023
Accepted 8 December 2023

DOI:https://doi.org/10.1103/PhysRevC.109.014607

Physics Subject Headings (PhySH)

Low & intermediate energy heavy-ion reactions Models & methods for nuclear reactions Synthesis of new superheavy elements

Nuclear Physics

Authors & Affiliations

V. Yu. Denisov

INFN Laboratori Nazionali di Legnaro, Legnaro, Italy; Institute for Nuclear Research, Kiev, Ukraine; and Faculty of Physics, Taras Shevchenko National University of Kiev, Kiev, Ukraine

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Issue

Vol. 109, Iss. 1 — January 2024

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Images

Figure 1
(a) The dependencies of the capture $σ_{ℓ}^{c} (E)$ and compound nucleus formation $σ_{ℓ}^{cn} (E)$ partial cross sections on $ℓ$ for the reaction ${}^{28}{Si} + {}^{28}{Si} \to {}^{56}{Ni}$ at collision energy $E = 70$ MeV. (b) The dependence of the probability of the compound-nucleus formation $P_{ℓ}$ on $ℓ$ for the same reaction and collision energy as in (a).
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Figure 2
(a) The dependencies of the capture $σ^{c} (E)$ and compound nucleus formation $σ^{cn} (E)$ cross sections on $E$ for the reaction ${}^{28}{Si} + {}^{28}{Si} \to {}^{56}{Ni}$ . The experimental data for the compound-nucleus formation cross-section are taken from Refs. [123, 124, 125, 126, 127, 128, 129]. (b) The dependence of the total probability of the compound nucleus formation $P (E)$ on $E$ for the same reaction as in (a). (c) The dependence of the critical angular momentum $ℓ_{cr} (E)$ on $E$ for the same reaction as in (a). $L_{fiss \max}$ is the value of the critical angular momentum related to the instability of the nucleus against prompt fission evaluated with the code barfit [100].
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Figure 3
(a) The dependencies of the capture $σ_{ℓ}^{c} (E)$ and compound nucleus formation $σ_{ℓ}^{cn} (E)$ partial cross sections on $ℓ$ for the reaction ${}^{40}{Ar} + {}^{121}{Sb} \to {}^{161}{Tm}$ at $E = 116$ MeV. (b) The dependence of the probability of the compound-nucleus formation $P_{ℓ}$ on $ℓ$ for the same reaction and collision energy as in (a).
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Figure 4
The comparison of the capture $σ^{c} (E)$ and compound nucleus formation $σ^{cn} (E)$ cross sections calculated in the model for the reactions ${}^{84}{Kr} + {}^{65}{Cu} \to {}^{149}{Tb}$ (a), ${}^{40}{Ar} + {}^{109}{Ag} \to {}^{149}{Tb}$ (b), ${}^{40}{Ar} + {}^{121}{Sb} \to {}^{161}{Tm}$ (c), and ${}^{132}{Xe} + {}^{30}{Si} \to {}^{162}{Er}$ (d) with the experimental data [132, 133].
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Figure 5
(a) The dependencies of the capture $σ^{c} (E)$ and compound nucleus formation $σ^{cn} (E)$ cross sections on the collision energy $E$ for the reaction ${}^{50}{Ti} + {}^{208}{Pb} \to {}^{258}{Rf}$ . The experimental data are taken from Refs. [20, 22, 24, 135, 136]. (b) The dependence of the total probability of the compound-nucleus formation, $P (E)$ , on the collision energy $E$ for the same reaction as in (a). The experimental data are taken from Refs. [20, 135, 136].
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Figure 6
(a) The dependence of the difference $B^{qe} - B^{cfn} (0)$ on the number of protons $Z$ in incident nuclei for the symmetric reactions $^{A} Z +^{A} Z \to^{2 A} 2 Z$ . (b) The dependence of the probability $P_{0}^{cn}$ of compound nucleus formation for $ℓ = 0$ on the number of protons $Z$ in incident nuclei in linear scale for the same reactions as in (a). (c) The same as in (b), but in logarithmic scale.
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