<p>This study aims to investigate the nature of the hindrance to complete fusion in heavy-ion collisions at energies near the Coulomb barrier. The research focuses on how the competition between compound nucleus (CN) formation and the quasifission process is influenced by the mass asymmetry of the entrance channel and the geometric alignment of the colliding nuclei. The formation and breakup of the dinuclear system (DNS) were calculated using the DNS model as a function of orientation angles and orbital angular momentum. The model incorporates a transport master equation to describe nucleon transfer from the light fragment to the heavy one, accounting for excitation energy <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varvec{E}_{\varvec{Z}}^{\varvec{*}}\)</EquationSource> </InlineEquation> and the potential energy surface (PES). The theoretical mass distributions were compared with experimental data for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(^{\varvec{48}}\)</EquationSource> </InlineEquation>Ca +<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(^{\varvec{168}}\)</EquationSource> </InlineEquation>Er (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\varvec{E}_{{\textbf {lab}}}=\varvec{194}\)</EquationSource> </InlineEquation> MeV) and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(^{\varvec{12}}\)</EquationSource> </InlineEquation>C +<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(^{\varvec{204}}\)</EquationSource> </InlineEquation>Pb (<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\varvec{E}_{{\textbf {lab}}}=\varvec{73} \)</EquationSource> </InlineEquation> MeV) reactions, leading to the formation of <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(^{\varvec{216}}\)</EquationSource> </InlineEquation> Ra with the same excitation energy <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\approx \)</EquationSource> </InlineEquation> 40 MeV. In these data quasifission yields were extracted by separating the fusion-fission component (<InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\varvec{Y}_{{\textbf {FF}}}\)</EquationSource> </InlineEquation>) from total binary yields using multi-Gaussian fitting. Quasifission yields are strongly dependent on the relative orientation of the symmetry axes. Elongated tip-to-tip configurations (small orientation angles) significantly favor quasifission over CN formation due to a higher intrinsic fusion barrier <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(\varvec{B}_{{\textbf {fus}}}^{\varvec{*}}\)</EquationSource> </InlineEquation>. In the less mass asymmetric <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(^{\varvec{48}}\)</EquationSource> </InlineEquation>Ca +<InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(^{\varvec{168}}\)</EquationSource> </InlineEquation>Er reaction, the quasifission yield is approximately one order of magnitude higher than in the highly asymmetric <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(^{\varvec{12}}\)</EquationSource> </InlineEquation>C +<InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(^{\varvec{204}}\)</EquationSource> </InlineEquation>Pb system. While the <InlineEquation ID="IEq16"> <EquationSource Format="TEX">\(^{\varvec{12}}\)</EquationSource> </InlineEquation>C-induced reaction leads to fusion with near-unity probability, the <InlineEquation ID="IEq17"> <EquationSource Format="TEX">\(^{\varvec{48}}\)</EquationSource> </InlineEquation>Ca +<InlineEquation ID="IEq18"> <EquationSource Format="TEX">\(^{\varvec{168}}\)</EquationSource> </InlineEquation>Er system is dominated by quasifission. The results confirm that the hindrance to complete fusion is primarily driven by the quasifission process, which acts as a major drain on the fusion channel. The relative alignment of deformed nuclei is a decisive factor, particularly in more symmetric entrance channels where elongated configurations act as a bottleneck for fusion. These findings provide critical insights for optimizing the synthesis of superheavy elements by identifying the most favorable collision geometries and mass asymmetries.</p>

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The role of orientation angles of colliding nuclei on the hindrance to complete fusion

  • Elzod Khusanov,
  • Avazbek Nasirov

摘要

This study aims to investigate the nature of the hindrance to complete fusion in heavy-ion collisions at energies near the Coulomb barrier. The research focuses on how the competition between compound nucleus (CN) formation and the quasifission process is influenced by the mass asymmetry of the entrance channel and the geometric alignment of the colliding nuclei. The formation and breakup of the dinuclear system (DNS) were calculated using the DNS model as a function of orientation angles and orbital angular momentum. The model incorporates a transport master equation to describe nucleon transfer from the light fragment to the heavy one, accounting for excitation energy \(\varvec{E}_{\varvec{Z}}^{\varvec{*}}\) and the potential energy surface (PES). The theoretical mass distributions were compared with experimental data for \(^{\varvec{48}}\) Ca + \(^{\varvec{168}}\) Er ( \(\varvec{E}_{{\textbf {lab}}}=\varvec{194}\) MeV) and \(^{\varvec{12}}\) C + \(^{\varvec{204}}\) Pb ( \(\varvec{E}_{{\textbf {lab}}}=\varvec{73} \) MeV) reactions, leading to the formation of \(^{\varvec{216}}\) Ra with the same excitation energy \(\approx \) 40 MeV. In these data quasifission yields were extracted by separating the fusion-fission component ( \(\varvec{Y}_{{\textbf {FF}}}\) ) from total binary yields using multi-Gaussian fitting. Quasifission yields are strongly dependent on the relative orientation of the symmetry axes. Elongated tip-to-tip configurations (small orientation angles) significantly favor quasifission over CN formation due to a higher intrinsic fusion barrier \(\varvec{B}_{{\textbf {fus}}}^{\varvec{*}}\) . In the less mass asymmetric \(^{\varvec{48}}\) Ca + \(^{\varvec{168}}\) Er reaction, the quasifission yield is approximately one order of magnitude higher than in the highly asymmetric \(^{\varvec{12}}\) C + \(^{\varvec{204}}\) Pb system. While the \(^{\varvec{12}}\) C-induced reaction leads to fusion with near-unity probability, the \(^{\varvec{48}}\) Ca + \(^{\varvec{168}}\) Er system is dominated by quasifission. The results confirm that the hindrance to complete fusion is primarily driven by the quasifission process, which acts as a major drain on the fusion channel. The relative alignment of deformed nuclei is a decisive factor, particularly in more symmetric entrance channels where elongated configurations act as a bottleneck for fusion. These findings provide critical insights for optimizing the synthesis of superheavy elements by identifying the most favorable collision geometries and mass asymmetries.