<p>The nearside-farside (NF) decomposition method developed originally by Fuller for elastic scattering of a nonidentical nucleus-nucleus system was generalized to study the nuclear rainbow pattern in a symmetric or core-symmetric dinuclear system. It has been shown that the projectile-target identity of an identical system implies a symmetric interchange of the nearside and farside components of elastic scattering amplitude around <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\theta _{\mathrm{c.m.}}=90^\circ $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>θ</mi> <mrow> <mi mathvariant="normal">c</mi> <mo>.</mo> <mi mathvariant="normal">m</mi> <mo>.</mo> </mrow> </msub> <mo>=</mo> <msup> <mn>90</mn> <mo>∘</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>. A similar interchange appears also in a nonidentical core-symmetric system due to elastic transfer of cluster or nucleon between two identical cores. The analysis of the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$^{12}\textrm{C}+^{12}\textrm{C}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>12</mn> </mmultiscripts> <mtext>C</mtext> <msup> <mo>+</mo> <mn>12</mn> </msup> <mtext>C</mtext> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$^{16}\textrm{O}+^{12}\textrm{C}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>16</mn> </mmultiscripts> <mtext>O</mtext> <msup> <mo>+</mo> <mn>12</mn> </msup> <mtext>C</mtext> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$^{13}\textrm{C}+^{12}\textrm{C}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>13</mn> </mmultiscripts> <mtext>C</mtext> <msup> <mo>+</mo> <mn>12</mn> </msup> <mtext>C</mtext> </mrow> </math></EquationSource> </InlineEquation> systems shows how the generalized NF decomposition method reveals the nuclear rainbow pattern in these systems, which can be helpful in probing the real optical potential and nuclear clustering.</p>

Nuclear Rainbow of Core-Symmetric Systems

期刊论文
发表日期：

2026年5月19日

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Nguyen Tri Toan Phuc,
Nguyen Hoang Phuc,
Dao T. Khoa

摘要

The nearside-farside (NF) decomposition method developed originally by Fuller for elastic scattering of a nonidentical nucleus-nucleus system was generalized to study the nuclear rainbow pattern in a symmetric or core-symmetric dinuclear system. It has been shown that the projectile-target identity of an identical system implies a symmetric interchange of the nearside and farside components of elastic scattering amplitude around $\theta _{\mathrm{c.m.}}=90^\circ $ $θ_{c . m .} = 90^{\circ}$ . A similar interchange appears also in a nonidentical core-symmetric system due to elastic transfer of cluster or nucleon between two identical cores. The analysis of the $^{12}\textrm{C}+^{12}\textrm{C}$ $^{12} C +^{12} C$ , $^{16}\textrm{O}+^{12}\textrm{C}$ $^{16} O +^{12} C$ , and $^{13}\textrm{C}+^{12}\textrm{C}$ $^{13} C +^{12} C$ systems shows how the generalized NF decomposition method reveals the nuclear rainbow pattern in these systems, which can be helpful in probing the real optical potential and nuclear clustering.