<p>In the present work, the capture and fission dynamics of <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq9.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">\(Z=\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>Z</mi> <mo>=</mo> </mrow> </math></EquationSource> </InlineEquation> 102 and 103 nuclear systems are investigated. The coupled channel model and the extended Wong model are used to address nuclear capture as well as fission cross-sections of <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq10.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{48}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>48</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Ca<InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq11.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(+\)</EquationSource> <EquationSource Format="MATHML"><math> <mo>+</mo> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq12.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{208}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>208</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Pb (leading to the composite system <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq13.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{256}_{102}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>102</mn> <mn>256</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>No<InlineEquation ID="IEq14"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq2.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="9" /> </InlineMediaObject> <EquationSource Format="TEX">\(^*\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∗</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>) and <InlineEquation ID="IEq15"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq15.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{50}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>50</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Ti<InlineEquation ID="IEq16"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq16.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">\(+^{208}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mo>+</mo> <mn>208</mn> </msup> </math></EquationSource> </InlineEquation>Pb (resulting in <InlineEquation ID="IEq17"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq17.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{258}_{104}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>104</mn> <mn>258</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Rf<InlineEquation ID="IEq18"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq2.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="9" /> </InlineMediaObject> <EquationSource Format="TEX">\(^*\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∗</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>) reactions in reference to the available experimental data. Furthermore, the isotopic analysis of the <InlineEquation ID="IEq19"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq19.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">\(Z =\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>Z</mi> <mo>=</mo> </mrow> </math></EquationSource> </InlineEquation> 102 nucleus is performed by changing the mass of the projectile–target (p–t) nuclei that leads to the synthesis of <InlineEquation ID="IEq20"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq20.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="61" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{252,254,256}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>252</mn> <mo>,</mo> <mn>254</mn> <mo>,</mo> <mn>256</mn> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>No<InlineEquation ID="IEq21"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq2.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="9" /> </InlineMediaObject> <EquationSource Format="TEX">\(^*\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∗</mo> </mmultiscripts> </math></EquationSource> </InlineEquation> composite systems. The study suggests relatively higher cross-sections and compound nucleus formation probability (<InlineEquation ID="IEq22"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq22.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">\(P_{\textrm{CN}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>P</mi> <mtext>CN</mtext> </msub> </math></EquationSource> </InlineEquation>) values for the reactions in which <InlineEquation ID="IEq23"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq10.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{48}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>48</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Ca projectile is involved with <InlineEquation ID="IEq24"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq12.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{208}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>208</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Pb. Also, with a decrease in neutron number for Ca projectile (i.e., <InlineEquation ID="IEq25"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq25.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{48,46,44}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>48</mn> <mo>,</mo> <mn>46</mn> <mo>,</mo> <mn>44</mn> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>Ca with <InlineEquation ID="IEq26"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq12.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{208}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>208</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Pb target) the fission cross-sections drop by 40<InlineEquation ID="IEq27"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq27.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mo>%</mo> </math></EquationSource> </InlineEquation> which otherwise for Pb target (<InlineEquation ID="IEq28"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq28.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="61" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{208,206,204}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>208</mn> <mo>,</mo> <mn>206</mn> <mo>,</mo> <mn>204</mn> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>Pb with <InlineEquation ID="IEq29"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq10.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{48}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>48</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Ca projectile) is 10<InlineEquation ID="IEq30"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq27.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mo>%</mo> </math></EquationSource> </InlineEquation>. Subsequently, an attempt is made to predict the nuclear capture and fission data of <InlineEquation ID="IEq31"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq9.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">\(Z=\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>Z</mi> <mo>=</mo> </mrow> </math></EquationSource> </InlineEquation> 103 (Lr<InlineEquation ID="IEq32"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq2.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="9" /> </InlineMediaObject> <EquationSource Format="TEX">\(^*\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∗</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>) nucleus within the mass domain of 249u to 261u (i.e., <InlineEquation ID="IEq33"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="82" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{249,253,257,261}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>249</mn> <mo>,</mo> <mn>253</mn> <mo>,</mo> <mn>257</mn> <mo>,</mo> <mn>261</mn> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>Lr<InlineEquation ID="IEq34"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq2.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="9" /> </InlineMediaObject> <EquationSource Format="TEX">\(^*\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∗</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>) using various heavy-ion fusion reactions. Along with this, the decay profiles of <InlineEquation ID="IEq35"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq35.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{249-261}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>249</mn> <mo>-</mo> <mn>261</mn> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>Lr<InlineEquation ID="IEq36"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq2.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="9" /> </InlineMediaObject> <EquationSource Format="TEX">\(^*\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>∗</mo> </mmultiscripts> </math></EquationSource> </InlineEquation> composite systems are examined within the framework of the dynamical cluster decay model (DCM) in reference to the fragmentation potential, preformation probability and average total kinetic energy (<InlineEquation ID="IEq37"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq37.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="60" /> </InlineMediaObject> <EquationSource Format="TEX">\(\langle \mathrm TKE\rangle \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">⟨</mo> <mi mathvariant="normal">T</mi> <mi>K</mi> <mi>E</mi> <mo stretchy="false">⟩</mo> </mrow> </math></EquationSource> </InlineEquation>) distribution. Apart from traditional Pb-valley, an additional dip around the entrance channel mass asymmetry of <InlineEquation ID="IEq38"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq38.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(\eta \approx 0.4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>η</mi> <mo>≈</mo> <mn>0.4</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq39"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12043_2025_2967_Article_IEq39.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">\(\eta \approx \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>η</mi> <mo>≈</mo> </mrow> </math></EquationSource> </InlineEquation> 0.2 is also noted for the reactions under consideration.</p>

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Fission and quasi-fission analysis of \(^{252, 254,256}\)No\(^*\) and \(^{249,253,257,261}\)Lr\(^*\) nuclei formed in different reactions

  • Gurjit Kaur,
  • Rajni,
  • Ajay Kumar Rai,
  • Manoj K Sharma

摘要

In the present work, the capture and fission dynamics of \(Z=\) Z = 102 and 103 nuclear systems are investigated. The coupled channel model and the extended Wong model are used to address nuclear capture as well as fission cross-sections of \(^{48}\) 48 Ca \(+\) + \(^{208}\) 208 Pb (leading to the composite system \(^{256}_{102}\) 102 256 No \(^*\) ) and \(^{50}\) 50 Ti \(+^{208}\) + 208 Pb (resulting in \(^{258}_{104}\) 104 258 Rf \(^*\) ) reactions in reference to the available experimental data. Furthermore, the isotopic analysis of the \(Z =\) Z = 102 nucleus is performed by changing the mass of the projectile–target (p–t) nuclei that leads to the synthesis of \(^{252,254,256}\) 252 , 254 , 256 No \(^*\) composite systems. The study suggests relatively higher cross-sections and compound nucleus formation probability ( \(P_{\textrm{CN}}\) P CN ) values for the reactions in which \(^{48}\) 48 Ca projectile is involved with \(^{208}\) 208 Pb. Also, with a decrease in neutron number for Ca projectile (i.e., \(^{48,46,44}\) 48 , 46 , 44 Ca with \(^{208}\) 208 Pb target) the fission cross-sections drop by 40 \(\%\) % which otherwise for Pb target ( \(^{208,206,204}\) 208 , 206 , 204 Pb with \(^{48}\) 48 Ca projectile) is 10 \(\%\) % . Subsequently, an attempt is made to predict the nuclear capture and fission data of \(Z=\) Z = 103 (Lr \(^*\) ) nucleus within the mass domain of 249u to 261u (i.e., \(^{249,253,257,261}\) 249 , 253 , 257 , 261 Lr \(^*\) ) using various heavy-ion fusion reactions. Along with this, the decay profiles of \(^{249-261}\) 249 - 261 Lr \(^*\) composite systems are examined within the framework of the dynamical cluster decay model (DCM) in reference to the fragmentation potential, preformation probability and average total kinetic energy ( \(\langle \mathrm TKE\rangle \) T K E ) distribution. Apart from traditional Pb-valley, an additional dip around the entrance channel mass asymmetry of \(\eta \approx 0.4\) η 0.4 and \(\eta \approx \) η 0.2 is also noted for the reactions under consideration.