Effects of entrance channels on the evaporation residue yields in reactions leading to the ${}^{220}\mathrm{Th}$ compound nucleus

The evaporation residue yields from the compound nuclei ${}^{220}\mathrm{Th}$ formed in the ${}^{16}\mathrm{O}+{}^{204}\mathrm{Pb}, {}^{40}\mathrm{Ar}+{}^{180}\mathrm{Hf}, {}^{82}\mathrm{Se}+{}^{138}\mathrm{Ba}$, and ${}^{124}\mathrm{Sn}+{}^{96}\mathrm{Zr}$ reactions are analyzed to study the entrance channel effects by comparison of the capture, fusion, and evaporation residue cross sections calculated by the combined dinuclear system (DNS) and advanced statistical models. The difference between evaporation residue (ER) cross sections can be related to the stages of compound nucleus formation and/or its survival against fission. The sensitivity of both stages in the evolution of the DNS up to the evaporation residue formation to the angular momentum of DNS is studied. The difference between fusion excitation functions is explained by the hindrance to complete fusion due to the larger intrinsic fusion barrier $B_{\mathrm{fus}}^{*}$ for the transformation of the DNS into a compound nucleus and the increase of the quasifission contribution due to the decreasing of the quasifission barrier $B_{\mathrm{qf}}$ as a function of the angular momentum. The largest value of the ER residue yields in the very mass asymmetric ${}^{16}\mathrm{O}+{}^{204}\mathrm{Pb}$ reaction is related to the large fusion probability and to the relatively low threshold of the excitation energy of the compound nucleus. Due to the large threshold of the excitation energy (35 MeV) of the ${}^{40}\mathrm{Ar}+{}^{180}\mathrm{Hf}$ reaction, it produces ER yields less than the almost mass symmetric ${}^{82}\mathrm{Se}+{}^{138}\mathrm{Ba}$ reaction having the lowest threshold value (12 MeV).

Figure 1

The total energy (solid curve) and nucleus-nucleus potential (dashed and dot-dashed curves) as a function of the relative distance $R$ between centers of mass of colliding nuclei calculated for the ${}^{82}\mathrm{Se}+{}^{138}\mathrm{Ba}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}=235$ MeV (left panel) and $E_{\mathrm{c}.\mathrm{m}.}=245$ MeV (right panel) with the initial orbital angular momenta $L_0=85\hslash$ and $25\hslash$, respectively. The left panel demonstrates a capture event when the outgoing path of the total energy is trapped in a potential well while the right panel shows a deep inelastic collision with an outgoing path to infinity after dissipation of a sufficient part of the kinetic energy of the relative motion. The dashed and dot-dashed lines are nucleus-nucleus potentials $\left[V\right(R\left)\right]$ for the ingoing and outgoing paths, calculated for the initial and final values of $L$.

Figure 2

Potential energy surface calculated as a function of the relative distance between the interacting nuclei and charge number ($Z$) of a fragment for reactions leading to the ${}^{220}\mathrm{Th}$ CN. Arrow (a) shows the capture path in the entrance channel; arrow (b) shows the direction of the complete fusion by multinucleon transfer from the light nucleus to the heavy one; (c) and (d) arrows show the directions of decay of the DNS into mass symmetric and asymmetric quasifission channels, respectively.

Figure 3

Driving potential of the DNS leading to formation of the ${}^{220}\mathrm{Th}$ compound nucleus. The barriers $B_{\mathrm{fus}}^{*}$ ($B_{\mathrm{sym}}^{*}$) pose hindrance to the evolution of the DNS to complete fusion (to reach its symmetric configurations) in the case of the ${}^{82}\mathrm{Se}+{}^{138}\mathrm{Ba}$ reaction ($Z=34$). The curve of the driving potential is obtained for the spherical shape of ${}^{138}\mathrm{Ba}$ and the value ${\alpha }_{\mathrm{Se}}={45}^{\circ }$ of the orientation angle of the projectile nucleus relative to the beam direction at $\ell =0$.

Figure 4

Dependence of the quasifission barrier on the angular momentum of the DNS formed in the ${}^{40}\mathrm{Ar}+{}^{180}\mathrm{Hf}$ reaction.

Figure 5

Comparison of the capture excitation functions calculated in this work for the ${}^{16}\mathrm{O}+{}^{204}\mathrm{Pb}$ (solid line), ${}^{40}\mathrm{Ar}+{}^{180}\mathrm{Hf}$ (dashed), ${}^{82}\mathrm{Se}+{}^{138}\mathrm{Ba}$ (dot-dashed), and ${}^{124}\mathrm{Sn}+{}^{96}\mathrm{Zr}$ (dot-dot-dashed) reactions.

Figure 6

Comparison of the fusion excitation functions calculated in this work for the ${}^{16}\mathrm{O}+{}^{204}\mathrm{Pb}$ (solid line), ${}^{40}\mathrm{Ar}+{}^{180}\mathrm{Hf}$ (dashed), ${}^{82}\mathrm{Se}+{}^{138}\mathrm{Ba}$ (dot-dashed), and ${}^{124}\mathrm{Sn}+{}^{96}\mathrm{Zr}$ (dot-dot-dashed) reactions.

Figure 7

The fusion probability $P_{\mathrm{CN}}={\sigma }_{\mathrm{fus}}/{\sigma }_{\mathrm{cap}}$ calculated for the ${}^{16}\mathrm{O}+{}^{204}\mathrm{Pb}, {}^{40}\mathrm{Ar}+{}^{180}\mathrm{Hf}, {}^{82}\mathrm{Se}+{}^{138}\mathrm{Ba}$, and ${}^{124}\mathrm{Sn}+{}^{96}\mathrm{Zr}$ reactions as a function of the CN excitation energy.

Figure 8

Partial capture cross section of the ${}^{40}\mathrm{Ar}+{}^{180}\mathrm{Hf}$ reaction.

Figure 9

Partial capture cross section of the ${}^{82}\mathrm{Se}+{}^{138}\mathrm{Ba}$ reaction.

Figure 10

Driving potential for the dinuclear system formed in the ${}^{82}\mathrm{Se}+{}^{138}\mathrm{Ba}$ reaction versus the charge number of its fragment for different values of angular momentum $\ell$.

Figure 11

The fusion probability $P_{\mathrm{CN}}(E_{\mathrm{CN}}^{*},\ell )={\sigma }_{\mathrm{fus}}(E_{\mathrm{CN}}^{*},\ell )/{\sigma }_{\mathrm{cap}}(E_{\mathrm{CN}}^{*},\ell )$ calculated for the ${}^{82}\mathrm{Se}+{}^{138}\mathrm{Ba}$ reaction as a function of the CN excitation energy and angular momentum.

Figure 12

Comparison between the theoretical excitation functions of the evaporation residues formed after neutron emission only in the ${}^{16}\mathrm{O}+{}^{204}\mathrm{Pb}$ (dashed line), ${}^{40}\mathrm{Ar}+{}^{180}\mathrm{Hf}$ (dot-dashed line), ${}^{82}\mathrm{Se}+{}^{138}\mathrm{Ba}$ (solid line), and ${}^{124}\mathrm{Sn}+{}^{96}\mathrm{Zr}$ (dotted line) reactions.

Figure 13

Comparison between the excitation functions of the total evaporation residues (dot-dashed line) and only neutron emission (dashed line) channels calculated for the ${}^{16}\mathrm{O}+{}^{204}\mathrm{Pb}$ reaction with the experimental data (diamonds) [3] of the total neutron emission channels. The solid line shows the fusion excitation function calculated in this work.

Figure 14

The charge distribution of the DNS fragments as a function of the interaction time for the ${}^{40}\mathrm{Ar}+{}^{180}\mathrm{Hf}$ reaction.

Figure 15

The same as in Fig. 12 but for the total evaporation residues.

Figure 16

The survival probability $W_{\mathrm{sur}}(E_{\mathrm{CN}}^{*},\ell )$ calculated for the ${}^{82}\mathrm{Se}+{}^{138}\mathrm{Ba}$ reaction as a function of the CN excitation energy and angular momentum.

Figure 17

Comparison between the excitation functions of $2n$ (dotted line), $3n$ (thin dashed line), $4n$ (thin solid line), and $5n$ (thin dot-dashed line) ER channels calculated in this work for the ${}^{40}\mathrm{Ar}+{}^{180}\mathrm{Hf}$ reaction with the ones measured in the experiment [25] for the $3n$ (squares), $4n$ (circles), and $5n$ (triangles) ER channels. The excitation functions of the total evaporation residues (thick solid line) and of only the neutron emission (thick dot-dashed line) channels, as well as of complete fusion (thick dashed line) calculated in this work are presented.

Figure 18

Comparison between the excitation functions of $2n$ (thin solid line), $3n$ (thin dot-dashed line), $4n$ (thin dot-dot-dashed line), and $5n$ (thin dotted line) ER channels calculated in this work for the ${}^{82}\mathrm{Se}+{}^{138}\mathrm{Ba}$ reaction with the ones measured in the experiment [26] for the $3n$ (circles), $4n$ (triangles), and $5n$ (diamonds) ER channels. The excitation functions of the total evaporation residues (thick solid line) and of only the neutron emission (thick dot-dashed line) channels, as well as of complete fusion (thick dashed line) calculated in this work are presented.

Figure 19

Comparison between the excitation functions of $1n$ (thin dotted line), $2n$ (solid line), $3n$ (thin dot-dashed line), $4n$ (thin dot-dot-dashed line), and $5n$ (thin dashed line) ER channels calculated in this work for the ${}^{124}\mathrm{Sn}+{}^{96}\mathrm{Zr}$ reaction with the ones measured in the experiment [2] for the $1n$ (open circles), $2n$ (filled circles), $3n$ (open squares), $4n$ (filled triangles), and $5n$ (open triangles) ER channels. The excitation functions of the total evaporation residues (thick solid line) and of only the neutron emission (thick dot-dashed line) channels, as well as of complete fusion (thick dashed line) calculated in this work are presented.

Figure 20

Partial fusion cross section of the ${}^{82}\mathrm{Se}+{}^{138}\mathrm{Ba}$ reaction.

Figure 21

Partial fusion cross section of the ${}^{124}\mathrm{Sn}+{}^{96}\mathrm{Zr}$ reaction.