Effects of nucleus orientation on transfer process and production of unknown neutron-rich isotopes with $Z=62–75$ in ${}^{204}\mathrm{Hg}+{}^{232}\mathrm{Th}$ based on the dinuclear system model

Within the framework of the dinuclear system model, the contributions of the constituent parts of the driving potentials in different orientation configurations in the ${}^{86}\mathrm{Kr}+{}^{166}\mathrm{Er}$ reaction are investigated. The Coulomb potential plays a predominant role in the change of driving potential among different configurations with mass number $A_1=52–200$. In the region of $A_1<52$ and $A_1>200$, the effects of the nuclear potential increased significantly. This work also studied the multinucleon transfer process of ${}^{204}\mathrm{Hg}+{}^{232}\mathrm{Th}$ in tip-to-tip and side-to-side configurations to produce unknown neutron-rich isotopes with $Z=62–75$. In the ${}^{204}\mathrm{Hg}+{}^{232}\mathrm{Th}$ reaction, the tip-to-tip configuration accounts for the main contribution to produce unknown neutron-rich isotopes with $Z=62–75$ because of the “inverse” quasifission process. The optimal incident energy is 678.1 MeV. Considering the experimental conditions provided by the experiments, there are 29 unknown isotopes whose production rate is greater than one count per day. Especially, the production rates per day of ${}^{179}\mathrm{Ho}, {}^{181,182}\mathrm{Er}, {}^{182,183,184}\mathrm{Tm}, {}^{186}\mathrm{Yb}, {}^{189}\mathrm{Lu}, {}^{191,192}\mathrm{Hf}$, and ${}^{195}\mathrm{Ta}$ are 21, 25, 13, 701, 1217, 29, 94, 29, 102, 29, and 20, respectively. The reaction of ${}^{204}\mathrm{Hg}+{}^{232}\mathrm{Th}$ at 678.1 MeV is a potential candidate to produce new neutron-rich nuclei with $Z=62–75$.

Figure 1

(a) The schematic diagram of the orientation configurations of two prolately deformed colliding nuclei, ${\beta }_2^{\left(i\right)}$ ($i=1,2$) is quadrupole deformation parameters. (b–e) The schematic diagram of tip-to-tip, side-to-side, tip-to-side, and side-to-tip collisions, respectively.

Figure 2

The driving potential of the tip-to-tip (black solid line), side-to-side (red dashed line), tip-to-side (olive short dotted line), and side-to-tip (blue dash-dotted line) configurations in the reaction of ${}^{86}\mathrm{Kr}+{}^{166}\mathrm{Er}$. The arrows indicate the injection points.

Figure 3

The mass distribution of total kinetic energy of the primary binary fragments in the reaction of ${}^{86}\mathrm{Kr}+{}^{166}\mathrm{Er}$ at $E_{\mathrm{c}.\mathrm{m}.}=464$ MeV, (a) and (b) denote tip-to-tip and side-to-side configurations, respectively; dashed and solid lines indicate bombarding energy and injection points, respectively.

Figure 4

(a) The nuclear potential. (b) The Coulomb potential and mass excess of four configurations in the reaction of ${}^{86}\mathrm{Kr}+{}^{166}\mathrm{Er}$.

Figure 5

The charge distributions of the primary reaction fragments in ${}^{86}\mathrm{Kr}+{}^{166}\mathrm{Er}$ at $E_{\mathrm{c}.\mathrm{m}.}=464$ MeV, the experimental data are taken from Ref. [83] denoted by solid red circles. The quadrupole deformation of ${}^{86}\mathrm{Kr}$ and ${}^{166}\mathrm{Er}$ are ${\beta }_2^{\left(1\right)}=0.053$ and ${\beta }_2^{\left(2\right)}=0.238$, respectively.

Figure 6

The same as described in the caption of Fig. 5 but the average results. The experimental data are taken from Ref. [83] denoted by solid red circles. ${\text{av}}_{\text{I}}$ and ${\text{av}}_{\text{II}}$ indicate the average of tip-to-tip and side-to-side configurations and the average of four typical configurations (tip-to-tip, side-to-side, tip-to-side, and side-to-tip), respectively.

Figure 7

The potential energy surface (PES) as functions of Z and N of the fragments in ${}^{204}\mathrm{Hg}+{}^{232}\mathrm{Th}$ reaction of tip-to-tip (a) and side-to-side (b) configurations, the red line represents the minimum value in the PES, and the stars indicate the injection points.

Figure 8

The driving potential in the reaction of ${}^{204}\mathrm{Hg}+{}^{232}\mathrm{Th}$. The downward arrows indicate the projectile and the target, the upward arrows indicate the sub shells which influenced the transfer process.

Figure 9

The interaction time with tip-to-tip (solid line) and side-to-side (dashed line) orientation configurations as a function of the impact parameters in the reactions of ${}^{204}\mathrm{Hg}+{}^{232}\mathrm{Th}$ at $E_{\mathrm{c}.\mathrm{m}.}=1.05V_{\mathrm{C}}, V_{\mathrm{C}}$ is the Bass interaction barrier [84].

Figure 10

Final isotopic production cross sections of isotopes with $Z=62–75$ in the ${}^{204}\mathrm{Hg}+{}^{232}\mathrm{Th}$ reaction at $E_{\mathrm{c}.\mathrm{m}.}=1.05V_{\mathrm{C}}$ (black solid line), $E_{\mathrm{c}.\mathrm{m}.}=1.10V_{\mathrm{C}}$ (red dashed line), $E_{\mathrm{c}.\mathrm{m}.}=1.15V_{\mathrm{C}}$ (blue dash-dotted line), and $E_{\mathrm{c}.\mathrm{m}.}=1.20V_{\mathrm{C}}$ (olive dash-dot-dotted line). The blank symbols denote the new nuclei. The experimental data are taken from Refs. [4] and [5], denoted by solid circles.

Figure 11

The nuclei with $Z=62–75$ on the nuclear map. The filled and open squares denote the known and new nuclei, respectively. Blue, red, black, yellow colors show the ${\beta }^{-}$ decay, ${\beta }^{+}$ decay, stable, and $\alpha$ decay, respectively. The production rate of new isotopes in the ${}^{204}\mathrm{Hg}+{}^{232}\mathrm{Th}$ reaction at 678.1 MeV are indicated in open squares of the figure, $<1$ means the counts per day is less than 1. The beam intensity took $1.3\times {10}^9$ particle/s produced at the ATLAS facility of the Argonne National Laboratory [24]. The thickness of Th target took $6.3\mathrm{mg}/{\mathrm{cm}}^2$ refer to Ref. [89].