Predictions of probable projectile-target combinations for the synthesis of superheavy isotopes of Ts

Taking the Coulomb and proximity potential as the interaction barrier, we have studied the production cross section of probable projectile-target combinations for the synthesis of superheavy element ${}^{297}\mathrm{Ts}$. The cold reaction valley of ${}^{297}\mathrm{Ts}$ is studied to identify the possible projectile-target combinations for the synthesis of ${}^{297}\mathrm{Ts}$. The entrance channel Coulomb barrier, the quasifission barrier, and barrier positions for all these combinations are calculated. The fusion probability and survival probability of the excited compound nucleus are evaluated. At energies near and above the Coulomb barrier, the excitation function [capture, fusion, and evaporation residue (ER) cross sections] of these combinations leading to superheavy element (SHE) ${}^{297}\mathrm{Ts}$ is investigated. It is found that the production cross sections of ${}^{297}\mathrm{Ts}$ in cold fusion reactions are very small compared to hot fusion reactions. The combinations ${}^{40}\mathrm{S}+{}^{257}\mathrm{Md}, {}^{42}\mathrm{S}+{}^{255}\mathrm{Md}, {}^{43}\mathrm{Cl}+{}^{254}\mathrm{Fm}, {}^{44}\mathrm{Ar}+{}^{253}\mathrm{Es}, {}^{46}\mathrm{Ar}+{}^{251}\mathrm{Es}, {}^{48}\mathrm{Ca}+{}^{249}\mathrm{Bk}, {}^{50}\mathrm{Ca}+{}^{247}\mathrm{Bk}, {}^{67}\mathrm{Co}+{}^{230}\mathrm{Th}, {}^{68}\mathrm{Ni}+{}^{229}\mathrm{Ac}, {}^{70}\mathrm{Ni}+{}^{227}\mathrm{Ac}$, and ${}^{72}\mathrm{Ni}+{}^{225}\mathrm{Ac}$ are observed to be the most favorable projectile-target pairs for the production of SHE ${}^{297}\mathrm{Ts}$. Our calculated results are compared with experimental data and with other theoretical studies for the reaction ${}^{48}\mathrm{Ca}+{}^{249}\mathrm{Bk}$ leading to ${}^{297}\mathrm{Ts}$, and are in good agreement with experimental observation of Oganessian et al. Furthermore, the ER cross section for the synthesis of isotopes ${}^{291-296}\mathrm{Ts}$ and ${}^{298-299}\mathrm{Ts}$ using ${}^{48}\mathrm{Ca}$ induced reactions are studied. Among these isotopes, the isotope ${}^{298}\mathrm{Ts}$ has larger cross section in the 3n channel using the reaction ${}^{48}\mathrm{Ca}+{}^{250}\mathrm{Bk}$, and ${}^{299}\mathrm{Ts}$ has larger cross section in the 4n channel using the reaction ${}^{48}\mathrm{Ca}+{}^{251}\mathrm{Bk}$. Therefore, our theoretical predictions to produce isotopes of the element Ts will be helpful for future experiments, as the isotopes have not been synthesized so far.

Figure 1

Cold reaction valley plot of superheavy nucleus ${}^{297}\mathrm{Ts}$.

Figure 2

Scattering potential for the combinations found in the region $6<A_P<61$ of the cold valley of ${}^{297}\mathrm{Ts}$.

Figure 3

Scattering potential for the combinations found in the region $62<A_P<87$ of the cold valley of ${}^{297}\mathrm{Ts}$.

Figure 4

Scattering potential for the combinations found in the regions $86<A_P<98$ and $127<A_P<134$ of the cold valley of ${}^{297}\mathrm{Ts}$.

Figure 5

Plot of $P_{CN}$ for the hot fusion reactions at excitation energy $E^{*}=40\mathrm{MeV}$ and for cold fusion reactions at $E^{*}=10\mathrm{MeV}$ vs mass number of the projectile $A_p$ for the SHE ${}^{297}\mathrm{Ts}$.

Figure 6

Evaporation residue cross section for the reactions ${}^{40}\mathrm{S}+{}^{257}\mathrm{Md}, {}^{42}\mathrm{S}+{}^{255}\mathrm{Md}, {}^{43}\mathrm{Cl}+{}^{254}\mathrm{Fm}$, and ${}^{44}\mathrm{Ar}+{}^{253}\mathrm{Es}$ leading to ${}^{297}\mathrm{Ts}$.

Figure 7

Evaporation residue cross section for the reactions, ${}^{46}\mathrm{Ar}+{}^{251}\mathrm{Es}, {}^{48}\mathrm{Ca}+{}^{249}\mathrm{Bk}, {}^{50}\mathrm{Ca}+{}^{247}\mathrm{Bk}$, and ${}^{52}\mathrm{Ca}+{}^{245}\mathrm{Bk}$ leading to ${}^{297}\mathrm{Ts}$.

Figure 8

Evaporation residue cross section for the reactions ${}^{53}\mathrm{Sc}+{}^{244}\mathrm{Cm}, {}^{54}\mathrm{Ti}+{}^{243}\mathrm{Am}, {}^{56}\mathrm{Ti}+{}^{241}\mathrm{Am}$, and ${}^{58}\mathrm{Cr}+{}^{239}\mathrm{Np}$ leading to ${}^{297}\mathrm{Ts}$.

Figure 9

Evaporation residue cross section for the reactions, ${}^{60}\mathrm{Cr}+{}^{237}\mathrm{Np}, {}^{63}\mathrm{Mn}+{}^{234}\mathrm{U}, {}^{64}\mathrm{Fe}+{}^{233}\mathrm{Pa}$, and ${}^{66}\mathrm{Fe}+{}^{231}\mathrm{Pa}$ leading to ${}^{297}\mathrm{Ts}$.

Figure 10

Evaporation residue cross section for the reactions ${}^{67}\mathrm{Co}+{}^{230}\mathrm{Th}, {}^{68}\mathrm{Ni}+{}^{229}\mathrm{Ac}, {}^{70}\mathrm{Ni}+{}^{227}\mathrm{Ac}$, and ${}^{72}\mathrm{Ni}+{}^{225}\mathrm{Ac}$ leading to ${}^{297}\mathrm{Ts}$.

Figure 11

Evaporation residue cross section for the reactions ${}^{80}\mathrm{Ge}+{}^{217}\mathrm{At}, {}^{82}\mathrm{Ge}+{}^{215}\mathrm{At}, {}^{83}\mathrm{As}+{}^{214}\mathrm{Po}$, and ${}^{84}\mathrm{Se}+{}^{213}\mathrm{Bi}$ leading to ${}^{297}\mathrm{Ts}$.

Figure 12

Evaporation residue cross section for the reactions ${}^{86}\mathrm{Se}+{}^{211}\mathrm{Bi}, {}^{87}\mathrm{Br}+{}^{210}\mathrm{Pb}, {}^{88}\mathrm{Br}+{}^{209}\mathrm{Pb}$, and ${}^{89}\mathrm{Br}+{}^{208}\mathrm{Pb}$ leading to ${}^{297}\mathrm{Ts}$.

Figure 13

Evaporation residue cross section for the reactions ${}^{90}\mathrm{Kr}+{}^{207}\mathrm{Tl}, {}^{91}\mathrm{Rb}+{}^{206}\mathrm{Hg}, {}^{92}\mathrm{Kr}+{}^{205}\mathrm{Tl}$, and ${}^{93}\mathrm{Rb}+{}^{204}\mathrm{Mg}$ leading to ${}^{297}\mathrm{Ts}$.

Figure 14

Evaporation residue cross section for the reactions ${}^{48}\mathrm{Ca}{+}^{243}\mathrm{Bk}\to {}^{291}\mathrm{Ts}, {}^{48}\mathrm{Ca}+{}^{244}\mathrm{Bk}{\to }^{292}\mathrm{Ts}, {}^{48}\mathrm{Ca}{+}^{245}\mathrm{Bk}\to {}^{293}\mathrm{Ts}$, and ${}^{48}\mathrm{Ca}{+}^{246}\mathrm{Bk}\to {}^{294}\mathrm{Ts}$.

Figure 15

Evaporation residue cross section for the reactions ${}^{48}\mathrm{Ca}{+}^{247}\mathrm{Bk}{\to }^{295}\mathrm{Ts}, {}^{48}\mathrm{Ca}+{}^{248}\mathrm{Bk}\to {}^{296}\mathrm{Ts}, {}^{48}\mathrm{Ca}{+}^{250}\mathrm{Bk}\to {}^{298}\mathrm{Ts}$, and ${}^{48}\mathrm{Ca}{+}^{251}\mathrm{Bk}\to {}^{299}\mathrm{Ts}$.

Figure 16

The fission barrier $B_f$ as function of excitation energy $E^{*}$ for the $\mathrm{C}\mathrm{N}{}^{291-299}\mathrm{Ts}$.