Production of unknown Fl isotopes in proton evaporation channels within the dinuclear system model

The production of Fl isotopes in proton evaporation channels is investigated systematically within the dinuclear system model. Because the proton evaporation is the easiest for Mc isotopes among the isotopes around $Z=114$, one can synthesize Fl isotopes in the proton evaporation channel. The calculated ER cross sections by the DNS model reproduce the experimental data very well. The dependence of the production cross sections on projectile isospin in capture, fusion, and survival processes in ${}^{32,34,36}\mathrm{S}+{}^{255}\mathrm{Es}$ reactions is studied. The capture cross sections and survival probability in the ${}^{36}\mathrm{S}+{}^{255}\mathrm{Es}$ reaction are the largest, while the fusion probability in the ${}^{32}\mathrm{S}+{}^{255}\mathrm{Es}$ reaction is the highest. The reaction ${}^{48}\mathrm{Ca}+{}^{244}\mathrm{Am}$ is a promising candidate to synthesize the unknown isotope ${}^{290}\mathrm{Fl}$ with the maximum ER cross section of 4.07 pb in the $p1n$ evaporation channel. Another new isotope ${}^{291}\mathrm{Fl}$ can be produced in the ${}^{54}\mathrm{Cr}+{}^{239}\mathrm{Pa}$ reaction and the production cross section is estimated to be 0.11 pb.

Figure 1

The ratios $R=B_{\text{f}}/(B_{\text{p}}+V_{\text{c}})$ of nuclei ${}^{286\text{–}297}\mathrm{Nh}$, ${}^{286\text{–}297}\mathrm{Fl}$, ${}^{285\text{–}296}\mathrm{Mc}$, and ${}^{286\text{–}297}\mathrm{Lv}$ are denoted by the squares, circles, pentagons, and triangles, respectively.

Figure 2

Comparisons of calculated ER cross sections with the experimental data in ${}^{48}\mathrm{Ca}+{}^{243}\mathrm{Am}$, ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cm}$, ${}^{48}\mathrm{Ca}+{}^{249}\mathrm{Bk}$, and ${}^{48}\mathrm{Ca}+{}^{249}\mathrm{Cf}$ reactions. The solid, dashed, and dash-dotted lines represent the calculated ER cross sections in $2n$, $3n$, and $4n$ evaporation channels, respectively. The triangles, squares, circles represent the experimental data with error bars in $2n$, $3n$, and $4n$ evaporation channels, respectively. The experimental data are obtained from Refs. [24, 25, 60, 61].

Figure 3

(a) The $V+Q$ values in ${}^{32}\mathrm{S}+{}^{255}\mathrm{Es}$, ${}^{34}\mathrm{S}+{}^{255}\mathrm{Es}$, and ${}^{36}\mathrm{S}+{}^{255}\mathrm{Es}$ reactions. The positions of Coulomb barrier are marked with open circle, triangle, and diamond. (b) The calculated capture cross sections in ${}^{32}\mathrm{S}+{}^{255}\mathrm{Es}$, ${}^{34}\mathrm{S}+{}^{255}\mathrm{Es}$, and ${}^{36}\mathrm{S}+{}^{255}\mathrm{Es}$ reactions, denoted by the solid, dashed, and dotted lines, respectively.

Figure 4

(a) The driving potential as a function of the mass asymmetry $\eta$ in ${}^{32}\mathrm{S}+{}^{255}\mathrm{Es}$, ${}^{34}\mathrm{S}+{}^{255}\mathrm{Es}$, and ${}^{36}\mathrm{S}+{}^{255}\mathrm{Es}$ reactions, represented by solid, dashed, and dotted lines, respectively. (b) The fusion probability in ${}^{32}\mathrm{S}+{}^{255}\mathrm{Es}$, ${}^{34}\mathrm{S}+{}^{255}\mathrm{Es}$, and ${}^{36}\mathrm{S}+{}^{255}\mathrm{Es}$ reactions.

Figure 5

(a) The survival probability in ${}^{32}\mathrm{S}+{}^{255}\mathrm{Es}$, ${}^{34}\mathrm{S}+{}^{255}\mathrm{Es}$, and ${}^{36}\mathrm{S}+{}^{255}\mathrm{Es}$ reactions, denoted by solid, dashed, and dash-dotted lines, respectively. The $p1n$, $p2n$, $p3n$, and $p4n$ channels are indicated by the black, red, blue, and pink lines, respectively. (b) The fission barrier of compound nucleus formed by reactions ${}^{32}\mathrm{S}+{}^{255}\mathrm{Es}$, ${}^{34}\mathrm{S}+{}^{255}\mathrm{Es}$, and ${}^{36}\mathrm{S}+{}^{255}\mathrm{Es}$ are represented by solid, dashed, and dash-dotted lines, respectively.

Figure 6

Comparisons of calculated ER cross sections in ${}^{36}\mathrm{S}+{}^{255}\mathrm{Es}$, ${}^{48}\mathrm{Ca}+{}^{243}\mathrm{Am}$, ${}^{48}\mathrm{Ca}+{}^{244}\mathrm{Am}$, and ${}^{54}\mathrm{Cr}+{}^{239}\mathrm{Pa}$ reactions. Solid, dashed, dash-dotted, and dotted lines represent $p1n$, $p2n$, $p3n$, and $p4n$ evaporation channels, respectively.