Production cross sections of ${}^{243–248}\mathrm{No}$ isotopes in fusion reactions

The production of ${}^{243–254}\mathrm{No}$ is investigated within the framework of the improved quantum molecular dynamical model incorporated with a statistical model. The calculated results of the ${}^{48}\mathrm{Ca}+{}^{208}\mathrm{Pb}$ fusion reaction can reproduce the experimental data well. The impact parameter and the incident energy influence the fusion probability and the lifetime of the neck in fusion reaction process. Furthermore, the evaporation residue cross sections of ${}^{40,44,48}\mathrm{Ca}+{}^{208}\mathrm{Pb}$, ${}^{20}\mathrm{Ne}+{}^{233,235,238}\mathrm{U}$, ${}^{16}\mathrm{O}+{}^{242}\mathrm{Pu}$, and ${}^{26}\mathrm{Mg}+{}^{232}\mathrm{Th}$ reactions are calculated. From investigation, the more neutrons there are in the projectile or target for the same projectile-target combination, the larger evaporation residue cross sections will be. Six unknown isotopes ${}^{243–248}\mathrm{No}$ are predicted with maximum evaporation residue cross sections 0.061 pb, 2.250 pb, 0.005 nb, 0.530 nb, 0.432 nb, and 3.518 nb, respectively. The corresponding fusion reactions are ${}^{208}\mathrm{Pb}({}^{40}\mathrm{Ca},5n){}^{243}\mathrm{No}$, ${}^{208}\mathrm{Pb}({}^{40}\mathrm{Ca},4n){}^{244}\mathrm{No}$, ${}^{208}\mathrm{Pb}({}^{40}\mathrm{Ca},3n){}^{245}\mathrm{No}$, ${}^{208}\mathrm{Pb}({}^{40}\mathrm{Ca},2n){}^{246}\mathrm{No}$, ${}^{233}\mathrm{U}({}^{20}\mathrm{Ne},6n){}^{247}\mathrm{No}$, and ${}^{233}\mathrm{U}({}^{20}\mathrm{Ne},5n){}^{248}\mathrm{No}$, respectively.

Figure 1

The time evolution of binding energies and root-mean-square charge radii for ${}^{48}\mathrm{Ca}$ and ${}^{208}\mathrm{Pb}$ calculated by the ImQMD model with parameter set IQ3a.

Figure 2

(a) The capture cross sections of the ${}^{48}\mathrm{Ca}+{}^{208}\mathrm{Pb}$ reaction. The solid and dashed lines denote the calculation results from the ImQMD and DNS models, respectively. The experimental data (solid circles) are from Ref. [69]. (b) The excitation functions of the $xn$-evaporation channels ($x=2–5$) in the reaction ${}^{48}\mathrm{Ca}+{}^{208}\mathrm{Pb}$. The solid, dashed, dotted, and dash-dotted lines indicate calculated results of the $2n$, $3n$, $4n$, and $5n$ channels by the ImQMD model, respectively. The open circles, open triangles, open diamonds, and open five-pointed stars represent calculated results of the $2n$, $3n$, $4n$, and $5n$ channels by the DNS model, respectively. The solid squares and circles represent the available experimental data for the $2n$ and $3n$ channels [70], respectively. The vertical arrow indicates the position of the corresponding Coulomb barrier.

Figure 3

The fusion probability $g_{\mathrm{fus}}(E_{\mathrm{c}.\mathrm{m}.},b)$ of the different fusion reactions (a) ${}^{48}\mathrm{Ca}+{}^{208}\mathrm{Pb}$, (b) ${}^{20}\mathrm{Ne}+{}^{238}\mathrm{U}$, (c) ${}^{16}\mathrm{O}+{}^{242}\mathrm{Pu}$, and (d) ${}^{26}\mathrm{Mg}+{}^{232}\mathrm{Th}$ at different incident energies with IQ3a parameters as a function of impact parameter $b$. $V_c$ is the static Coulomb barrier.

Figure 4

Time evolution of density profiles for head-on collisions of ${}^{20}\mathrm{Ne}+{}^{238}\mathrm{U}$ at three incident energies (a) $E_{\mathrm{c}.\mathrm{m}.}=115\mathrm{MeV}$, (b) $E_{\mathrm{c}.\mathrm{m}.}=125\mathrm{MeV}$, and (c) $E_{\mathrm{c}.\mathrm{m}.}=135\mathrm{MeV}$.

Figure 5

The calculated excitation functions in the (a) $2n$-evaporation channel, (b) $3n$-evaporation channel, (c) $4n$-evaporation channel, and (d) $5n$-evaporation channel of the reactions ${}^{40,44,48}\mathrm{Ca}+{}^{208}\mathrm{Pb}$, respectively. The solid, dashed, and dash-dotted lines indicate the calculated results for the reactions ${}^{48}\mathrm{Ca}+{}^{208}\mathrm{Pb}$, ${}^{44}\mathrm{Ca}+{}^{208}\mathrm{Pb}$, and ${}^{40}\mathrm{Ca}+{}^{208}\mathrm{Pb}$, respectively. The vertical arrows indicate the positions of the corresponding Coulomb barriers. The statistical errors in the calculations are given by the shaded areas.

Figure 6

The calculated excitation functions in the (a) $4n$-evaporation channel, (b) $5n$-evaporation channel, and (c) $6n$-evaporation channel of the reactions ${}^{20}\mathrm{Ne}+{}^{233,235,238}\mathrm{U}$, respectively. The solid, dashed, and dash-dotted lines indicate the calculated results for the reactions ${}^{20}\mathrm{Ne}+{}^{238}\mathrm{U}$, ${}^{20}\mathrm{Ne}+{}^{235}\mathrm{U}$, and ${}^{20}\mathrm{Ne}+{}^{233}\mathrm{U}$, respectively. The vertical arrows indicate the positions of the corresponding Coulomb barriers. The statistical errors in the calculations are given by the shaded areas.

Figure 7

The static barriers in collisions of ${}^{44}\mathrm{Ca}+{}^{208}\mathrm{Pb}$ and ${}^{20}\mathrm{Ne}+{}^{233}\mathrm{U}$ for the production of nuclei ${}^{248}\mathrm{No}$ at the optimal incident energy.

Figure 8

Heavy nuclei region near No ($Z=102)$ on the nuclear map. The filled and open squares denote the known and unknown nuclei, respectively. Olive, yellow, and red colors show the spontaneous fission, $\alpha$ decay, and ${\beta }^{+}$ decay, respectively. The production cross sections of unknown No isotopes are indicated in the figure.