Possible production of neutron-rich No isotopes

We investigate possible production of neutron-rich isotopes of nobelium. We calculate the production cross sections of ${}^{261–266}\mathrm{No}$ in the multinucleon transfer reactions of the same projectiles (${}^{36}\mathrm{S},{}^{40}\mathrm{Ar},{}^{48}\mathrm{Ca}$, and ${}^{50}\mathrm{Ti}$) and targets (${}^{254}\mathrm{Es}$ and ${}^{248–251}\mathrm{Cf}$) that were used in the previous study for the possible production of neutron-rich isotopes of Md. We find that the production cross sections of neutron-rich No isotopes are about an order of magnitude smaller than those for neutron-rich Md isotopes. By combining the results for the production of neutron-rich No and Md isotopes, we suggest simple expressions which can trace the isotopic trends of the production cross sections of heavy neutron-rich isotopes. The logarithm of the production cross section is proportional to isospin of projectile or target and the $Q$ value.

Figure 1

The production cross sections of neutron-rich isotopes ${}^{258–266}\mathrm{No}$ calculated in the $0n$ evaporation channel as a function of incident energy $E_{\mathrm{c}.\mathrm{m}.}$. Following multinucleon transfer, reactions are calculated: ${}^{36}\mathrm{S}+{}^{254}\mathrm{Es}$ (squares), ${}^{40}\mathrm{Ar}+{}^{254}\mathrm{Es}$ (circles), ${}^{48}\mathrm{Ca}+{}^{254}\mathrm{Es}$ (triangles), and ${}^{50}\mathrm{Ti}+{}^{254}\mathrm{Es}$ (stars). Lines with the same colors are drawn to trace the results of the same isotope of No.

Figure 2

The same as in Fig. 1 but in the $1n$ evaporation channel.

Figure 3

The production cross sections of neutron-rich isotopes ${}^{261–266}\mathrm{No}$ calculated in the $0n$ evaporation channel as a function of incident energy $E_{\mathrm{c}.\mathrm{m}.}$. Following multinucleon transfer, reactions are calculated: ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cf}$ (squares), ${}^{48}\mathrm{Ca}+{}^{249}\mathrm{Cf}$ (circles), ${}^{48}\mathrm{Ca}+{}^{250}\mathrm{Cf}$ (triangles), and ${}^{48}\mathrm{Ca}+{}^{251}\mathrm{Cf}$ (stars). Lines with the same colors are drawn to trace the results for the same isotope of No.

Figure 4

The same as in Fig. 3 but in the $1n$ evaporation channel.

Figure 5

The production cross sections of neutron-rich isotopes ${}^{258–266}\mathrm{No}$ calculated in the $0n$ evaporation channel as a function of incident energy $E_{\mathrm{c}.\mathrm{m}.}$. Following multinucleon transfer, reactions are calculated: ${}^{36}\mathrm{S}+{}^{251}\mathrm{Cf}$ (squares), ${}^{40}\mathrm{Ar}+{}^{251}\mathrm{Cf}$ (circles), ${}^{48}\mathrm{Ca}+{}^{251}\mathrm{Cf}$ (triangles), and ${}^{50}\mathrm{Ti}+{}^{251}\mathrm{Cf}$ (stars). Lines with the same colors are drawn to trace the results for the same isotope of No.

Figure 6

The predicted values of ${log}_{10}{\sigma }_{Z,N}/(N_P-Z_P)$ for ${}^{264}\mathrm{No}$ as a function of $Q$. Panels (a) and (b) show the results in the $0n$ and $1n$ evaporation channels, respectively. The solid lines connect the results of different projectiles but obtained for the same target nucleus. The red dashed lines correspond to $k\approx 0.1$ in Eq. (2).

Figure 7

The same as in Fig. 6 but for the production of ${}^{264}\mathrm{Md}$.

Figure 8

The predicted values of ${log}_{10}{\sigma }_{Z,N}/(N_T-Z_T)$ for ${}^{263–266}\mathrm{No}$ as a function of $Q$. The following reactions are calculated in the $0n$ evaporation channel: (a) ${}^{36}\mathrm{S}+{}^{248–251}\mathrm{Cf}$ and (b) ${}^{40}\mathrm{Ar}+{}^{248–251}\mathrm{Cf}$. The solid lines of the same colors connect the results obtained for the same isotope.

Figure 9

The same as in Fig. 8 but for the reactions (a) ${}^{48}\mathrm{Ca}+{}^{248–251}\mathrm{Cf}$ and (b) ${}^{50}\mathrm{Ti}+{}^{248–251}\mathrm{Cf}$.

Figure 10

The same as in Fig. 8 but for the $1n$ evaporation channel.

Figure 11

The same as in Fig. 9 but for the $1n$ evaporation channel.

Figure 12

The predicted values of ${log}_{10}{\sigma }_{Z,N}/(N_T-Z_T)$ for ${}^{263–265}\mathrm{Md}$ as a function of $Q$ obtained in our previous study. The ${}^{48}\mathrm{Ca}+{}^{249–251}\mathrm{Cf}$ multinucleon transfer reactions are calculated in the (a) $0n$ and (b) $1n$ channels. The solid lines of the same colors connect the results for the same isotope.