Charge distributions of Ra recoil ions produced in ${}^{12}\mathrm{C}+\mathrm{Pb}$ fusion-evaporation reactions

Charge state distributions of the Ra recoil ions produced in the ${}^{12}\mathrm{C}+\text{Pb}$ fusion-evaporation reactions have been obtained by measuring their yields as a function of the high voltage applied to an electrostatic deflector. Well-defined two-humped yield curves for evaporation residues (ERs) were observed. Such observations can be explained by the different sets of charge states inherent in Ra recoil ions. These charge sets correspond to the equilibrated and nonequilibrated components, as earlier observed for evaporation residues produced in different reactions. The main parameters of the distributions (mean charge values, widths, and relative intensities) for both components have been estimated using Monte Carlo simulations of the transmission of the Ra recoil ions through the deflector. For the equilibrated component the values of the mean charge and width are close to those given by different empirical systematics. For the nonequilibrated component these parameters have been obtained for the first time. The additional nonequilibrated ionization is presumably due to the formation of inner shell vacancies produced by the internal conversion of nuclear isomeric transitions of ERs. Nonequilibrated charge parameters obtained for Ra recoil ions are compared to similar available experimental data and some theoretical predictions.

Figure 1

(a) Measured charge state distribution of ${}^{153}\mathrm{Dy}$ ERs produced in the fusion-evaporation reaction and emerging from the target (histogram) and observed after a carbon reset foil (open circles) as compared to Gaussian approximations according to the parametrization [3, 4, 7, 8, 9] (five different lines of corresponding colors). (b) Charge state distribution of ${}^{149}\mathrm{Dy}$ ERs emerging from a La target (full circles) [11]. In both panels, one- or two-component fits to the data are shown, as obtained with log-normal functions (thick solid lines). For the two-component fits the equilibrated and nonequilibrated components are shown by dotted violet lines and by brown dash-dotted lines, respectively.

Figure 2

The yield of ERs produced in the ${}^{16}\mathrm{O}+{}^{197}\mathrm{Au}$ reaction as a function of a high voltage applied to the deflector [18] (full circles). Our fits to the data with the two- and three-component log-normal function, corresponding to the two- and three-component charge distributions are shown by dotted line and solid line, respectively. The decomposition of both fits is also shown by dash-dotted and dashed lines for the equilibrated and nonequilibrated components, respectively.

Figure 3

Several examples of $\alpha$-spectra collected in our measurements using ${}^{208}\mathrm{Pb}$ target at the 90- and 69-MeV beam energy, panels (a) and (b), respectively; ${}^{206}\mathrm{Pb}$ target at the 90 MeV beam energy, panel (c); and ${}^{204}\mathrm{Pb}$ target at the 69-MeV beam energy, panel (d). Ra isotopes and their daughters identified according to the $\alpha$-particle energies are indicated.

Figure 4

The measured transmission efficiency for ${}^{210}\mathrm{Fr}$ produced in the ${}^{197}\mathrm{Au}({}^{18}\mathrm{O},5n$) reaction as a function of the electric field strength [24, 28] (large filled circles with error bars). (a) Results of the two-component log-normal function fit to the measurements are shown by solid line with the decomposition into the equilibrated and nonequilibrated components (dashed and dash-dotted lines, respectively). (b) Results of the simulation using the equilibrated charges only and three-component charge distribution [28] with the mean values and standard deviations expressed through those for the equilibrated charge $Q_{\mathrm{m}}^{\mathrm{eq}}$ and ${\sigma }_{\mathrm{Q}}^{\mathrm{eq}}$ [8] are shown by different lines with small symbols. The indicated parameter values were adjusted to reproduce the measurements.

Figure 5

The energy distributions obtained with the Monte Carlo simulations as described in the text (a) for ${}^{210}\mathrm{Fr}$ produced in the ${}^{197}\mathrm{Au}({}^{18}\mathrm{O},5n$) reaction and (b) for ${}^{214}\mathrm{Ra}$ produced in the ${}^{206}\mathrm{Pb}({}^{12}\mathrm{C},4n$) reaction (filled symbols). The energy distributions for the events extracted according to the deflector angular acceptance are shown by open symbols with the Gaussian fits to the data (solid lines).

Figure 6

The angular distributions measured for the same ERs produced in the same reaction as shown in Fig. 5 (filled symbols) in comparison with those obtained using Monte Carlo simulations (open symbols).

Figure 7

Transmission efficiency curves measured (a) for ${}^{214}\mathrm{Ra}$ and (b) for ${}^{215}\mathrm{Ra}$ produced in the ${}^{208}\mathrm{Pb}({}^{12}\mathrm{C},6n$) and ${}^{208}\mathrm{Pb}({}^{12}\mathrm{C},5n$) reactions, respectively [24] (large symbols). Open symbols correspond to the yield data obtained at the studies [21] and normalized to the transmission curves. Simulations with the adjusted parameter values are shown by small open symbols connected with different lines. In the case of ${}^{215}\mathrm{Ra}$, the adjustment was performed with the two-component nonequilibrated charge distribution. The simulated transmission curves corresponding to the equilibrated charges [8] are also shown for the comparison (full diamonds connected by dotted lines). The relative weights of the equilibrated component $W_{\mathrm{eq}}$, mean values and standard deviations of the equilibrated and nonequilibrated components are expressed with the values corresponding to the equilibrated charges $Q_{\mathrm{m}}^{\mathrm{eq}}$ and ${\sigma }_{\mathrm{Q}}^{\mathrm{eq}}$ [8].

Figure 8

Charge state distributions (a) for ${}^{214}\mathrm{Ra}$ and (b) for ${}^{215}\mathrm{Ra}$, which correspond to the best adjustment of simulations to the measurements shown in Fig. 7 (open symbols). The parameter values are also indicated.

Figure 9

The same as in Fig. 7 but (a) for the yield of ${}^{213}\mathrm{Rn}$ and (b) for the yield of ${}^{217}\mathrm{Ra}$ produced at the beam energy of 69 MeV. The yield curves obtained with simulations are normalized to the experimental maxima observed for the equilibrated charges at $U=1.846$ kV/cm.

Figure 10

The angular distributions (a) for ${}^{213}\mathrm{Rn}$ and (b) for ${}^{217}\mathrm{Ra}$ produced at the beam energy of 69 MeV (large symbols), as obtained in our measurements. Simulations for the $3n$ and $\alpha 3n$ evaporation channels, which are normalized to the experimental maxima of the distributions, are shown by small symbols connected with the solid lines and dashed line, respectively.

Figure 11

The energy distributions (a) for ${}^{217}\mathrm{Ra}$ and (b) for ${}^{213}\mathrm{Rn}$ obtained with the simulations as the result of the $3n$ and $\alpha 3n$ fusion-evaporation reactions for all ER events (open symbols connected with solid lines). The events corresponding to the angles ${\theta }_{\mathrm{ER}}={(4\pm 0.3)}^{\circ }$ are shown by solid symbols. The results of one- and two-component Gaussian fits to these distributions are shown by dashed lines.

Figure 12

The same as in Fig. 8, but (a) for the ${}^{213}\mathrm{Rn}$ charge distribution and (b) for the ${}^{217}\mathrm{Ra}$ charge distribution, which correspond to the best adjustments of simulations to the measurements shown in Fig. 9.

Figure 13

The same as in Figs. 7 and 9, but (a) for the yield of ${}^{213}\mathrm{Ra}$ and (b) for the yield of ${}^{212}\mathrm{Ra}$, which are produced in the $5n$ and $6n$ evaporation channels, respectively, on the ${}^{206}\mathrm{Pb}$ target at $E_{\mathrm{lab}}=90$ MeV. The simulated curves were normalized to the measured maximum yields corresponding to the equilibrated charges.

Figure 14

The same as in Fig. 13, but for the yield of ${}^{214}\mathrm{Ra}$ produced in the $4n$ evaporation channel.

Figure 15

The same as in Fig. 8, but (a) for the ${}^{214}\mathrm{Ra}$ charge distribution, (b) for the ${}^{213}\mathrm{Ra}$ charge distribution, and (c) for the ${}^{212}\mathrm{Ra}$ charge distribution, which correspond to the best adjustments of simulations to the measurements shown in Figs. 13 and 14.

Figure 16

The same as in Fig. 14 but for ${}^{211}\mathrm{Ra}$ produced in the ${}^{204}\mathrm{Pb}({}^{12}\mathrm{C},5n$) reaction.

Figure 17

The same as in Fig. 16, but (a) for the yield of ${}^{213}\mathrm{Ra}$ and (b) for the yield of ${}^{212}\mathrm{Ra}$, which are produced in the $3n$ and $4n$ reactions, respectively, at the beam energy $E_{\mathrm{lab}}=69$ MeV.

Figure 18

The same as in Fig. 15, but (a) for the ${}^{213}\mathrm{Ra}$ charge distribution, (b) for the ${}^{212}\mathrm{Ra}$ charge distribution, and (c) for the ${}^{211}\mathrm{Ra}$ charge distribution, which correspond to the best adjustments of simulations to the measurements shown in Figs. 16 and 17.

Figure 19

The same as in Fig. 15, but for the charge distribution of ${}^{210}\mathrm{Fr}$ produced in the ${}^{197}\mathrm{Au}({}^{18}\mathrm{O},5n$) reaction at $E_{\mathrm{lab}}=90$ MeV. The charge parameter values correspond to the best adjustments of simulations to the measurements shown in Fig. 4.

Figure 20

(a),(b) The relative values of the equilibrated charges contribution $w_{\mathrm{eq}}$ to the total charge distributions as obtained with the MC simulations for Ra ERs transmitted through the deflector. (c),(d) The relative values of the mean charges for the nonequilibrated charges expressed as $Q_{\mathrm{m}}^{\mathrm{neq}}/Q_{\mathrm{m}}^{\mathrm{eq}}$. (e),(f) Standard deviations for the nonequilibrated charges expressed as ${\sigma }_{\mathrm{Q}}^{\mathrm{neq}}/{\sigma }_{\mathrm{Q}}^{\mathrm{eq}}$. The relative parameter data obtained in simulations for the equilibrated and nonequilibrated charges are referred to the corresponding parameter values given by the systematics [8]. Panels (a), (c), and (e) correspond to the relative velocities of Ra ERs $V/V_0=0.95–\text{0.97}$, whereas panels (b), (d), and (f) correspond to the relative velocities of Ra ERs $V/V_0=0.83–0.85$.

Figure 21

(a) Contour map of the transmission efficiency values for ${}^{215}\mathrm{Ra}$ simulated with a uniform charge distribution (UCD) as a function of the ionic charge and electric field strength. (b) The transmission efficiency curve for ${}^{215}\mathrm{Ra}$, which was obtained with the integration over uniform charges transmitted through the deflector [shown in panel (a)] as a function of the electric field strength.