Charge-state distribution of ${}^{238}\mathrm{U}$ in nitrogen gas and carbon foil at 14 and $15\mathrm{MeV}/\mathrm{nucleon}$

The charge-state distributions of ${}^{238}\mathrm{U}$ with energies of 14 and $15\mathrm{MeV}/\mathrm{nucleon}$ were measured using nitrogen (${\mathrm{N}}_2$) gas and carbon foil (C-foil) charge strippers. The most probable charge states of ${}^{238}\mathrm{U}$ with energies of 14 and $15\mathrm{MeV}/\mathrm{nucleon}$ in ${\mathrm{N}}_2$ gas attain equilibrium at 60.8 and 62.4, whereas those in C-foils attain equilibrium at 75.8 and 76.7, respectively. Novel empirical formulas for the accurate prediction of the equilibrium charge states of ${}^{238}\mathrm{U}$ with energies $10–20\mathrm{MeV}/\mathrm{nucleon}$ in gases and C-foil were derived by fitting the data in the energy range of $1–20\mathrm{MeV}/\mathrm{nucleon}$. The charge states predicted by using the formulas for gases and C-foil are in good agreement with the data in the energy range of $10–20\mathrm{MeV}/\mathrm{nucleon}$ within an average of 0.23 and 0.21, respectively.

Figure 1

Acceleration scheme of the experiment. The charge stripper is located downstream of the RRC. The uranium ions were extracted from the SC-ECRIS on the high-voltage platform of the Cockcroft-Walton preinjector in the RILAC facility. The first two resonators (A1 and A2) of the booster linac were used for the beam energies of 14 and $15\mathrm{MeV}/\mathrm{nucleon}$, where the RRC was operated at the harmonic number of $h=8$.

Figure 2

Schematic view of the beam line around the gas charge stripper. The beam intensity upstream of the gas charge stripper was measured using a Faraday cup (FC-D17). Stripped beams were analyzed using a pair of dipole magnets DAD4 and DMD4. The beam intensity downstream of DAD4 and DMD4 was measured using a Faraday cup (FC-F41).

Figure 3

Schematic view of the beam line around the C-foil charge stripper. The beam intensity upstream of the C-foil charge stripper was measured using a Faraday cup (FC-A01a). Stripped beams were analyzed using a pair of dipole magnets DAA1 and DMA1. The beam intensity downstream of DAA1 and DMA1 was measured using a Faraday cup (FC-A11).

Figure 4

Charge-state distributions of ${}^{238}\mathrm{U}$ at different energies measured using the ${\mathrm{N}}_2$ gas charge stripper. The data of the fractions calculated for (a) 11, (b) 14, and (c) $15\mathrm{MeV}/\mathrm{nucleon}$ are plotted. (a) The data for stripper thicknesses of 48, 65, 84, 150, 334, and $752\mu \mathrm{g}/{\mathrm{cm}}^2$ at $11\mathrm{MeV}/\mathrm{nucleon}$ are denoted by crosses, asterisks, x marks, open triangles, open squares, and open diamonds, respectively. The data for stripper thicknesses of 48, 84, 334, and $752\mu \mathrm{g}/{\mathrm{cm}}^2$ along with one data set of $150\mu \mathrm{g}/{\mathrm{cm}}^2$ were obtained from a previous study [4]. (b) The data for stripper thicknesses of 64, 132, 201, 314, and $709\mu \mathrm{g}/{\mathrm{cm}}^2$ at $14\mathrm{MeV}/\mathrm{nucleon}$ are denoted by asterisks, open triangles, open circles, open squares, and open diamonds, respectively. (c) The data for stripper thicknesses of 67, 134, 197, 316, and $712\mu \mathrm{g}/{\mathrm{cm}}^2$ at $15\mathrm{MeV}/\mathrm{nucleon}$ are denoted by asterisks, open triangles, open circles, open squares, and open diamonds, respectively.

Figure 5

Charge-state distributions of ${}^{238}\mathrm{U}$ at different energies measured using the C-foil charge stripper. The data for stripper thicknesses of 39.9, 85.8, 109, 223, 299, 550, and $991\mu \mathrm{g}/{\mathrm{cm}}^2$ are denoted by asterisks, solid triangles, solid circles, solid diamonds, open triangles, open circles, and open diamonds, respectively. The values of the fractions calculated for (a) 11, (b) 14, and (c) $15\mathrm{MeV}/\mathrm{nucleon}$ are plotted.

Figure 6

Most probable charge states of ${}^{238}\mathrm{U}$ plotted as a function of ${\mathrm{N}}_2$ gas and C-foil thickness. The data for ${\mathrm{N}}_2$ gas at 11, 14, and 15 $\mathrm{MeV}/\mathrm{nucleon}$ are represented by solid circles, solid triangles, and open squares, respectively. Fitting functions are represented by dotted, dashed, and solid curves at 11, 14, and $15\mathrm{MeV}/\mathrm{nucleon}$, respectively. The data for C-foils at 11, 14, and $15\mathrm{MeV}/\mathrm{nucleon}$ are represented by open circles, open triangles, and open diamonds, respectively. Fitting functions are represented by dotted, dashed, and solid curves at 11, 14, and $15\mathrm{MeV}/\mathrm{nucleon}$, respectively.

Figure 7

Data of the equilibrium charge state of uranium ions in (a) ${\mathrm{N}}_2$, Ar, and ${\mathrm{CO}}_2$ gases [4, 19, 20] and (b) C-foil [1, 19, 20, 21, 22] in the energy range of $1–20\mathrm{MeV}/\mathrm{nucleon}$. (a) Solid squares represent the data obtained in this study. Open squares represent the results of previous measurements [4]. Open circles represent the data for gases [19, 20]. The equilibrium charge states in gases, as predicted by the new fitting function $q_{\mathrm{eq}}^{\mathrm{gas}}=Z[1-0.784\exp \{-(v/v_0{)}^{1.63}{Z}^{-1.17}\}]$ are represented by the solid curve. The dashed curve represents the charge states predicted using the empirical formula [4]. (b) The data obtained in this study is represented by solid squares. Open circles represent the data available for C-foil [1, 19, 20, 21, 22]. The data at $11\mathrm{MeV}/\mathrm{nucleon}$ obtained in this study is in good agreement with previous data [1]. The blue, orange, green, magenta, gray, and brown curves represent the charge states for solid materials, as predicted by the empirical formulas proposed by us, i.e., $q_{\mathrm{eq}}^{\mathrm{C}\mathrm{\text{−}}\mathrm{foil}}=Z[1-0.835\exp \{-(v/v_0{)}^{1.20}{Z}^{-0.736}\}]$, Leon et al. [24], Baron et al. [5], McMahan et al. [25, 26], Schiwietz et al. [27], and Strehl [28], respectively.