Aspects of charge distribution measurement for ${}^{252}\mathrm{Cf}$(sf)

Measurements of charge distributions of fragments in the spontaneous fission of ${}^{252}\mathrm{Cf}$ have been performed using a unique detector setup consisting of a typical grid-ionization chamber coupled with a $\mathrm{\Delta }E-E$ charged particle telescope. We find that the fragment mass dependency of the kinetic-energy-averaged width of the charge distribution shows a systematically decreasing trend with obvious fluctuations. The variation of the widths of the charge distribution with kinetic energy shows a pan-like shape. This is due to the large number of neutrons emitted at the high excitation energies and cold fragmentation at the low excitation energies. Deviation of the kinetic-energy-averaged most probable charge $Z_p$ from the unchanged charge distribution (UCD), $\mathrm{\Delta }Z$, as a function of the mass number of primary fragments, $A^{*}$, changes from negative for mass asymmetric fission to positive near the symmetric fissions. Concerning the kinetic energy dependence of $Z_p$ given primary mass number $A^{*}$, obvious increasing tendencies of $Z_p$ with increasing kinetic energy are observed.

Figure 1

Schematic view of the grid-ionization chamber coupled with a charged particle telescope detector system [12].

Figure 2

The fitting for $\mathrm{\Delta }E$ spectra using multi-Gaussian functions with the conditions (a) $A^{*}=86$ u, $E_{kL}^{*}=105–108$ MeV; (b) $A^{*}=99$ u, $E_{kL}^{*}=120–123$ MeV [12].

Figure 3

Charge dispersion for products with $A^{*}=101$ u and 118.5 MeV average kinetic energy.

Figure 4

The fragment mass dependency of kinetic energy averaged widths ${\sigma }_{Z_{\mathrm{ave}}}$ of the charge distributions; the solid points indicate the present experimental data, the triangles represent the calculation results from GEF code [15], and the solid line is the linear function fitting.

Figure 5

The widths ${\sigma }_Z$ of charge distributions depend on the kinetic energy of the light fragments $E_{kL}^{*}$: (a), (b), (c), and (d) correspond to the primary fragment masses 101, 103, 107, and 109 u, respectively.

Figure 6

Charge polarization $\mathrm{\Delta }Z$ as a function of the mass number of primary fission fragments $A^{*}$. The solid points indicate the present experimental data, the triangles represent the calculation results from GEF code [15]. The dotted line indicates the neutron number $N_H=82$ and proton number $Z_H=50$ for heavy fragments. The dash-dotted line indicates the symmetry fission.

Figure 7

Kinetic fragment energies dependence of the most probable charge $Z_p$ for ${}^{252}\mathrm{Cf}$: (a), (b), (c), and (d) corresponding to the primary fragment masses 101, 103, 107, and 109 u, respectively.

Figure 8

The average most probable charge $Z_{p_{\mathrm{ave}}}\mathrm{as}$ a function of mass number of light fragments for ${}^{252}\mathrm{Cf}$. The solid curve is the results of calculations using Waldo's formula.