Correlated mass, energy, and angular distributions from bremsstrahlung-induced fission of ${}^{234}\mathrm{U}$ and ${}^{232}\mathrm{Th}$ in the energy region of the fission barrier

The bremstrahlung-induced fission of ${}^{234}\mathrm{U}$ and ${}^{232}\mathrm{Th}$ has been studied at the superconducting Darmstadt linear accelerator (S-DALINAC) in the excitation energy region close to the fission barrier. Fission-fragment mass and total kinetic energy (TKE) distributions from ${}^{234}\mathrm{U}$ were studied for the first time in this energy region. The results have been analysed in terms of fission modes, and a dominant yield of the mass-asymmetric standard-2 mode was found in both nuclei. No strong dependence of the fission-mode weights on the excitation energy of the compound nucleus was found. Correlations among mass, TKE, and angular distributions have also been investigated. A correlation in the form of an increased anisotropy for far-asymmetric masses and low TKE were found in both fissioning systems. A possible interpretation of this correlation in terms of fission modes is discussed.

Figure 1

Bremsstrahlung spectra with endpoint energies of 9.0, 7.5, and 6.4 MeV (a), and 9.5 and 8.0 MeV (b). The solid, dashed, and dotted-dashed lines represent polynomial fits to the data simulated with GEANT4 [14], represented by the black squares. Also shown are corresponding calculated fission yields per $\mu \mathrm{A}$ electron beam current and per $\mu {\mathrm{g}/\mathrm{cm}}^2$ fission target mass thickness for ${}^{234}\mathrm{U}$ (c) and for ${}^{232}\mathrm{Th}$ (d) using cross sections from Refs. [15, 16].

Figure 2

Fission-fragment mass yield distributions from the reactions ${}^{234}\mathrm{U}(\gamma ,f)$ (a) and ${}^{232}\mathrm{Th}(\gamma ,f)$ (b). The curves are consecutively displaced by 2% and labeled with the average excitation energy.

Figure 3

Yield as a function of heavy-fragment mass number (a) and TKE (c) as well as average TKE (b) and width (d) as function of the fragment mass from ${}^{234}\mathrm{U}(\gamma ,f)$ at $\langle E_x\rangle =7.23\mathrm{MeV}$. The lines represent results from fits according to Eq. (4). The solid red line corresponds to the weighted sum of the individual fission modes. The individual fission modes are represented by the other, differently colored, lines.

Figure 4

Yield as a function of heavy-fragment mass number (a) and $TKE$ (c) as well as average $TKE$ (b) and width (d) as function of the fragment mass from ${}^{232}\mathrm{Th}(\gamma ,f)$ at $\langle E_x\rangle =7.26\mathrm{MeV}$. The lines represent results from fits according to Eq. (4). The solid red line corresponds to the weighted sum of the individual fission modes. The individual fission modes are represented by the other, differently colored, lines.

Figure 5

The relative yield of the S1 mode $Y_{S1}$ averaged over the excitation energies as a function of the neutron number of the compound nucleus. Literature data on neutron-induced fission of ${}^{235}\mathrm{U}$ [28] and ${}^{238}\mathrm{U}$ [29] as well as spontaneous fission of four different Pu isotopes [30] is included for comparison.

Figure 6

Illustration of the target composition and the angle-dependent energy loss.

Figure 7

Fragment yield (a) and average $TKE$ (b) as a function of the fragment mass number for ${}^{234}\mathrm{U}(\gamma ,f)$ at $E_0=9.0\mathrm{MeV}$. The open circles represent results obtained with a $190.0\mu g/{\mathrm{cm}}^2$ target [6], full squares represent results obtained in the present experiment with a $46.6\mu g/{\mathrm{cm}}^2$ target. The red line represent the simulated effect of the energy loss in the $190.0\mu g/{\mathrm{cm}}^2$ target on the data obtained with the $46.6\mu g/{\mathrm{cm}}^2$ target.

Figure 8

Fission-fragment angular distribution from ${}^{232}\mathrm{Th}(\gamma ,f)$ at bremsstrahlung endpoint energies $E_0=8.0\mathrm{MeV}$ (a) and $E_0=9.5\mathrm{MeV}$ (b). The red line shows the fit of Eq. (8) to the region indicated by the full black circles, the data points visualized by open squares have been omitted from the fit.

Figure 9

Fission-fragment angular distribution from ${}^{234}\mathrm{U}(\gamma ,f)$ at bremsstrahlung endpoint energies $E_0=6.4\mathrm{MeV}$ (a), $E_0=7.5\mathrm{MeV}$ (b), and $E_0=9.5\mathrm{MeV}$ (c). The red line shows the fit of Eq. (8) to the region indicated by the full black circles, the data points visualized by open squares have been omitted from the fit.

Figure 10

${}^{232}\mathrm{Th}(\gamma ,f)$ angular distribution parameter ratios as a function of the bremsstrahlung end-point energy in comparison with literature data [3, 33].

Figure 11

${}^{234}\mathrm{U}(\gamma ,f)$ angular distribution parameter ratios as a function of the bremsstrahlung end-point energy from data obtained with a $46.6\mu {\mathrm{g}/\mathrm{cm}}^2$ target.

Figure 12

Dependence of fission-fragment angular distributions in ${}^{232}\mathrm{Th}(\gamma ,f)$ at $E_0=9.5\mathrm{MeV}$ on the parameters $M^{*}$ [(a) and (b)] and ${TKE}^{*}$ [(c) and (d)], as introduced in Eqs. (9) and (10). The solid red lines show the expected behavior assuming specific angular distributions for the two standard modes.

Figure 13

Dependence of fission-fragment angular distributions in ${}^{234}\mathrm{U}(\gamma ,f)$ at $E_0=9.0\mathrm{MeV}$ on the parameters $M^{*}$ [(a) and (b)] and ${TKE}^{*}$ [(c) and (d)], as introduced in Eqs. (9) and (10). The solid red lines show the expected behavior assuming specific angular distributions for the two standard modes.

Figure 14

Ratios $B/A$ of the angular distribution coefficients determined for the two standard fission modes in ${}^{234}\mathrm{U}(\gamma ,f)$ and in ${}^{232}\mathrm{Th}(\gamma ,f)$ as a function of the bremsstrahlung end-point energy.