First isomeric yield ratio measurements by direct ion counting and implications for the angular momentum of the primary fission fragments

We report the first experimental determination of independent isomeric yield ratios using direct ion counting with a Penning trap, which offered such a high resolution in mass that isomeric states could be separated. The measurements were performed at the Ion Guide Isotope Separator On-Line (IGISOL) facility at the University of Jyväskylä. The isomer production ratios of ${}^{81}\mathrm{Ge}$, ${}^{96,97}\mathrm{Y}$, ${}^{128,130}\mathrm{Sn}$, and ${}^{129}\mathrm{Sb}$ in the 25-MeV proton-induced fission of ${}^{\mathrm{nat}}\mathrm{U}$ and ${}^{232}\mathrm{Th}$ were studied. Three isomeric pairs (${}^{81}\mathrm{Ge}$, ${}^{96}\mathrm{Y}$, and ${}^{129}\mathrm{Sb}$) were measured for the first time for the ${}^{\mathrm{nat}}\mathrm{U}(p,f$) reaction, while all the reported yield ratios for the ${}^{232}\mathrm{Th}(p,f$) reaction were determined for the first time. The comparison of the experimentally determined isomeric yield ratios with data available in the literature shows a reasonable agreement, except for the case of ${}^{130}\mathrm{Sn}$ for unspecified reasons. The obtained results were also compared with the gef model, where good agreement can be noticed in most cases for both reactions. Serious discrepancies can only be observed for the cases of ${}^{96,97}\mathrm{Y}$ for both reactions. Moreover, based on the isomeric yield ratios, the root-mean-square angular momenta ($J_{\text{rms}}$) of the fission fragments after scission were estimated using the talys code. The experimentally determined isomeric yield ratios, and consequently the deduced $J_{\text{rms}}$, for ${}^{130}\mathrm{Sn}$ are significantly lower compared to ${}^{128}\mathrm{Sn}$ for both fissioning systems. This can be attributed to the more spherical shape of the fragments that contribute to the formation of ${}^{130}\mathrm{Sn}$, due to their proximity to the $N=82$ shell closure. The values of $J_{\text{rms}}$ for ${}^{129}\mathrm{Sb}$ are higher than ${}^{128}\mathrm{Sn}$ for both reactions, despite the same neutron number of both nuclides ($N=78$), indicating the odd-$Z$ effect where fission fragments with odd-$Z$ number tend to bear larger angular momentum than even-$Z$ fragments. The isomer production ratio for the isotopes of Sn is more enhanced in the ${}^{\mathrm{nat}}\mathrm{U}(p,f$) reaction than in ${}^{232}\mathrm{Th}(p,f$). The opposite is observed for ${}^{96}\mathrm{Y}$ and ${}^{97}\mathrm{Y}$. These discrepancies might be associated to different scission shapes of the fragments for the two fission reactions, indicating the impact that the different fission modes can have on the isomeric yield ratios.

Figure 1

A typical TOF spectrum, where the most prominent peak corresponds to the TOF of the ions with the desired mass ($A=97$) after their purification. The red dashed lines represent the applied TOF gate ($200–250\mu \mathrm{s}$) for the selection of the ions. Ions that do not match the correct TOF are discarded from the analysis.

Figure 2

Quadrupole frequency scan at $A=81$. The peak positions (vertical dashed lines) of ${}^{81\mathrm{m}}\mathrm{Ge}$ and ${}^{81}\mathrm{Ge}$ are calculated relative to ${}^{81}\mathrm{As}$, which is taken as reference. The peak identification is based on a frequency to mass calibration. The red line shows the fitted Gaussian functions used to extract the isomeric yield ratio. The shadowed areas under the peaks correspond to the number of detected nuclei for each state.

Figure 3

Isomeric yield ratios for the six studied nuclei. Our results are shown in red circles ($•$) for the ${}^{\mathrm{nat}}\mathrm{U}(p,f$) reaction and in red triangles ($▴$) for the ${}^{232}\mathrm{Th}(p,f$) reaction. In black markers, the results from the gef code are depicted. The results by Tanikawa et al. [48] are also presented ($\circ$).

Figure 4

The experimentally observed isomeric yield ratios from this work, compared with data available in the literature for different fissioning systems and excitation energies. The excitation energies ($E^{*}$) of each formed compound nucleus are given in the legend.

Figure 5

The isomeric yield ratios of the nuclides with the same spin differences between the high-spin $J_{\mathrm{h}}$ and low-spin $J_{\mathrm{l}}$ states. On the left, the isomeric yield ratios of ${}^{81}\mathrm{Ge}$ and ${}^{97}\mathrm{Y}$ are shown $(\mathrm{\Delta }J=4)$, and on the right, the results of ${}^{128,130}\mathrm{Sn}$ $(\mathrm{\Delta }J=7)$. Black circles ($•$) represent the ${}^{\mathrm{nat}}\mathrm{U}(p,f$) reaction and red triangles ($▴$) represent the ${}^{232}\mathrm{Th}(p,f$) reaction.

Figure 6

The isomeric yield ratio as a function of $\sigma$ of the primary fragment for different level density models as calculated in the present work for the ${}^{\mathrm{nat}}\mathrm{U}(p,f$) reaction. The shadowed green areas illustrate the experimental results with their respective uncertainties. For all nuclides, except for ${}^{81}\mathrm{Ge}$, the plots on the left show the isomeric yield ratio as the result of the de-excitation of the primary fragment after emitting one neutron ($n=1$) and on the right after emitting two neutrons ($n=2$). For ${}^{81}\mathrm{Ge}$, zero ($n=0$) and one ($n=1$) emitted neutrons were considered respectively. For more information, see Sec. 6b.

Figure 7

Same as Fig. 6, but for the ${}^{232}\mathrm{Th}(p,f$) reaction. Note that for ${}^{96}\mathrm{Y}$, in the case of two emitted neutrons from the primary fragment, the crossing between the experimental value and the calculations performed with talys occurs outside the window range of the plot, at $\sigma =13.6\hslash$.

Figure 8

The case of ${}^{129}\mathrm{Sb}$, where the calculations were performed with the level scheme of RIPL-3 and the updated level scheme from Ref. [88]. In red, the results for the BSFGM and in black for the MLD model.

Figure 9

The deduced $J_{\text{rms}}$ for the two fissioning systems as a function of the neutron number of the fission products.