Population of high-spin isomeric states following fragmentation of ${}^{238}$U

Isomeric ratios have been determined for 23 metastable states identified in $A\approx 200$ nuclei from Pt to Rn near the valley of stability following fragmentation of ${}^{238}$U. This includes high-spin states with angular momenta ranging from (39/2)$\hslash$ to 25$\hslash$. The experimental results are discussed together with those of similar experiments performed in this mass region. Isomeric ratios are compared with theoretical predictions where the angular momentum of the fragment arises purely due to the angular momentum of nucleons removed from the projectile. The theoretical yield of low-spin states is generally overestimated. In these cases the assumption of 100$\%$ feeding of the isomer may require modification. However, the yield of high-spin isomeric states [$I_m$ $\ge$ (39/2)$\hslash$] is significantly underestimated and highlights the requirement for a more complete theoretical framework in relation to the generation of fragment angular momentum. The enhanced population of high-spin states reported here is advantageous to future studies involving isomeric beams at fragmentation facilities such as the Rikagaku Kenkyusho RI Beam Factory (Japan) and next-generation facilities at the Facility for Antiproton and Ion Research (Germany) and Facility for Rare Isotope Beams (USA).

Figure 1

Atomic number $Z$ of radioactive fragments correlated with the mass-to-charge ratio $A/Q$ following projectile fragmentation of uranium. Rings indicate the loci for which delayed $\gamma$ rays were observed in coincidence with nuclei implanted in an ion catcher, identified as ${}^{214–215}$Rn, ${}^{211–213}$At, ${}^{208–211}$Po, ${}^{207}$Bi, ${}^{202–206}$Pb, ${}^{201–204}$Tl, and ${}^{195,197}$Au.

Figure 2

Delayed $\gamma$-ray spectra associated with ${}^{202–206}$Pb [(a)–(e)] identified following the de-excitation of known isomeric states [19, 20, 21, 22, 23]. A time gate $\Delta t$ was applied to separate the isomeric decay from the prompt radiation flash observed by some germanium detectors following fragment implantation.

Figure 3

Nuclear chart ($N$ vs $Z$) summarizing selected experimentally measured isomeric ratios in heavy nuclei. Squares indicate nuclei produced using ${}^{208}$Pb fragmentation beams [6, 8, 49, 51] while circles show nuclei produced using ${}^{238}$U [1, 9, 10, 48, 50], including the current work. See Table for details.

Figure 4

Experimental isomeric ratios plotted as a function of angular momentum and excitation energy of the isomeric state for both ${}^{238}$U [(a)–(b)] and ${}^{208}$Pb [(c)–(d)] fragmentation studies [1, 6, 8, 9, 10, 48, 49, 50, 51]. See Table for details.

Figure 5

Comparison of experimental isomeric ratios reported in ${}^{238}$U fragmentation studies [1, 9, 10, 48, 50]. $R_{\exp }$ is plotted against the angular momentum of the isomeric state for identical states in the same nucleus. The mass loss of the fragments compared with the beam is also shown. See Table for details.

Figure 6

Experimental isomeric ratios determined in the current study (see Table ) compared with the theoretical population plotted as a function of angular momentum of the isomeric state. Inset: $R_{\mathrm{th}}^f/R_{\mathrm{th}}^{\mathrm{stat}}$. The theoretical isomeric ratio calculated using Eq. (3) is compared with the yield provided by the Monte Carlo–type model ABRABLA as a function of angular momentum.

Figure 7

Experimental isomeric ratios measured following uranium fragmentation [1, 9, 10, 48, 50] compared with the theoretical population plotted as a function of angular momentum of the isomeric state, including results from the current work. Data in the top and bottom panels are compared with isomeric yields calculated using (a) Eq. (3) and (b) the Monte Carlo–type model ABRABLA [25], respectively. See Table for details.

Figure 8

Isomeric ratios determined in the current study (see Table ) compared with the theoretical population predicted by the analytical formula only [Eq. (3)] plotted as a function of angular momentum of the isomeric state. The spin-cutoff parameter in Eq. (3) was multiplied by a factor of 2.