Colloquium: Beta-delayed fission of atomic nuclei

This Colloquium reviews the studies of exotic type of low-energy nuclear fission, the $\beta$-delayed fission ($\beta \mathrm{DF}$). Emphasis is made on the new data from very neutron-deficient nuclei in the lead region, previously scarcely studied as far as fission is concerned. These data establish the new region of asymmetric fission in addition to the previously known one in the transuranium nuclei. New production and identification techniques, which emerged in the last two decades, such as the wider use of electromagnetic separators and the application of selective laser ionization to produce intense isotopically or even isomerically pure radioactive beams are highlighted. A critical analysis of presently available $\beta \mathrm{DF}$ data is presented and the importance of detailed quantitative $\beta \mathrm{DF}$ studies, which become possible now, is stressed, along with the recent theory efforts in the domain of low-energy fission.

Figure 1

The nuclei for which fission fragments mass or nuclear-charge distributions have been measured by low-energy fission. The distributions are shown for selected systems. Circles: distributions, measured in conventional particle-induced fission experiments and spontaneous fission. Crosses: nuclear-charge distributions, measured by Coulex excitation (78; 76). Diamonds: 26 known $\beta \mathrm{DF}$ cases; the fissioning daughter is indicated. Filled diamonds: 11 daughter nuclides for which mass distribution was measured, two of them (${}^{180}\mathrm{Hg}$ and ${}^{242}\mathrm{Cf}$) are shown in the plot. References for $\beta \mathrm{DF}$ precursors are in Table . Adapted from 77.

Figure 2

Simplified diagram for the ${\beta }^{+}/\mathrm{EC}$ delayed fission in the neutron-deficient nuclei. Shown are the ground states of the parent $(A,Z)$ and daughter ($A$, $Z-1$) nuclei, and as a function of elongation, the potential energy of the daughter nucleus. The $Q_{\mathrm{EC}}$ value of the parent and fission barrier $B_f$ of the daughter nuclei are indicated by vertical arrows. The $\beta \mathrm{DF}$ of excited states with $E^{*}\sim B_f$ in the daughter nucleus is shown by horizontal arrows.

Figure 3

Calculated $Q_{\mathrm{EC}}(\mathrm{\text{parent}})-B_f(\mathrm{\text{daughter}})$ difference for neutron-deficient Hg-Md nuclei within the framework of FRDM-FRLDM models. $\beta \mathrm{DF}$ is expected to be observable in the nuclei on the right-hand side of the sloped lines, which approximately delineate the region of nuclei with $b_{\beta }>1\%$. The known $\beta \mathrm{DF}$ nuclei are marked by the circles. The references for data are in Table . Adapted from 64.

Figure 4

Calculated $Q_{\mathrm{EC}}$ (At) values (filled symbols) for the parent At isotopes and calculated fission barriers $B_f$ (Po) (open symbols) of the daughter Po isotopes according to the FRDM-FRLDM and TF models. The extrapolated or experimental $Q_{\mathrm{EC}}$ (At) values (where available) are from AME2012 (13).

Figure 5

Schematic view of the ISOLDE and RILIS operation as applied in the $\beta \mathrm{DF}$ studies of ${}^{180}\mathrm{Tl}$ (7; 23). The 1.4-GeV $2\mu \mathrm{A}$ proton beam impinges on the thick $50\mathrm{g}/{\mathrm{cm}}^2$ ${}^{238}\mathrm{U}$ target, producing a variety of reaction products via the spallation, fragmentation, and fission reactions. The neutral reaction products diffuse toward the hot cavity where the thallium atoms are selectively ionized to a $1^{+}$ charge state by two overlapping synchronized laser beams precisely tuned to provide thallium ionization in a two-color excitation and ionization scheme. The ionized thallium ions are extracted by the high-voltage potential of 30 kV, followed by the $A=180$ mass separation with the ISOLDE dipole magnet. The mass-separated ${}^{180}\mathrm{Tl}$ ions are finally implanted in the carbon foils of the windmill system, shown in Fig. 8, for subsequent measurements of their decays. Adapted from 75.

Figure 6

Preneutron-emission mass-yield distribution for the $\beta \mathrm{DF}$ of ${}^{242}\mathrm{Es}$. The fissioning daughter nucleus is ${}^{242}\mathrm{Cf}$. From 80.

Figure 7

Partial decay scheme of ${}^{246}\mathrm{Md}$ modified from 11. The energies of the 4.4 and 0.9 s states are almost degenerate; however, no relative ordering could be given. They are denoted as $m1$ and $m2$. Shown are $\alpha$-decay energies and EC-decay branches. The arrows marked by ECDF show schematically the fission of the excited state(s) in ${}^{246}\mathrm{Fm}$ populated by EC decays of ${}^{246m2}\mathrm{Md}$ ($\beta \mathrm{DF}$ of ${}^{246m2}\mathrm{Md}$) and fission of excited state(s) in ${}^{242}\mathrm{Cf}$, populated by the EC decay of ${}^{242}\mathrm{Es}$ ($\beta \mathrm{DF}$ of ${}^{242}\mathrm{Es}$).

Figure 8

Left: The windmill setup used in the experiments at ISOLDE to study $\beta \mathrm{DF}$ of ${}^{178,180}\mathrm{Tl}$, ${}^{194,196}\mathrm{At}$, and ${}^{200,202}\mathrm{Fr}$. Right: A zoom of the detector arrangement. The case of ${}^{180}\mathrm{Tl}$ is shown as an example, with mass-separated ${}^{180}\mathrm{Tl}$ ions being implanted through a hole in an annular silicon detector ($300\mu \mathrm{m}$ thickness) into a thin carbon foil of $20\mu \mathrm{g}/{\mathrm{cm}}^2$ thickness. A second Si detector ($300\mu \mathrm{m}$ thickness) is placed 3 mm behind the foil. A set of Ge detectors is used for $\gamma$- and $K$ x-ray measurements in coincidence with particle decays. From 7.

Figure 9

Top: A coincidence energy spectrum for $\beta \mathrm{DF}$ of ${}^{180}\mathrm{Tl}$ measured by two silicon detectors. The two-peaked structure originates because the two fission fragments have different energies, a direct result of the asymmetric mass distribution. Bottom: The derived fission-fragment distribution of the daughter isotope ${}^{180}\mathrm{Hg}$ as a function of the fragment mass and the total kinetic energy; From 7 and 23.

Figure 10

Singles silicon energy spectrum for $\beta \mathrm{DF}$ of (a) ${}^{178}\mathrm{Tl}$ and for $\beta \mathrm{DF}$ of (b) ${}^{180}\mathrm{Tl}$. From 56.

Figure 11

(a) Total energy spectrum in the PSSD in the reaction ${}^{141}\mathrm{Pr}({}^{56}\mathrm{Fe},3n){}^{194}\mathrm{At}$ at the beam energy of $E({}^{56}\mathrm{Fe})=259(1)\mathrm{MeV}$ in front of the target. (b) The same as (a), but within 15 ms of the “beam off” interval, showing the 66 fission events of ${}^{194}\mathrm{Po}$. Adapted from 10.

Figure 12

Partial $\beta \mathrm{DF}$ half-lives (on a logarithm scale) for ${}^{178,180}\mathrm{Tl}$, ${}^{228}\mathrm{Np}$, ${}^{232,234}\mathrm{Am}$, ${}^{238,240}\mathrm{Bk}$, and ${}^{242,244,246,248}\mathrm{Es}$ as a function of the $Q_{\mathrm{EC}}$ value for (a) FRDM-FRLDM and (b) TF models. (c) and (d) The same, but as a function of the $Q_{\mathrm{EC}}-B_f$ value.

Figure 13

Calculated PES surfaces for ${}^{180}\mathrm{Hg}$ and ${}^{236}\mathrm{U}$ as a function of the dimensionless quadrupole moment and the mass asymmetry. The shapes of the nuclei at several key locations as they proceed to fission are drawn, connected to the points on the surface by arrows. Adapted from 43.

Figure 14

Yields of neutron-rich francium isotopes measured at ISOLDE with uranium and thorium targets. From 70.