Probing fission fragment angular momenta by photon measurements

We discuss how the measurement of photon angular correlations can reveal information about the orientation of the fission fragment angular momenta. Photons from identified stretched $E2$ collective transitions in even-even fission product nuclei are particularly suitable because they do not affect the orientation of the nuclear spin. Their angular distribution relative to the direction of a fission fragment may reveal the orientation of the fragment spins relative to the fission axis. A novel means of probing the correlated fission fragment spins is the distribution of the opening angle between $E2$ photons from even-even partner fragments which reveals the mutual correlation of the fragment spins, if the photon helicities can be determined, demonstrating the potential power of helicity measurements in fission.

Figure 1

The calculated relaxation times $t_m$ for wriggling (bottom curve, green), bending (middle three curves, blue), and twisting (top curve, red), shown as functions of the neck radius $c$ for a tip separation of $d=4\mathrm{fm}$. For wriggling is also shown the result for touching spheres, $d=0$ (dashed green). For bending, the solid curve is for the mass division $108:144$ (the most probable), while the dashed curves are for $100:152$ (lower) and $118:134$ (upper), which are each half as probable. Also shown are $t_{\mathrm{fiss}}=1$ and $t_{\mathrm{fiss}}=4$ zs (horizontal lines).

Figure 2

The angular distribution of the collective $E2$ photons relative to the direction of the emitting product nucleus for four different scenarios: (a) The standard $\mathrm{FREYA}$ scenario, in which the perpendicular modes (wriggling and bending) are fully agitated, while the parallel mode (twisting) is absent; (b) a perhaps more realistic scenario in which bending is not fully agitated while twisting is somewhat agitated; (c) a (probably less realistic) scenario in which the perpendicular and the parallel modes are equally agitated; and (d) an extreme scenario in which only twisting is present. The specified values of $(c_{\mathrm{wrig}},c_{\mathrm{bend}},c_{\mathrm{twst}})$ are indicated for each scenario. The Legendre fits (solid curves) and their symmetric parts (dots) are shown, as are the distributions for perfectly perpendicular or perfectly parallel emitter spins.

Figure 3

The ratio of the photon yield in the direction of the fragment, $W\left(0^{\circ }\right)$, and the transverse yield $W\left({90}^{\circ }\right)$ as a function of the coefficient $c_{\mathrm{twst}}$ controlling the degree of agitation of the twisting mode, $T_{\mathrm{twst}}=c_{\mathrm{twst}}{T}_{\mathrm{sc}}$.

Figure 4

The distribution of the opening angle ${\psi }_{12}$ between pairs of $E2$ photons emitted from even-even product partners, for various scenarios for the dinuclear rotational modes at scission: (a) Only wriggling is present; (b) only bending is present; (c) only twisting is present; and (d) the standard $\mathrm{FREYA}$ scenario: wriggling and bending are equally present. Each panel shows the result of the $\mathrm{FREYA}$ simulations (dots) and the associated Legendre fit (solid curve), as well as the result of perfectly parallel or antiparallel fragment spins at the time of emission. Only photon pairs with the same helicity are included; the results for photon pairs having opposite helicities would be reflected around ${\psi }_{12}={90}^{\circ }$.