Slow fission of highly excited plutonium nuclei

Background: Earlier measurements of fission lifetimes of the highly excited uraniumlike nuclei by K x-ray fluorescence and crystal blocking techniques obtained slow fission (fission time $\sim {10}^{-18}\mathrm{s}$) for most of the fission events and were shown to be incompatible with the very short fission time ($\sim {10}^{-20}\mathrm{s}$) obtained by the nuclear techniques and also with the very small (≤5%) percentage of such slow fission events predicted by simple statistical models. One weakness of the earlier fluorescence experiments is that the observed K x-ray peaks were very broad [full width at half maximum $\left(\mathrm{FWHM}\right)\approx 15\mathrm{keV}$] and the precise energies of the relevant K x-ray lines could not be determined from such measurements.

Purpose: The purpose is to look at the relevant K x-ray energy region in coincidence with the fission fragments with a high resolution (≈1 keV) spectrometer to obtain evidence of slow fission and determine its percentage.

Method: Highly excited plutonium nuclei were produced in the fusion of ${}^4\mathrm{He}+{}^{238}\mathrm{U}$ at $E{\left({}^4\mathrm{He}\right)}_{\mathrm{Lab}}=60\mathrm{MeV}$. The intrinsic width of plutonium K x-ray lines in coincidence with the fission fragments was determined as a direct measure (or lower limit) of the fission time of the slow ($\sim {10}^{-18}\mathrm{s}$) fission events. The minimum percentage of slow fission events has been determined from the K x-ray multiplicity per fission event and the probability of creation of K-orbital vacancies in plutonium.

Results: A narrow peak (FWHM ≈ 1 keV) observed in the coincidence photon spectrum at (102.8 ± 0.5) keV, just below the characteristic plutonium $K_{\alpha 1}$ line (103.7 keV) has been attributed to the plutonium $K_{\alpha 1}$ line on the basis of supporting evidence and calculations and we deduce that most of the fission events are slow (fission time $>{10}^{-18}\mathrm{s}$). No peak has been observed exactly at 103.7 keV.

Conclusions: The shift [(0.9 ± 0.5) keV] of plutonium K x-ray lines is plausible, if the fissioning plutonium nucleus spends most of its long fission time in a highly deformed dumbbell shape (beyond saddle) and the corresponding results are in agreement with those obtained earlier by the atomic techniques. Alternatively, if no significant shift of plutonium K x-ray lines can be expected, the absence of a peak at 103.7 keV contradicts earlier atomic technique claims of a significant percentage of slow fission events.

Figure 1

Fission delay time vs pre-fission neutron multiplicity for ${}^4\mathrm{He}+{}^{238}\mathrm{U}$ reaction at $E_{\mathrm{LAB}}\left({}^4\mathrm{He}\right)=60\mathrm{MeV}$ as obtained from JOANNE2 code calculations.

Figure 2

Fission fragment spectrum in coincidence with the LEPS detector for ${}^4\mathrm{He}+{}^{238}\mathrm{U}$ reaction at $E_{\mathrm{LAB}}\left({}^4\mathrm{He}\right)=60\mathrm{MeV}$.

Figure 3

Prompt gated photon spectrum with a red background (upper panel). Prompt gated and background subtracted photon spectrum (bottom panel).

Figure 4

Random coincidence corrected photon spectrum and different backgrounds shown by Bkg-1 (solid red), Bkg-2 (dotted blue), and Bkg-3 (dot-dashed green) curves. Different peaks are shown in magenta color (see text for details).

Figure 5

Random coincidence corrected photon spectrum with Bkg-1 (solid red) background is shown in the upper panel. Bkg-1 subtracted coincidence spectrum is shown in the lower panel. geant3 simulations of a fission fragment K x ray at 65 keV and a fission fragment γ ray at 88 keV are shown in magenta color. The peaks at 98.4 keV and around 103 keV are also shown in magenta color.

Figure 6

Singles LEPS detector spectrum of ${}^4\mathrm{He}+{}^{232}\mathrm{Th}$ reaction at $E_{\mathrm{LAB}}\left({}^4\mathrm{He}\right)=60\mathrm{MeV}$.

Figure 7

Random corrected coincidence spectrum for Bkg-1 subtraction with statistical error bars shown in the energy range between 96.6 and 107 keV. Dashed blue and dot-dashed green curves represent geant3 simulation of a sharp 101-keV γ-ray line from a fission fragment with additional yield at 98.4 keV. The solid red curve shows Gaussian fit of the data points with two isolated peaks (see text for details).

Figure 8

Random corrected coincidence spectrum for Bkg-1 subtraction with statistical error bars in the energy range from 100.5 to 105.9 keV. Dot-dashed green curve is the high energy hump for best fitted geant3 simulation of 101-keV fission fragment γ-ray. Dotted red curve is the best fit for a combination of geant3 simulation of fission fragment γ ray and a Gaussian peak around 103 keV with $\mathrm{FWHM}=1\mathrm{keV}$ as discussed in the text.

Figure 9

Photon multiplicities of the 103-keV [panel (a)], 88-keV [panel (c)], and 65-keV [panel (b)] peaks as obtained by gating on different regions of fission fragment energy spectrum. The horizontal error bar on each data point indicates the regions of the fission fragment kinetic energy spectrum over which gating has been done.

Figure 10

Random corrected coincidence photon spectrum with Bkg-2 (dotted blue) background is shown in the upper panel. Bkg-2 subtracted coincidence spectrum is shown in the lower panel. geant3 simulation of a fission fragment K x ray at 65 keV and a fission fragment γ ray at 88 keV are shown in magenta color. The peaks around 98.4 and 103 keV are also shown in magenta color.

Figure 11

Bkg-2 subtracted coincidence photon spectrum with the statistical error bars is shown in the energy range from 96.6 to 107 keV. Dashed blue and dot-dashed green curves represent geant3 simulation of a sharp 101-keV γ-ray line from a fission fragment with additional yield at 98.4 keV. The solid red curve shows Gaussian fit of the data points with two isolated peaks (see text for details).

Figure 12

Random corrected coincidence spectrum for Bkg-2 subtraction with statistical error bars in the energy range from 100.5 to 105.9 keV. Dot-dashed green curve is the high energy hump for best fitted geant3 simulation of 101-keV fission fragment γ ray. Dotted red curve is the best fit for a combination of geant3 simulation of fission fragment γ-ray and a Gaussian peak around 103 keV with $\mathrm{FWHM}=1\mathrm{keV}$ as discussed in the text.

Figure 13

Random corrected coincidence photon spectrum with Bkg-3 (dashed green) background is shown in the upper panel. Bkg-3 subtracted coincidence photon spectrum is shown in the lower panel.

Figure 14

Random corrected coincidence spectrum for Bkg-3 subtraction with the statistical error bars is shown in the energy range from 96.6 and 107 keV. Dash blue curve represents geant3 simulation of a sharp 101-keV γ-ray line from a fission fragment with additional yield at 98.4 keV. The red curve and dot-dashed green line show the Gaussian and linear fits of the data points around 103 keV respectively. Solid red curve indicates the region used for Gaussian fit and the dotted red curve is the extrapolation of the Gaussian fit (see text for details).