Comparing ﬁssion-product yields from photon-induced ﬁssion of 240 Pu and neutron-induced ﬁssion of 239 Pu as a test of the Bohr hypothesis in nuclear ﬁssion

. Fission product yields (FPYs) are a uniquely sensitive probe of the ﬁssion process, with well established dependence on the species of nucleus un-dergoing ﬁssion, its excitation energy and spin. Thus FPYs are well suited for testing Bohr’s hypothesis in the context of nuclear ﬁssion, which states that the decay of a compound nucleus with a given excitation energy, spin and parity is independent of its formation. Using FPYs, we have performed a new high-precision test of the combined e ﬀ ects of the entrance channel, spin and parity on the ﬁssion process from two of the most commonly used particles to induce ﬁssion - neutrons and photons. The 239 Pu(n,f) reaction at E n = 4 . 6 MeV and the 240 Pu( γ ,f) reaction at E γ = 11 . 2 MeV were used to produce a 240 Pu ∗ compound nucleus with the same excitation energy. The FPYs from these two reactions were measured using quasimonoenergetic neutron beams from the TUNL’s FN tandem Van de Graa ﬀ accelerator and quasimonenergetic photon beams from the High Intensity γ -ray Source (HI γ S) facility. The FPYs from these two reactions are compared quantitatively for the ﬁrst time.


Introduction
Since the discovery of nuclear fission in 1938, there has been extensive efforts to develop a theoretical description of the fission mechanism. The compound reaction-channel formalism of Bohr and Wheeler, first proposed in 1939 [1] is remarkably successful at describing the fission process. An essential assumption of this theory is that the nucleus proceeds through the fission process in a well defined quantum state. Thus the state of the nucleus influences the fission process, while the formation mechanism of the compound nucleus does not. Consequently all fission theory relies on the "Bohr hypothesis", which states that the decay of a compound nucleus for a given excitation energy, spin, and parity is independent of its formation [2]. The Bohr hypothesis is a particularly reasonable assumption for nuclear fission, where the timescale for the formation of the compound nucleus (∼ 10 −16 seconds) is long compared to the time needed to reach an equilibrium. However, despite the Bohr hypothesis underlying nearly every modern theoretical fission model, it has yet to be tested experimentally to a high degree of precision. Currently, the Bohr hypothesis is verified to about 20% accuracy in fission using nuclear reactions such as (t,pf), ( 3 He,df), and ( 3 He,tf) [3][4][5][6][7]. In this work we propose to test Bohr's hypothesis in the context of nuclear fission by comparing the fission product yields (FPYs) from a compound 240 Pu * nucleus produced via two different nuclear reactions: 239 Pu(n,f) and 240 Pu(γ,f).

Experiment
In this work we performed the first-ever experiment to identify the practical consequences of the Bohr hypothesis in the context of induced nuclear fission. We measured the FPYs from the 240 Pu(γ,f) reaction at the HIγS facility at Triangle Universities Nuclear Laboratory (TUNL) [8] and compared the results to the FPYs obtained from the 239 Pu(n,f) reaction that our group recently measured at the TUNL Tandem Van de Graaff accelerator [9][10][11][12]. Both reactions produced a 240 Pu compound nucleus with the same excitation energy since the energies of the incident neutron and photon beams were purposely chosen to account for the 6.5 MeV difference in binding energy between 239 Pu and 240 Pu. The only difference was the spinparity distributions from n + 239 Pu and J π = 1 − from γ + 240 Pu, which is widely believed to be inconsequential at high excitation energies.

Dual-fission chambers
One of the most significant components in measurements of fission product yields is determining the number of fission reactions that occurred in the target. In the present work the fission reactions are counted using a Dual-fission ionization Chamber (DFC) [9], based on the design by Grundl et al. [13] for FPY measurements in reactors and critical assemblies [14].
The irradiation for the 239 Pu(n,f) measurements in Gooden et al. [11] were performed with the thick 239 Pu activation target mounted in the center of the DFC, as is the standard procedure used by our group [9][10][11]15]. The two FCs then measure the effective neutron flux just before and after the target, and the effects of the beam divergence can be accounted for with Monte Carlo calculations [9]. The previously published data for 239 Pu(n,f) at E n = 4.6 MeV were only sensitive to FPYs with half lives of ∼days or longer, so the data were augmented with a new recent measurement using the same experimental procedure and target but with only 2 hours of irradiation, in order to measure the yields of FPYs with half lives of a few minutes to a few hours.
In the case of the 240 Pu photofission measurements, the thick 240 Pu activation targets were positioned just outside of the DFC, with the long-activation target upstream and the short-activation target downstream with respect to the γ-ray beam. Unlike the neutron beams at TUNL, the HIγS γ-ray beam is highly parallel with negligible divergence over a few cm distance. Thus it is not necessary to account for the spread of the γ-ray beam between the FC and the targets. This assumption was confirmed by comparing the relative beam flux measured in each chamber in the DFC. When a DFC is mounted in the neutron beam at TUNL, the beam divergence causes the upstream FC to typically see ∼ 25% greater flux than the downstream FC, after accounting for the masses of the reference foils in each chamber. In the HIγS γ-ray beam, the 240 Pu DFC upstream to downstream FC ratio of 1.02 ± 0.01 was reasonably consistent with negligible γ-ray beam divergence. In addition, the self-absorption and scattering of the 11.2 MeV γ-ray beam from the thick foils was less than 1%, as calculated by MCNP simulations.

Activation targets & reference foils
The 240 Pu targets used in this measurement both consist of 240 PuO 2 powder which is compressed into a 1.27 cm diameter Al cylinder, the same diameter as the 239 Pu target that was used in Ref. [11]. The 240 Pu mass of each target was 73.01±0.04 mg and 89.11±0.05 mg, with both targets enriched to 99.873% 240 Pu. The Al holders have a mass of ∼ 19 mg, with a 1.91 cm outer diameter and a 0.191 cm thickness. The Al material is relatively transparent to the γ-rays emitted by the β-decay of fission products and also is not activated by exposure to the 11.2 MeV γ-ray beam.
The reference foils for the DFC consist of 240 Pu electroplated onto a 1.27 cm diameter area on a Ti backing with 240 Pu masses of 25.97±0.18 µg and 23.60±0.12 µg and an isotopic enrichment of 99.873%. The spatial uniformity of the deposition was verified by scanning the surface of the foils with a 1 mm aperture α-detector. Like the 239 Pu reference foils, the 240 Pu deposits were sufficiently thin that fission fragments could easily escape the electroplated material and deposit their energy in the gas of the ionization chambers with nearly 100% efficiency.

Monoenergetic photon beams from the HIγS facility
The HIγS facility produces intense, quasimonoenergetic γ-ray beams via intra-cavity Compton backscattering of free electron laser photons and relativistic electrons [8]. Photofission measurements require intense γ-ray beams such as the ones provided by the HIγS facility since the (γ,f) reaction is typically a factor of ∼5-10 smaller than the (n,f) reaction for a given target nucleus.
For this work, the HIγS facility was operated using 540 nm free electron laser photons to produce linearly-polarized, 11.2 MeV γ-ray beams with a resolution of approximately 360 keV (FWHM) and an average flux on target of 1.95 × 10 7 γ-rays/(cm 2 s). The γ-ray beam was collimated with a 1.27 cm diameter, 15.24 cm long Pb collimator placed ∼2.5 m upstream of the target assembly. The energy spectrum of the γ-ray beam was measured with a 123% high-purity germanium (HPGe) detector positioned in the beam axis, while copper attenuators were inserted into the γ-ray beam far upstream of the collimator to reduce the flux.
One 240 Pu target (#1) was irradiated with E γ =11.2 MeV γ-ray beam for 2 hours to measure the short-lived FPYs (minutes to hours), the other (#2) for 92.6 hours to build up activity of long-lived FPYs (days). The 2 hour irradiation induced a total of 8.25±0.15×10 6 fissions in the short-lived FPY target, while the 92.6 hour irradiation induced a total of 4.38 ± 0.07 × 10 8 fission events.

Detection of γ-rays from the β-decay of fission products
After irradiation by the HIγS γ-ray beam, the activated 240 Pu targets were monitored by a 60% relative efficiency HPGe. The first target with 2 hours of irradiation was counted for ∼ 90 hours while the second, long-lived FPY target was being irradiated. After the long irradiation was completed, the second 240 Pu target replaced the first one in the same HPGe counting station. Thus both 240 Pu targets were monitored by the same HPGe at the same distance. Since this HPGe detector is the same one that was used in the 239 Pu(n,f) measurements of Gooden et al. [11] (and in the supplemental 239 Pu(n,f) measurements made recently), all of the FPY measurements are on the same systematic footing. Consequently this work posseses a unique sensitivity for comparing FPY distributions from the 239 Pu(n,f) and 240 Pu(γ,f) reactions. The measured fission product γ-ray spectra from the 239 Pu(n,f) and 240 Pu(γ,f) reactions are compared in Fig. 1.  Figure 1. γ-ray spectra from fission products from 240 Pu(γ,f) at E γ = 11.2 MeV and 239 Pu(n,f) at E n = 4.6 MeV, measured by a 60% relative efficiency HPGe. Both spectra come from targets which were irradiated for 2 hours.

Analysis & data reduction
Yields of specific fission products are determined by counting γ-rays emitted by the decay of the corresponding fission products. Choosing the counting window in time is complicated by the interplay of the activity of the γ-ray of interest, interfering background peaks and the smooth continuum background. Because all of these features are time dependent, it can be difficult to predict a priori what the ideal integral time window is to fit the net photopeak area. In this work, a procedure was developed to automatically determine the integration time in a way which minimizes the uncertainty in the net photopeak counts, which is often one of the largest sources of uncertainty in the short-lived FPY measurements. Multiple spectra were generated with each successive spectrum having a longer counting time. The photopeak of interest was fit in each spectrum with a Gaussian function, including a linear background and other Gaussian peaks. The uncertainty of the net photopeak counts from the fit was then plotted as a function of counting time. In addition to minimizing the uncertainty in the photopeak counts, this method removes the choice of the counting period as a potential source of bias.
Using the same formalism as in Ref. [11], the FPYs can be defined as: Cumulative Yield % The correction factors include effects due to beam fluctuations, γ-ray attenuation and summing in the HPGe.

Results and discussion
The 35 unique FPYs measured from 240 Pu(γ,f) at E γ = 11.2 MeV are plotted in Fig. 2 along with the corresponding yields from 239 Pu(n,f) at E n = 4.6 MeV, if available. There were 29 unique FPYs which were measured for both sets of data. The FPYs are generally in good agreement, though there are some notable differences where the yields differ by multiple standard deviations. Significantly, the light mass peak in the FPY distribution doesn't show a systematic shift between the two distributions. Such a shift is expected in the case where the fissioning compound nucleus has a different mass, as the heavy fragment tends to remain constant due to shell closures, and additional nucleons are added to the light fragment. The lack of a systematic difference between the two FPY distributions is consistent with Bohr's hypothesis.
In order to quantify the similarity between the two sets of FPYs, a goodness of fit value may be defined as where Y240 Pu(γ, f ) ( A Z i ) and Y239 Pu(n, f ) ( A Z i ), are the yields of the fission product A Z i from 240 Pu(γ, f ) and 239 Pu(n, f ), respectively; and σ240 Pu(γ, f ) and σ239 Pu(n, f ) are the uncertainty in the 240 Pu(γ,f) and 239 Pu(n,f) FPYs, respectively. The number of degrees of freedom is equal to the number of pairs of FPYs. A histogram of the χ 2 for each individual FPY pair is shown in Fig. 3. The total χ 2 per degree of freedom for this work is 1.36, reasonably consistent with the expected value of 1 if the FPY distributions from 240 Pu(γ,f) and 239 Pu(n,f) at the same compound nuclear excitation energy are the same. Thus, these preliminary results are consistent with Bohr's hypothesis.

Conclusion & Future Work
This work represents the first quantitative comparison of FPYs from the 240 Pu(γ,f) and 239 Pu(n,f) reactions at the same compound nuclear excitation energy. The primary goal of the present experiments was to obtain an accurate comparison of the 240 Pu(γ,f) and 239 Pu(n,f) FPY measurements. The required accuracy was obtained by using the same experimental techniques and exact same HPGe detectors for both measurments, eliminating systematic errors which would otherwise make a direct comparison of the data sets difficult.
In order to improve the validation of Bohr's hypothesis in the context of fission, we have performed additional measurements of the FPYs from the 240 Pu(γ,f) reaction at E γ = 8.0 and 11.2 MeV. The 11.2 MeV measurement was performed with significantly greater γ-ray beam flux, which will increase the number of measurable yields and decrease the statistical uncertainties on the FPYs presented in this work. The 8.0 MeV data set can be compared to existing 239 Pu(n,f) data at E n = 1.5 MeV [11], allowing us to test if the energy evolution of the FPYs from 240 Pu(γ,f) and 239 Pu(n,f) are consistent. the E γ = 8.0 MeV data, in conjunction with the E n = 1.5 MeV data, should also be more sensitive to the pairing and shell effects which are more pronounced at these relatively low excitation energies. In this case the small mismatch of the angular momentum in the entrance channel will be further investigated.