Investigation of the ${}^{238}\mathrm{U}\left(d,p\right)$ surrogate reaction via the simultaneous measurement of $\gamma$-decay and fission probabilities

We investigated the ${}^{238}\mathrm{U}\left(d,p\right)$ reaction as a surrogate for the $n+{}^{238}\mathrm{U}$ reaction. For this purpose we measured for the first time the $\gamma$-decay and fission probabilities of ${}^{239}\mathrm{U}^{*}$ simultaneously and compared them to the corresponding neutron-induced data. We present the details of the procedure to infer the decay probabilities, as well as a thorough uncertainty analysis, including parameter correlations. Calculations based on the continuum-discretized coupled-channels method and the distorted-wave Born approximation (DWBA) were used to correct our data from detected protons originating from elastic and inelastic deuteron breakup. In the region where fission and $\gamma$ emission compete, the corrected fission probability is in agreement with neutron-induced data, whereas the $\gamma$-decay probability is much higher than the neutron-induced data. We have performed calculations of the decay probabilities with the statistical model and of the average angular momentum populated in the ${}^{238}\mathrm{U}\left(d,p\right)$ reaction with the DWBA to interpret these results.

Figure 1

Schematic representation of the surrogate-reaction method. The surrogate reaction depicted here is a transfer reaction $X$($y,w$)$A{}^{*}$. Three of the possible exit channels (fission, $\gamma$ emission, and neutron emission) are represented.

Figure 2

Schematic view of the setup used at the Oslo Cyclotron Laboratory for the simultaneous measurement of fission and $\gamma$-decay probabilities.

Figure 3

Energy loss versus residual energy of the ejectile measured at 126 degrees. The ejectiles corresponding to different hydrogen isotopes are indicated. The arrows in the lower part indicate the ${}^{17}\mathrm{O}$ and ${}^{13}\mathrm{C}$ states used for the energy calibration of the telescopes, where ${}^{13}\mathrm{C}_0$ corresponds to the ground state of ${}^{13}\mathrm{C}, {}^{13}\mathrm{C}_1$ to the first excited state, etc.

Figure 4

Number of detected protons as a function of the excitation energy of ${}^{239}\mathrm{U}^{*}$ measured at 126 degrees. The blue dashed line is the proton spectrum, $N_p$. The red dashed-dotted line, $N_c$, corresponds to the spectrum obtained with the carbon backing without normalization factor. The spectrum obtained after subtraction of the carbon spectrum, $N_{p-c}$, is represented by the pink dotted line. The singles spectrum $N^S$ is shown as a black solid line. The vertical dotted line represents the neutron separation energy of ${}^{239}\mathrm{U}$. The peaks related to the formation of ${}^{17}\mathrm{O}$ and ${}^{13}\mathrm{C}$ in the ground and first excited states are indicated with the same notation as in Fig. 3.

Figure 5

The red dotted line, $N_{f-\mathrm{raw}}^c$, is the spectrum of protons detected in coincidence with a signal in the fission detector as a function of the excitation energy of ${}^{239}\mathrm{U}^{*}$. The blue dashed-dotted line corresponds to the normalized random-coincidence spectrum, $N_{f-\mathrm{random}}^c$. The fission coincidence spectrum, $N_f^C$, is shown as the solid black line.

Figure 6

Excitation energy of ${}^{239}\mathrm{U}$ versus detected $\gamma$-ray energy. The applied energy threshold, $E_{\gamma }^{\mathrm{th}}$, is represented by the vertical dotted line. Excitation energies corresponding to $S_n$ and $S_n+E_{\gamma }^{\mathrm{th}}$ are indicated by horizontal dotted lines. The 45-degree lines with origin at $E^{*}=0$ and $E^{*}=S_n$ are represented by full lines. The region used in the analysis of the $\gamma$-decay probability is highlighted by the red dashed line.

Figure 7

The blue dashed-dotted line $N_{\gamma }^{C,\mathrm{tot}}$ represents the number of protons detected in coincidence with a $\gamma$ ray detected in any of the CACTUS detectors as a function of the excitation energy of ${}^{239}\mathrm{U}$ measured at 126 degrees. A threshold in the $\gamma$-ray energy $E_{\gamma }^{\mathrm{th}}>1.5\mathrm{MeV}$ and a time window of 11 ns were used to obtain this spectrum. The red-dotted line is the fission-$\gamma$ coincidence spectrum $N_{\gamma ,f}^C$ divided by the fission efficiency ${\varepsilon }_f$. The black line represents the $\gamma$-coincidence spectrum $N_{\gamma }^C$. The green dashed line is the singles spectrum $N^S$. The arrow indicates the neutron separation energy of ${}^{239}\mathrm{U}^{*}$.

Figure 8

Ratio between the $\gamma$-coincidence and the singles spectra. The vertical dotted line indicates the neutron separation energy of ${}^{239}\mathrm{U}$ and the red solid line is a linear fit to the data in the ${\mathrm{E}}^{*}$ interval $[2\mathrm{MeV};S_n]$.

Figure 9

Measured $N_f^C$ as a function of $N^S$ (a) and as function of $N^{\mathrm{AC}}=N^S-N_f^C$ (b). The values of $N^S$ have been sampled from a Gaussian distribution centered at $\langle N^S\rangle =200$ and with standard deviation $\sqrt{\langle N^S\rangle }=\sqrt{200}$.

Figure 10

Measured $\gamma$-decay (a) and fission (b) probabilities as a function of excitation energy (symbols) compared to the results of several evaluations (lines). Correlation matrix for the $\gamma$-decay (c) and fission (d) probabilities measured at 126 degrees. The vertical dotted line in panel (a) represents the neutron separation energy of ${}^{239}\mathrm{U}^{*}$.

Figure 11

Calculated contributions to the total deuteron breakup process (TB), as a function of the excitation energy of ${}^{239}\mathrm{U}$ for a deuteron beam energy of 15 MeV and a proton angle of 140 degrees (a) and for a beam energy of 18 MeV and proton angle of 150 degrees (b). NEB corresponds to nonelastic breakup, BF to breakup fusion, and EB to elastic breakup. Note that $\mathrm{TB}=\mathrm{NEB}+\mathrm{EB}$. The vertical dotted lines indicate the neutron separation energy of ${}^{239}\mathrm{U}$.

Figure 12

Measured $P_{\chi }^{\mathrm{mes}}$ and corrected $P_{\chi }^{\mathrm{corr}}$ decay probabilities as a function of excitation energy. The neutron-induced decay probabilities from different evaluations are represented by the lines. The $\gamma$-decay probabilities are shown in panel (a) and the fission probabilities in panel (b). The vertical dotted line in panel (a) indicates the neutron separation energy of ${}^{239}\mathrm{U}$.

Figure 13

Fission and $\gamma$-decay probabilities as a function of excitation energy compared to the corresponding neutron-induced decay probabilities according to different evaluations. Note that only the fission probability has been corrected for deuteron breakup.

Figure 14

Decay probabilities as a function of excitation energy for different values of angular momentum and parity of ${}^{239}\mathrm{U}^{*}$ calculated with evita. The decay probabilities measured in this work (full circles) and the neutron-induced decay probabilities obtained with evita (thick blue lines) are also shown. $\gamma$-decay probabilities with positive and negative parities are shown in panels (a) and (b), respectively. Fission probabilities are shown in panels (c) and (d).

Figure 15

Fission probability as a function of excitation energy. Our corrected data (dots) and EVITA results for the neutron-induced probability (full line) are compared to an EVITA calculation performed with the initial spin distribution deduced from a fit to our $\gamma$-decay probability (dashed line).