Simultaneous Determination of Neutron-Induced Fission and Radiative Capture Cross Sections from Decay Probabilities Obtained with a Surrogate Reaction

Reliable neutron-induced-reaction cross sections of unstable nuclei are essential for nuclear astrophysics and applications but their direct measurement is often impossible. The surrogate-reaction method is one of the most promising alternatives to access these cross sections. In this work, we successfully applied the surrogate-reaction method to infer for the first time both the neutron-induced fission and radiative capture cross sections of ${}^{239}\mathrm{Pu}$ in a consistent manner from a single measurement. This was achieved by combining simultaneously measured fission and $\gamma$-emission probabilities for the ${}^{240}\mathrm{Pu}({}^4\mathrm{He},{}^4{\mathrm{He}}^{\prime })$ surrogate reaction with a calculation of the angular-momentum and parity distributions populated in this reaction. While other experiments measure the probabilities for some selected $\gamma$-ray transitions, we measure the $\gamma$-emission probability. This enlarges the applicability of the surrogate-reaction method.

Figure 1

Decay probabilities for fission (blue squares) and $\gamma$ emission (red triangles) measured for the ${}^{240}\mathrm{Pu}({}^4\mathrm{He},{}^4{\mathrm{He}}^{\prime }){}^{240}{\mathrm{Pu}}^{*}$ reaction as a function of the excitation energy $E^{*}$ of ${}^{240}{\mathrm{Pu}}^{*}$. The sum of the two probabilities is given by the black circles. The $P_{s,f}$ and $P_{s,\gamma }$ calculated with Eq. (1) and the values of the adjusted Talys parameters that led to the minimum ${\chi }^2$ value are represented by the blue and red solid lines, respectively. The $E^{*}$ range used for parameter adjustment is delimited by the vertical green lines. The vertical dotted line indicates the neutron separation energy $S_n$ of ${}^{240}\mathrm{Pu}$. The horizontal black line at a constant value of 1 serves to guide the eye.

Figure 2

Neutron-induced fission (a) and radiative capture (b) cross sections of ${}^{239}\mathrm{Pu}$ as a function of neutron energy. The red squares are the cross sections obtained with the WE approximation [Eq. (2)]. The cross sections calculated with the parameters deduced from the measured decay probabilities are shown as blue solid lines. The shaded blue areas indicate the associated uncertainties. The dash-dotted, dotted, and dashed lines represent different evaluations. The black dots indicate the neutron-induced data of [32] (a) and [33] (b).

Figure 3

Calculated spin-parity distribution $F_s$ of ${}^{240}{\mathrm{Pu}}^{*}$ populated by the ${}^{240}\mathrm{Pu}({}^4\mathrm{He},{}^4{\mathrm{He}}^{\prime })$ reaction at $E^{*}=7.5\mathrm{MeV}$ and ${\theta }_{4{\mathrm{He}}^{\prime }}=140°$.