Photoneutron cross sections for Mo isotopes: A step toward a unified understanding of $(\gamma ,n)$ and $(n,\gamma )$ reactions

Photoneutron cross sections were measured for ${}^{94}$Mo, ${}^{95}$Mo, ${}^{96}$Mo, ${}^{97}$Mo, ${}^{98}$Mo, and ${}^{100}$Mo near the neutron threshold with quasi-monochromatic laser-Compton scattering $\gamma$ rays. The photoneutron data were analyzed with the Skyrme Hartree-Fock-Bogoliubov (HFB) plus quasiparticle random phase approximation (QRPA) model and the axially symmetric-deformed Gogny HFB plus QRPA model of $E1$ $\gamma$-ray strength. Combining the $\gamma$-ray strength function constrained by the present photoneutron data with either the nuclear resonance fluorescence data or the updated Oslo data to supplement the data below the neutron threshold, a thorough analysis of the reverse $(n,\gamma )$ cross sections is made whenever measurements are available. The Oslo data and the corresponding uncertainties are updated based on the latest results of the $s$-wave neutron spacing and the average radiative width determined in particular for ${}^{96}$Mo. Finally, radiative neutron capture cross sections for two radioactive nuclei, ${}^{93}$Mo and ${}^{99}$Mo, are deduced with the $\gamma$-ray strength function method.

Figure 1

The chart of nuclei depicting our systematic analysis of $(\gamma ,n)$ and $(n,\gamma )$ cross sections for Mo isotopes in the context of the $\gamma$-ray strength function method. Photoneutron cross sections measured in the present experiment are shown by left arrows. Radiative neutron capture cross sections discussed in the present systematic analysis are shown by right arrows. Photoneutron cross sections for two radioactive nuclei, ${}^{93}$Mo and ${}^{99}$Mo, are deduced with the $\gamma$-ray strength function method.

Figure 2

A typical energy distribution of the LCS $\gamma$-ray beam used in the present experiment.

Figure 3

Comparison between the present photoneutron emission cross sections and previously measured ones [17, 18] for six Mo isotopes, ${}^{94}$Mo (a), ${}^{95}$Mo (b), ${}^{96}$Mo (c), ${}^{97}$Mo (d), ${}^{98}$Mo (e), and ${}^{100}$Mo (f). Also included are the predictions from Skyrme HFB+QRPA (based on the BSk7 interaction) [20] and axially deformed Gogny HFB+QRPA models (based on the D1M interaction) [23].

Figure 4

Comparison between the measured photoabsorption cross sections derived from photoneutron experiments (including ours) [17, 18] as well as particle-$\gamma$ coincidence measurements [8, 25] (see also text for the corresponding error bars) and ($\gamma$,${\gamma }^{\prime }$) data [24] for three Mo isotopes, ${}^{94}$Mo (a), ${}^{96}$Mo (b), and ${}^{98}$Mo (c). Predictions from Skyrme HFB+QRPA (based on the BSk7 interaction) [20] and axially deformed Gogny HFB+QRPA models (based on the D1M interaction) [23] are also included.

Figure 5

Same as Fig. 4 for ${}^{95}$Mo (a), ${}^{97}$Mo (b), and ${}^{100}$Mo (c) isotopes for which the present ($\gamma$,$n$) data are available and either the particle-$\gamma$ or the ($\gamma$,${\gamma }^{\prime }$) data.

Figure 6

Comparison between the measured radiative neutron capture cross sections for ${}^{94}$Mo (a), ${}^{95}$Mo (b), ${}^{96}$Mo (c), and ${}^{97}$Mo (d) [30, 32, 33] with talys calculation making use of the D1M+QRPA calculation for the $E1$ strength supplemented either with the Oslo or the ($\gamma$,${\gamma }^{\prime }$) data, as given in Figs. 4 and 5. See text for more details.

Figure 7

talys predictions for the radiative neutron capture cross sections of ${}^{93}$Mo($n$,$\gamma$)${}^{94}$Mo (a) and ${}^{99}$Mo($n$,$\gamma$)${}^{100}$Mo (b) making use of the Oslo or the ($\gamma$,${\gamma }^{\prime }$) data whenever available. The error bands include uncertainties in the experimental $\gamma$SF as well as the theoretical nuclear level densities. The dotted, dashed, and dash-dot curves correspond to the Japanese JENDL-4.0, American ENDF/B-VII.1, and Russian ROSFOND-2010 evaluations [37], respectively, whenever available.