Consistency of photon strength function models with data from the ${}^{94}\mathrm{Mo}(d,p\gamma \gamma )$ reaction

Recently published study on the $\gamma$-ray energy dependence of photon strength functions (PSFs) from the population of ${}^{95}\mathrm{Mo}$ low-lying levels in the ${}^{94}\mathrm{Mo}(d,p\gamma \gamma ){}^{95}\mathrm{Mo}$ reaction set out to answer some important questions related to the PSFs below the neutron separation energy in the Mo region. In this paper we discuss in detail actual relations of the quantities measured in this reaction to the PSFs and check the consistency of several available PSF models with experimental data. A broad variety of models was found to be consistent with experimental data at low $E_{\gamma }$. Although the photon strength very likely increases with decreasing energy at $E_{\gamma }\lesssim 3$ MeV, the data are unable to clearly differentiate whether the decrease follows the shape proposed from Oslo-type experiments or predictions of the generalized Lorentzian $E1$ model. The PSF shape at energies of $5\text{–}7$ MeV is steeper than predicted by any standard model.

Figure 1

Illustration of the procedure for determining intensities $N_{L_j}(E_i,E_{{\gamma }_1})$: (a) The proton energy deposited in $\mathrm{\Delta }E-E$ telescopes determines the excitation energy $E_i$ of the ${}^{95}\mathrm{Mo}$ nucleus populated in the ${}^{94}\mathrm{Mo}(d,p)$ reaction. (b) Additional coincidence of two $\gamma$ rays—primary $\gamma$ ray with $E_{{\gamma }_1}=E_i-E_{L_j}$ and a secondary $\gamma$ ray with $E_{{\gamma }_2}$—which is known to deexcite a low-lying level at $E_{L_j}$, is required to validate the event.

Figure 2

Comparison of experimental $N_{L_j}(E_i,E_{\gamma })/E_{\gamma }^3$ data with predictions of the PSF model describing $\left(n,\gamma \right)$ data in ${}^{96}\mathrm{Mo}$ (model $A)$. Different colors of experimental data correspond to different $E_i$, in agreement with the model color coding; different symbols are used for different spins of $L_j$. Experimental data are normalized to corresponding modeled $E_i$ curves.

Figure 3

Comparison of experimental data with tested PSF models; for details of the models, see the main text. Two curves in panel (a), corresponding to transitions from $S_n$ (upper curve) and transitions to the ground state (lower curve) are plotted for model $A$, which depends on the excitation energy. Normalization of experimental data from each $E_i$ and $J_{L_j}$ is made with respect to model $D$ in both panels of the figure. For a quantitative comparison of experimental data with predictions, individual normalization factors must be applied for each model and each pair of $E_i$ and $J_{L_j}$. Symbols used for experimental data are the same as those in Fig. 2.