Test of the Brink-Axel Hypothesis for the Pygmy Dipole Resonance

The gamma strength function and level density of $1^{-}$ states in ${}^{96}\mathrm{Mo}$ have been extracted from a high-resolution study of the ($\overrightarrow{p}$, ${\overrightarrow{p}}^{\prime }$) reaction at 295 MeV and extreme forward angles. By comparison with compound nucleus $\gamma$ decay experiments, this allows a test of the generalized Brink-Axel hypothesis in the energy region of the pygmy dipole resonance. The Brink-Axel hypothesis is commonly assumed in astrophysical reaction network calculations and states that the gamma strength function in nuclei is independent of the structure of the initial and final state. The present results validate the Brink-Axel hypothesis for ${}^{96}\mathrm{Mo}$ and provide independent confirmation of the methods used to separate gamma strength function and level density in $\gamma$ decay experiments.

Figure 1

(a) Spectra of the ${}^{96}\mathrm{Mo}(\overrightarrow{p},{\overrightarrow{p}}^{\prime })$ reaction at $E_p=295\mathrm{MeV}$ with the spectrometer placed at 0° (blue), 3° (yellow), and 4.5° (red). (b) Total spin transfer $\mathrm{\Sigma }$, Eq. (1). (c) Examples of the MDA for selected energy bins.

Figure 2

Relative yield $R$ of nonspin-flip ($\mathrm{\Delta }S=0$) and spin-flip ($\mathrm{\Delta }S=1$) cross section parts of the ${}^{96}\mathrm{Mo}(\overrightarrow{p},{\overrightarrow{p}}^{\prime })$ spectrum in the excitation energy region 6–11 MeV based on the MDA and PTA, respectively. Agreement between the two independent methods is observed within error bars.

Figure 3

(a) GSF of ${}^{96}\mathrm{Mo}$ from the present work (red circles) compared with (${}^3\mathrm{He}$, ${}^3{\mathrm{He}}^{\prime }\gamma$) [22, 23] (open circles), ($\gamma$, $xn$) [48] (grey squares), ($\gamma$, $n$) [49], (blue upward triangles), and ($\gamma$, ${\gamma }^{\prime }$) [24] data including a statistical model correction for unobserved branching ratios (black circles) (b) Expanded range from 5 MeV to neutron threshold.

Figure 4

Total LD in ${}^{96}\mathrm{Mo}$ deduced from the fine structure of the ($p$, $p^{\prime }$) data in the energy region of the IVGDR (red diamonds) compared with the results from the (${}^3\mathrm{He}$, ${{}^3\mathrm{He}}^{\prime }\gamma$) Oslo experiment (blue squares) [22, 23]. The black circle point stems from $s$-wave resonance neutron capture [49]. BSFG models normalized to the value at $S_n$ are shown as green solid [44], cyan dashed [53], and purple dashed-dotted [54] lines. The inlet shows the LD of $1^{-}$ states in comparison with absolute predictions of the models.