$\gamma$ strength function and level density of ${}^{208}\text{Pb}$ from forward-angle proton scattering at 295 MeV

Background: $\gamma$ strength functions (GSFs) and level densities (LDs) are essential ingredients of statistical nuclear reaction theory with many applications in astrophysics, reactor design, and waste transmutation.

Purpose: The aim of the present work is a test of systematic parametrizations of the GSF recommended by the RIPL-3 database for the case of ${}^{208}\text{Pb}$. The upward GSF and LD in ${}^{208}\text{Pb}$ are compared to $\gamma$ decay data from an Oslo-type experiment to examine the validity of the Brink-Axel (BA) hypothesis.

Methods: The $E1$ and M1 parts of the total GSF are determined from high-resolution forward angle inelastic proton scattering data taken at 295 MeV at the Research Center for Nuclear Physics (RCNP), Osaka, Japan. The total LD in ${}^{208}\text{Pb}$ is derived from the $1^{-}$ LD extracted with a fluctuation analysis in the energy region of the isovector giant dipole resonance.

Results: The $E1$ GSF is compared to parametrizations recommended by the RIPL-3 database showing systematic deficiencies of all models in the energy region around neutron threshold. The new data for the poorly known spin-flip $M1$ resonance call for a substantial revision of the model suggested in RIPL-3. The total GSF derived from the present data is larger in the PDR energy region than the Oslo data but the strong fluctuations due to the low LD resulting from the double shell closure of ${}^{208}\text{Pb}$ prevent a conclusion on a possible violation of the BA hypothesis. Using the parameters suggested by RIPL-3 for a description of the LD in ${}^{208}\text{Pb}$ with the back-shifted Fermi gas model, remarkable agreement between the two experiments spanning a wide excitation energy range is obtained.

Conclusions: Systematic parametrizations of the $E1$ and $M1$ GSF parts need to be reconsidered at low excitation energies. The good agreement of the LD provides an independent confirmation of the approach underlying the decomposition of GSF and LD in Oslo-type experiments.

Figure 1

$E1$ GSF of ${}^{208}\text{Pb}$ deduced from the $(p,p^{\prime })$ data [23, 24] (blue diamonds) in comparison with the SLO (green line), MLO (cyan line), and EGLO (magenta line) models explained in the text. The black circle shows the prediction from experimental systematics at the neutron separation threshold [30].

Figure 2

Same as Fig. 1 but for the $M1$ component of the GSF.

Figure 3

$E2$ GSF deduced from Ref. [39] in comparison to the SLO model with parameters from Ref. [40]. The GSF was multiplied by $E_x^2$ to make the units comparable to the $E1$ and $M1$ GSFs.

Figure 4

Comparison of $E1, M1$, and $E2$ contributions to the GSF of ${}^{208}\text{Pb}$.

Figure 5

Total GSF of ${}^{208}\text{Pb}$ from the $(p,p^{\prime })$ data [23, 24] in comparison to the reanalyzed [42] results from the Oslo experiment [41]. The inset shows an expanded view of the low-energy region, $5–8$ MeV.

Figure 6

Spin distribution functions of LDs in ${}^{208}\text{Pb}$ at excitation energies of 8 and 15 MeV from BSFG model predictions with the parameters of Ref. [41] (magenta dashed-dotted lines), Ref. [30] (green solid lines), and Ref. [48] (cyan dashed lines). The vertical dashed lines indicate the values for spin $J=1$.

Figure 7

Total level density of ${}^{208}\text{Pb}$ between 9 and 12.5 MeV obtained with the spin distribution functions of Ref. [41] (right-pointing magenta triangles), Ref. [30] (green upward triangles), and Ref. [48] (cyan downward triangles). Mean values averaged over the three models are shown as blue diamonds.

Figure 8

Total LD from the $(p,p^{\prime })$ data [23, 24] in comparison to the reanalyzed [42] results from the Oslo experiment [41]. The black downward triangles are results from from counting the levels identified in Ref. [52] in 200 keV bins. The magenta dashed-dotted, green solid, and cyan dashed lines are BSFG model predictions with the parameters of Refs. [41], [30], and [48], respectively.