Study of photon strength functions via (γ→, γ′, γ′′) reactions at the γ3-setup

One of the basic ingredients for the modelling of the nucleosynthesis of heavy elements are so-called photon strength functions and the assumption of the Brink-Axel hypothesis. This hypothesis has been studied for many years by numerous experiments using different and complementary reactions. The present manuscript aims to introduce a model-independent approach to study photon strength functions via γ-γ coincidence spectroscopy of photoexcited states in 128Te. The experimental results provide evidence that the photon strength function extracted from photoabsorption cross sections is not in an overall agreement with the one determined from direct transitions to low-lying excited states.


Introduction
The photon strength function (PSF) serves as an essential input for nuclear astrophysical model calculations. It plays an important role in capture and photo-disintegration reactions as well as in astrophysical scenarios describing the nucleosynthesis. In the past, different experimental methods and approaches have been used to study the PSF (see, e.g., Refs. [1][2][3][4][5] and references therein). However, many of these methods are model dependent either in the reaction mechanism itself or in the data analysis. In this contribution, we present a modelindependent approach, exemplarily for 128 Te, to extract the PSF in real-photon scattering experiments using quasi-monochromatic photon beams provided by the High Intensity γ-ray Source (HIγS) [6] at Duke University, Durham, NC, USA.

Methods
In the following, two independent methods are introduced to determine the PSF for the excitation as well as for the decay channel in a single experiment exploiting the monochromatic character of the photon beam provided by the HIγS facility.
The photoabsorption cross section σ γ (= σ γγ + σ γγ' ) is linked to the PSF built on the ground state by f (E γ ) ∝ σ γ /E γ assuming predominantly dipole transitions. The procedure to determine σ γ as a function of the excitation energy at HIγS was discussed in detail in previous works, such as [5,[7][8][9]. The idea is sketched in Fig. 1.a). After photoexcitation of the nucleus in a given enery range defined by the energy and the width of the quasimonochromatic photon beam, σ γ is reconstructed by measuring all ground-state transitions (σ γγ ) and all events cascading via intermediate levels (σ γγ ), where σ γγ can be approximated by the intensity observed for the 2 + 1 → 0 + 1 transition [7]. The second approach is illustrated in Fig. 1.b) and c) and was firstly introduced in Ref. [2] using proton-γ-γ correlations in 94 Mo(d, p) 95 Mo reactions. Due to the novel γ-γ coicidence setup γ 3 [10] it is feasible for the first time to apply this method in ( γ, γ γ ) reactions, here shown for the example of 128 Te. Primary transitions from excited states at E x 1 to lowlying excited levels yield information on the PSF at the corresponding transition energies: with I x 1 →2 + 1 being the associated transition intensity. The observation of several direct transitions to low-lying states per excitation energy and beam-energy setting, respectively, allows to reconstruct the PSF over a broad γ-ray energy range, which is schematically shown in Fig. 1.c) for a hypothetical PSF. These two outlined approaches allow to independently study the PSF in the excitation and the decay channel, respectively.

Experiment & Results
For the present work a metallic and highly-enriched (99.8 %) 128 Te target was used to perform photon-scattering experiments with quasi-monochromatic γ-ray beams with energies between 3 MeV and 9 MeV in steps of about 250 keV. The spectral distribution of the beam is usually about FWHM ≈ 3 % of the beam energy.
Typical γ-ray spectra for the measurement of primary transitions to low-lying excited states after photo-excitation via an 8 MeV γ-ray beam are shown in Fig. 2.a). The blue spectrum is obtained from a gate on the energy of the 2 + 1 → 0 + 1 transition (E γ = 743 keV). The peak at ∼ 7.26 MeV corresponds to the full-energy events of the direct population of the 2 + 1 level from excited states at 8 MeV. Primary transitions to other levels, such as 2 + 3 (green spectrum) and 2 + 4 (red spectrum) are determined in a similar fashion. The individual transition intensities can be converted into values of the PSF at the corresponding γ-ray energy.
All measured transition intensities for beam energies from 5.8 MeV to 8.5 MeV are shown in Fig. 2.b) as a function of the γ-ray energy (black filled squares). For the measurements with beam energies above 6.4 MeV decays into up to the 2 + 8 state are observed. Due to the steps of ∼ 250 keV between two measurements it is possible to obtain data points at the same or similar γ-ray energy from different beam-energy settings. The fluctuations of the data points exhibit a factor of about 2-3, which is larger than expected from Porter-Thomas fluctuations of around 5 % to 15 %. This is one indication that the average decay properties of photo-excited states in 128 Te below the neutron separation threshold (S n = 8.78 MeV) cannot be described by a single excitation-energy independent PSF.
Nevertheless, the current data set is used to compute a moving average weighted by a Gaussian distribution with FWHM = 300 keV (grey shaded band). That averaged PSF is compared to the PSF extracted from photoabsorption cross sections (blue filled squares) shown in Fig. 2.c). A deviation of both PSFs as a function of the γ-ray energy is observed. This observation additionally indicates that the PSF built on the ground state (photo-excitation) differs from the PSF built on excited states (photo-deexcitation) for the present case of 128 Te, which is in contradiction to the Brink-Axel hypothesis [11,12]. However, additional systematic studies applying the outlined approach and comparison to data from complementary experiments are crucial before general conclusions on the Brink-Axel hypothesis can be drawn.