Investigation of photoneutron reactions close to and above the neutron emission threshold in the rare earth region

We have investigated the photoneutron cross section of the isotopes ${}^{148,150}\mathrm{Nd}$, ${}^{154}\mathrm{Sm}$, and ${}^{154,160}\mathrm{Gd}$ close to the neutron emission threshold in photoactivation experiments at the superconducting Darmstadt electron linear accelerator S-DALINAC. Naturally composed targets were activated with a high-intensity bremsstrahlung beam at various energies and the reaction yields have been determined by measuring the activity of the produced radioactive isotopes with HPGe detectors. The results are compared to two different statistical model calculations.

Figure 1

The $s$-process flow (solid lines) in the rare-earth region. The thickness of the solid lines indicates the strength of the reaction flow. The reaction path is influenced by several branching points (dashed boxes). Unstable isotopes are shaded light gray (${\beta }^{-}$) and dark gray (${\beta }^{+},\epsilon$). Most isotopes also have nucleosynthesis contributions from the $r$ and $p$ processes (dotted lines), respectively. The photoneutron reactions of the hatched isotopes have been studied in this work.

Figure 2

Schematic layout of the photoactivation setup. A monoenergetic electron beam produces bremsstrahlung in a massive copper radiator with a thickness of 1.2 cm (1). The photons activate the target of interest ($x_1\approx 5$ cm), which is sandwiched between several calibration targets (2). Behind a thick copper collimator system (3) a boron target (4) is mounted ($x_2\approx 150$ cm) to monitor the photon flux via the photon scattering reaction ${}^{11}\mathrm{B}$$(\gamma ,{\gamma }^{\text{'}})$ with actively shielded HPGe detectors (5).

Figure 3

Available photon flux $n_{\gamma }$ at our photoactivation setup for a photon energy of $E_{\gamma }=S_n({}^{148}$Nd$)=7332.9$ keV as a function of the maximum photon energy of the spectral distribution $E_{\max }$. A mean electron current of $I_e=25$ μA on the radiator has been assumed. The photon flux was obtained from a simulation using the Monte Carlo code GEANT4 [18] and confirmed experimentally by the two approaches discussed in the text. The photon flux in front of the collimator is about 270 times more intense than behind the collimator and the energy dependence is nearly equal.

Figure 4

The simulated photon flux distribution at the target position behind the collimator for $E_{\max }=9050$ keV. The simulation was normalized to the experimental data obtained from the reaction yields of the photon-scattering reaction ${}^{11}\mathrm{B}$$(\gamma ,{\gamma }^{\text{'}})$ (see text for details).

Figure 5

The ratio of the normalization factors $N_{\gamma ,0}$ found for the photon flux intensities at different energies $E_{\max }$ using the reactions ${}^{187}\mathrm{Re}$$(\gamma ,n)$ and ${}^{11}\mathrm{B}$$(\gamma ,{\gamma }^{\text{'}})$, respectively. Both reactions are in good agreement with regard to the experimental error bars and the uncertainty of the photoneutron cross section of ${}^{187}\mathrm{Re}$ (gray error band) [10]. The mean ratio of both approaches is indicated by the dashed line. At $E_{\max }=7450$ keV and $E_{\max }=7600$ keV the ${}^{187}\mathrm{Re}$$(\gamma ,n)$ reaction yield was too low to obtain data points behind the collimator.

Figure 6

Typical γ-decay spectrum of a neodymium target irradiated at $E_{\max }=8600$ keV for a duration of about 13 h. The spectrum was accumulated over a period of 3 h at the LEPS setup. The strongest γ transitions following the β decays of ${}^{147}\mathrm{Nd}$ into ${}^{147}\mathrm{Pm}$ and ${}^{149}\mathrm{Nd}$ into ${}^{149}\mathrm{Pm}$, respectively, are indicated.

Figure 7

Absolute detection efficiency of the HPGe and LEPS setup. Standard calibration sources were used to normalize the efficiency curve calculated with GEANT4. Due to large summing effects of coincident γ rays at small distances between detector and source, only those calibration sources without γ cascades were used for the normalization in case of the LEPS setup.

Figure 8

The top panel shows the simulated spectral distribution of bremsstrahlung at different energies $E_{\max }$ of (1) 8050 keV, (2) 8600 keV, (3) 9050 keV, and (4) 9650 keV (solid lines) in comparison to the photoneutron cross section ${\sigma }_{(\gamma ,n)}$ of ${}^{154}\mathrm{Sm}$ (dashed line) predicted by the NON-SMOKER${}^{\mathrm{WEB}}$ code [20]. The product of ${\sigma }_{(\gamma ,n)}$ and $n_{\gamma }$ yields the integrand of Eq. (1), which covers a broad energy range close to the neutron separation energy as shown in the bottom panel.

Figure 9

The top panel shows a thermal Planck spectrum at $T=2.5\times {10}^9$ K. The weighted sum of different bremsstrahlung spectra yields a good approximation of the Planck spectrum within the Gamow-like window. The bottom panel shows that this energy region is defined by the product of photon flux $n_{\gamma }^{\mathrm{Planck}}$ and photoneutron cross section ${\sigma }_{(\gamma ,n)}$ [21]. In this figure ${\sigma }_{(\gamma ,n)}$ was calculated with the NON-SMOKER${}^{\mathrm{WEB}}$ code [20] for the case of ${}^{154}\mathrm{Sm}$.

Figure 10

Normalization factors $f$ derived for two different theoretical predictions of the photoneutron cross section at various energies $E_{\max }$. The gray error band denotes the experimental uncertainty $\Delta f_{\mathrm{total}}$ discussed in the text. The triangular data points at $E_{\max }=9050$ keV for ${}^{154}\mathrm{Sm}$ are independent remeasurements to test the reproducibility of our experimental results.

Figure 11

Comparison of experimental data for the photoneutron cross section from various photodisintegration experiments [32, 33, 34, 35, 36, 37] and theoretical predictions using the TALYS (dashed line) and NON-SMOKER${}^{\mathrm{WEB}}$ code (solid line). The theoretical calculations were normalized with the factors presented in Table . Note that the error bands of the theoretical predictions due to the experimental uncertainties of the applied normalization factors have been omitted in the graphs.

Figure 12

The expected $(\gamma ,n)$ reaction yield of a ${}^{154}\mathrm{Sm}$ target (top panel) using a NON-SMOKER${}^{\mathrm{WEB}}$ calculation for the photoneutron cross section (solid line). The dashed and dotted lines indicate the error bands assuming uncertainties of $E_{\max }$ of 25 and 50 keV, respectively. The bottom panel shows that close to the neutron threshold this uncertainty clearly dominates the uncertainty stemming from the photon flux determination (gray band).