Dipole strength in ${}^{78}$Se below the neutron separation energy from a combined analysis of ${}^{77}$Se($n,\gamma$) and ${}^{78}$Se($\gamma ,{\gamma }^{\prime }$) experiments

The dipole strength function and the nuclear level density of the compound nucleus ${}^{78}$Se were studied in a combined analysis of a cold neutron capture experiment on ${}^{77}$Se performed at the research reactor in Budapest and a photon-scattering experiment on ${}^{78}$Se performed at the electron linear accelerator ELBE with bremsstrahlung produced at a kinetic electron energy of $11.5\mathrm{M}\mathrm{e}\mathrm{V}$. In the combined analysis we developed the extreme statistical code $\gamma$dex for the simulation of radiative cascade deexcitations occurring in neutron capture and photon scattering. Comparisons of experimental and simulated neutron capture spectra allow us to estimate a temperature of $T=900\mathrm{k}\mathrm{e}\mathrm{V}$ for the level density according to the constant-temperature model for ${}^{78}$Se. Using $\gamma$dex, we were also able to estimate ground-state branching ratios and intensities of inelastic transitions for states in ${}^{78}$Se excited via photon scattering. In this way, we derived the photoabsorption cross section from $4\mathrm{M}\mathrm{e}\mathrm{V}$ up to the neutron separation energy from the measured photon-scattering data. The results obtained match the photoabsorption cross section derived from ($\gamma ,n$) measurements and show an enhancement of dipole strength around $9\mathrm{M}\mathrm{e}\mathrm{V}$.

Figure 1

Measured (red) and detector-response-corrected spectrum (black) in the ${}^{77}$Se($n,\gamma$) reaction.

Figure 2

Spectrum of photons scattered from ${}^{78}$Se, measured at 127${}^{\circ }$ relative to the incident beam, corrected for room background and detector response (orange bars), compared to the simulated spectrum of the atomic background (black line), multiplied with efficiency and measuring time. The blue spectrum results from a subtraction of the atomic background from the experimental spectrum. The prominent peaks at $4.44$, $5.02$, $7.29$, and $8.91\mathrm{M}\mathrm{e}\mathrm{V}$ are transitions in ${}^{11}$B.

Figure 3

Spectrum of primary $E1$ transitions (gray area) from an excited state at $10.5\mathrm{M}\mathrm{e}\mathrm{V}$ as a product of the LD at the final state (blue solid line) and the E1 PSF (orange dashed line) given by the tail of the GDR. The LD is exponentially declining on this scale because it is plotted as a function of the transition energy $E_{\gamma }$. The scale of the ordinate is linear.

Figure 4

Block diagram and scheme of the algorithm for the simulation of nuclear radiative deexcitations.

Figure 5

Simulated ${}^{77}$Se($n,\gamma$) spectrum using $\gamma$dex (orange bars) and dicebox (transparent bars with black edges and black error bars). In both cases identical CTM LD ($T=900\mathrm{k}\mathrm{e}\mathrm{V}$, $D_0=121\mathrm{e}\mathrm{V}$) and PSFs were used. The dicebox spectrum is the mean of 200 nuclear realizations, each containing ${10}^5$ simulated deexcitations. The error bars represent one standard deviation of the 200 realizations. The $\gamma$dex spectrum contains ${10}^6$ simulated events and is normalized to the intensity of the transition at $10.5\mathrm{M}\mathrm{e}\mathrm{V}$ obtained in dicebox.

Figure 6

Rebinned experimental spectrum (transparent bars with black edges) corrected for detector response and efficiency in comparisons with simulated ${}^{77}$Se($n,\gamma$) spectra (colored bars) using different CTM temperatures. The simulated spectra are divided into primary (red bars), secondary (gray bars), and higher order $\gamma$ rays (orange bars) plotted on top of each other. In all cases ${10}^6$ deexcitations were simulated. The parameters ($T$ and $E_0$) of the CTM LD model are 700 and $2329\mathrm{k}\mathrm{e}\mathrm{V}$ in (a), 900 and $-230\mathrm{k}\mathrm{e}\mathrm{V}$ in (b), and 1100 and $-2836\mathrm{k}\mathrm{e}\mathrm{V}$ in (c). The back-shift energy $E_0$ was calculated separately for each $T$ from $D_0=121\mathrm{e}\mathrm{V}$ using Eqs. (6) and (7) and a spin cutoff parameter $\sigma \left(S_{\mathrm{n}}\right)=4.4$.

Figure 7

Same as Fig. 6 using a CTM LD with $T=900\mathrm{k}\mathrm{e}\mathrm{V}$ and $E_0=-230\mathrm{k}\mathrm{e}\mathrm{V}$ and the $E1$ PSF obtained in the ($\gamma$,${\gamma }^{\prime }$) analysis shown in Fig. 11b.

Figure 8

Simulated deexcitation spectra for excited $1^{-}$ states in ${}^{78}$Se($\gamma$,${\gamma }^{\prime }$) in steps of $200\mathrm{k}\mathrm{e}\mathrm{V}$. For each excitation energy $250,000$ deexcitations were simulated. A CTM level density with $T=900\mathrm{k}\mathrm{e}\mathrm{V}$ and an $E1$ PSF that was obtained from an iterative analysis of the photon-scattering data as shown in Fig. 11b were used as input parameters.

Figure 9

Simulated enhanced ground-state branching ratios (blue circles, left ordinate) and statistical fluctuation factors (orange squares, right ordinate) for excited $1^{-}$ states in ${}^{78}$Se using the same LD and PSFs as in Fig. 8.

Figure 10

Spectral bremsstrahlung fluence at the target deduced from four known transitions in ${}^{11}$B (black circles) and the simulated detector efficiency. The dashed black line shows the calculated fluence distribution using the Seltzer and Berger formula [36]. The solid black line takes the influence of the aluminum hardener in front of the collimator into account. Both curves are normalized to the fluence at $8.92\mathrm{M}\mathrm{e}\mathrm{V}$. The gray bands correspond to the uncertainty arising from a $200-\mathrm{k}\mathrm{e}\mathrm{V}$ uncertainty of the $11.5-\mathrm{M}\mathrm{e}\mathrm{V}$ kinetic electron endpoint energy.

Figure 11

Iterative determination of the dipole PSF from photon scattering. The black circles are data from the ($\gamma$,${\gamma }^{\prime }$) experiment corrected for inelastic transitions and branching. The black squares are ($\gamma ,n$) data from Ref. [39] scaled with 0.85 following a proposal in Ref. [40]. The black triangles are the sum of ($\gamma$,${\gamma }^{\prime }$) and ($\gamma ,n$) in the region near the neutron threshold. The solid red line and the orange band are the deduced $E1$ PSF corresponding to a global fit and its $95\%$ confidence interval to all data using a tail of the GDR plus an extra Lorentzian resonance. Since the correction for inelastic transitions and branching itself depends on the PSFs below the neutron threshold, the input $E1$ (blue dashed line) and $M1$ PSF (black dotted line) are shown for comparison. The values for the dipole PSF obtained in the first iteration using a TLO $E1$ PSF as input are shown in (a). Moreover, the results of the fourth iteration using an input $E1$ PSF fitted to the data of the third iteration are displayed in (b).

Figure 12

Cross section from uncorrected data (blue triangles), elastic photon-scattering cross section (gray squares), and photoabsorption cross section (orange circles) measured via photon scattering at HZDR in comparison with ($\gamma ,n$) data from Ref. [39] (black squares) scaled with 0.85 following a proposal in Ref. [40]. In addition the prediction of the $E1$ TLO (black solid line) [2], $E1$ SLO (black dashed line) [6], and $E1$ TLO plus $M1$ (black dotted line) [24] models for the average photoabsorption cross section calculated from the PSFs are shown.

Figure 13

Statistical enhancement factor $S_{XL}$ for $E1$ excitations (black circles) and for $M1$ excitations (orange squares) as a function of excitation energy simulated for ${}^{78}$Se using the $E1$ PSF obtained from the analysis of the ($\gamma$,${\gamma }^{\prime }$) experiment and $M1$ according to the data from Ref. [24] and a CTM LD with $T=900\mathrm{k}\mathrm{e}\mathrm{V}$ and $D_0=121\mathrm{e}\mathrm{V}$. The uncertainties correspond to one standard deviation of all runs performed for one excitation energy and the gray dashed lines indicate the asymptotic values for $S$.

Figure 14

Statistical enhancement factor $S$ for $E1$ excitations simulated with different CTM level densities with $T=700\mathrm{k}\mathrm{e}\mathrm{V}$ (orange squares), $T=900\mathrm{k}\mathrm{e}\mathrm{V}$ (black circles), and $T=1100\mathrm{k}\mathrm{e}\mathrm{V}$ (blue triangles). For all simulations $D_0=121\mathrm{e}\mathrm{V}$ and the PSF shown in Fig. 11b were used. The uncertainties have been omitted for better visibility. (a) $S$ as a function of the excitation energy. (b) $S$ as a function of the ratio of the average total transition width to the average ground-state transition width. The gray dashed lines indicate the asymptotic values for $S$.