Constraints on the dipole photon strength for the odd uranium isotopes

Background: The photon strength functions (PSFs) and nuclear level density (NLD) are key ingredients for calculation of the photon interaction with nuclei, in particular the reaction cross sections. These cross sections are important especially in nuclear astrophysics and in the development of advanced nuclear technologies.

Purpose: The role of the scissors mode in the $M1$ PSF of (well-deformed) actinides was investigated by several experimental techniques. The analyses of different experiments result in significant differences, especially on the strength of the mode. The shape of the low-energy tail of the giant electric dipole resonance is uncertain as well. In particular, some works proposed a presence of the $E1$ pygmy resonance just above 7 MeV. Because of these inconsistencies additional information on PSFs in this region is of great interest.

Methods: The $\gamma$-ray spectra from neutron-capture reactions on the ${}^{234}\mathrm{U}$, ${}^{236}\mathrm{U}$, and ${}^{238}\mathrm{U}$ nuclei have been measured with the total absorption calorimeter of the n_TOF facility at CERN. The background-corrected sum-energy and multi-step-cascade spectra were extracted for several isolated $s$-wave resonances up to about 140 eV.

Results: The experimental spectra were compared to statistical model predictions coming from a large selection of models of photon strength functions and nuclear level density. No combination of PSF and NLD models from literature is able to globally describe our spectra. After extensive search we were able to find model combinations with modified generalized Lorentzian (MGLO) $E1$ PSF, which match the experimental spectra as well as the total radiative widths.

Conclusions: The constant temperature energy dependence is favored for a NLD. The tail of giant electric dipole resonance is well described by the MGLO model of the $E1$ PSF with no hint of pygmy resonance. The $M1$ PSF must contain a very strong, relatively wide, and likely double-resonance scissors mode. The mode is responsible for about a half of the total radiative width of neutron resonances and significantly affects the radiative cross section.

Figure 1

One hemisphere of the TAC showing the ${\mathrm{BaF}}_2$ crystals and photomultipliers mounted in the support structure. The vacuum time-of-flight tube traversing the detector is split at the center of the TAC where the sample holder in air is positioned, surrounded by the neutron absorber of which only the lower half is shown.

Figure 2

The time-of-flight spectra for the $(n,\gamma )$ reactions on ${}^{234}\mathrm{U}$, ${}^{236}\mathrm{U}$, and ${}^{238}\mathrm{U}$ for $m\ge 2$ TAC events. The top axis shows the corresponding neutron-energy scale. The blue regions are used for the analysis while the red ones correspond to the windows for the background subtraction; see text for details.

Figure 3

Sum energy spectra for the first resonance in $(n,\gamma )$ reaction on ${}^{234}\mathrm{U}$, ${}^{236}\mathrm{U}$, and ${}^{238}\mathrm{U}$, not corrected for background, for different crystal multiplicity criteria. The counts for $m=1$, attributed mainly to background events, go up as high as $120\times {10}^3$ counts/bin. The $Q$ values of the ${}^{234,236,238}\mathrm{U}(n,\gamma )$ reactions are 5.3, 5.1, and 4.8 MeV respectively, in practice equivalent to the $S_n$ values listed in Table 1.

Figure 4

The sum-energy and MSC spectra for individual resonances and multiplicities $m=2\text{–}5$ after background subtraction for ${}^{234}\mathrm{U}(n,\gamma )$. The label “$\gamma$-ray energy” refers to the deposited energy in any crystal. The “Average spectra” band represents the average of resonances plus/minus one standard deviation representing the fluctuation among the resonances. The shaded interval depicts the $E_s$ range used for the construction of MSC spectra.

Figure 5

Crystal multiplicity distribution for each uranium isotope from the same $E_s$ energies as used for the construction of MSC spectra. The individual resonances after background subtraction are plotted following the color scheme in the legend of Fig. 4. The average spectra and the standard deviation are represented by the band.

Figure 6

Photon strength functions of ${}^{239}\mathrm{U}$ as a function of $\gamma$-ray energy for some of the models used in our simulations. The panels (a) and (b) display the $E1$ and $M1$ PSFs, respectively. For the model parameters see Table 2. The IAEA-19 $E1$ and $M1$ PSFs were calculated by Goriely et al. [20] and the average resonance capture data were compiled by Kopecky [12]. For the temperature dependent GLO model the lower and upper curve correspond to excitation above ground state and decay from the capturing state, respectively. The panel (c) shows the sum of the $E1$ and the corresponding $M1$ PSF [from panels (a) and (b)] compared to the Oslo data from the $(d,p){}^{239}\mathrm{U}$ reaction [7].

Figure 7

Spin- and parity-summed level density for ${}^{239}\mathrm{U}$ according to the CT and BSFG models and the HFB calculations [46]. The parameters of the CT and BSFG NLDs were taken from Refs. [45, 50], denoted as (vEB06) and (vEB09) respectively. The experimental data from the Oslo method [7] are shown. Note that the differences at $S_n$ stem from different spin distributions in the models. The point corresponding to the $s$-wave resonance spacing [51] was converted using the spin distribution with the spin-cutoff parameter from Ref. [50]. The significant deviation of the Oslo data at higher energies hints to the normalization issue, which was discussed in detail by Ullmann et al. [11].

Figure 8

Comparison of ${}^{234}\mathrm{U}(n,\gamma )$ sum-energy (left) and MSC (right) spectra using the model combinations RIPL-3, IAEA-19, Oslo, and DANCE. The label “$\gamma$-ray energy” refers to the deposited energy in any crystal.

Figure 9

Comparison of experimental and simulated sum-energy and MSC spectra for all three nuclei with the MGLO ($k=1.8$, $T=0.3\mathrm{MeV}$) model. The label “$\gamma$-ray energy” refers to the deposited energy in any crystal.

Figure 10

Comparison of experimental MSC spectra for ${}^{234}\mathrm{U}(n,\gamma )$ (left) and ${}^{238}\mathrm{U}(n,\gamma )$ (right) with simulations in which one of the double-resonance SC was withdrawn. The simulations are labeled with the kept SC resonance. The $m=4\mathrm{MSC}$ spectra are not shown as they exhibit the same behavior as the $m=3$ ones. The label “$\gamma$-ray energy” refers to the deposited energy in any crystal.