$\gamma$-ray strength function for thallium isotopes relevant to the ${}^{205}\mathrm{Pb}-{}^{205}\mathrm{Tl}$ chronometry

Photoneutron cross sections were measured for ${}^{203}\mathrm{Tl}$ and ${}^{205}\mathrm{Tl}$ at energies between the one- and two-neutron thresholds using quasimonochromatic $\gamma$-ray beams produced in laser Compton scattering at the NewSUBARU synchrotron radiation facility. Our measurement results in cross sections significantly different from the previously reported bremsstrahlung experiment, leading to rather different giant dipole resonance (GDR) parameters, in particular to lower GDR peak energies and higher peak cross sections. The photoneutron data are used to constrain the $\gamma$-ray strength function on the basis of the Hartree-Fock-Bogolyubov plus quasiparticle random-phase approximation using the Gogny D1M interaction. Supplementing the experimentally constrained $\gamma$-ray strength function with the zero-limit $E1$ and $M1$ contributions for the de-excitation mode, we estimate the Maxwellian-averaged cross section for the s-process branching-point nucleus ${}^{204}\mathrm{Tl}$ in the context of the ${}^{205}\mathrm{Pb}-{}^{205}\mathrm{Tl}$ chronometry.

Figure 1

An excerpt of the chart of nuclei depicting the Tl-Pb region in the s-process path.

Figure 2

A schematic illustration of the experimental set up at NewSUBARU used in the ($\gamma , n$) cross-section measurements.

Figure 3

The simulated energy profiles for the $\gamma$ beams used in the ${}^{203,205}\mathrm{Tl}$ measurements.

Figure 4

Monochromatic cross sections of ${}^{203}\mathrm{Tl}$ (red open circles) and ${}^{205}\mathrm{Tl}$ (blue filled squares). The error bars contain statistical uncertainties from the number of detected neutrons, the uncertainty in the efficiency of the neutron detector, and the uncertainly in the pile-up method used to determine the number of incoming $\gamma$'s on target.

Figure 5

Cross sections of ${}^{203}\mathrm{Tl}$. The red open circles are the monochromatic cross sections from Fig. 4. The red, shaded area displays the unfolded cross section.

Figure 6

Cross sections of ${}^{205}\mathrm{Tl}$. The blue open circles are the monochromatic cross sections from Fig. 4. The blue, shaded area displays the unfolded cross section.

Figure 7

The recommended unfolded cross sections of ${}^{203.205}\mathrm{Tl}$. Here, the error bars represent the difference between the upper and lower limits shown in Figs. 5 and 6.

Figure 8

(a) Present ${}^{203}\mathrm{Tl}(\gamma ,n){}^{202}\mathrm{Tl}$ measured cross sections compared with the D1M+QRPA calculations and previous measurements (open squares) [44]. (b) Same for ${}^{205}\mathrm{Tl}(\gamma ,\mathrm{n}){}^{204}\mathrm{Tl}$.

Figure 9

(a) ${}^{203}\mathrm{Tl}(n,\gamma ){}^{204}\mathrm{Tl}$ measured cross section compared with the D1M+QRPA+0lim calculations (blue shaded lines). The hashed area is obtained making use of different nuclear densities. (b) Same for ${}^{205}\mathrm{Tl}(n,\gamma ){}^{206}\mathrm{Tl}$. Previous experimental data are taken from Refs. [46, 47, 48, 49].

Figure 10

${}^{204}\mathrm{Tl}(n,\gamma ){}^{205}\mathrm{Tl}$ Maxwellian-averaged cross section calculated with the D1M+QRPA+0lim strength function (red lines) as a function of the temperature $T$. The hashed area is obtained making use of different nuclear densities. Also included is the recommended cross section of Bao et al. (2000) [53].