Absolute ${}^{96}\mathrm{Mo}(p,n){}^{96m+g}\mathrm{Tc}$ cross sections and a new branching for the ${}^{96m}\mathrm{Tc}$ decay

Background: Radionuclides in the Mo-Tc region play an important role in modern medical diagnostics. These applications require a $\gamma$-emitting radioisotope that is injected into the patient. Various production methods of those radionuclides have been investigated in the past; among them are ($p,x$) reactions on natural or enriched molybdenum. Reliable estimations for the produced activity of the radionuclides and radioactive byproducts are required. Therefore, either precise theoretical calculations or a firm experimental database for the nuclear production reactions are needed. In addition, experimental cross-section data of proton-induced reactions on heavy nuclei are very valuable to test nuclear models that enter theoretical calculations of reaction rates relevant for nuclear astrophysics.

Purpose: The present paper reports on experimental cross sections of the ${}^{96}\mathrm{Mo}(p,n){}^{96m+g}\mathrm{Tc}$ reaction. The contribution of the ground-state population as well as for the population of the metastable state in ${}^{96}\mathrm{Tc}$ are determined individually. The obtained results are very valuable to test existing models that enter statistical model calculations. In addition, the present work aims at remeasuring the branching ratio of the decay of the metastable state ${}^{96m}\mathrm{Tc}$.

Method: Highly enriched ${}^{96}\mathrm{Mo}$ targets were irradiated with protons at energies between $E_p=3.9\mathrm{MeV}$ and $E_p=5.4\mathrm{MeV}$, which are slightly above the ($p,n$) threshold ($E_{th}=3.8\mathrm{MeV}$). By employing an offline analysis, the $\gamma$-ray decay of the reaction product was investigated and reaction cross sections were calculated by means of the activation technique.

Results: Individual reaction cross sections for the production channel of the metastable state ${\sigma }_m$ and the ground state ${\sigma }_{gs}$ as well as the branching of the ${}^{96m}\mathrm{Tc}\to {}^{96}\mathrm{Tc}$ decay were determined.

Conclusion: The measured cross sections are in good agreement with previously measured cross sections as well as with recent Hauser-Feshbach calculations. The new branching ratio for the direct decay of ${}^{96m}\mathrm{Tc}$ into ${}^{96}\mathrm{Mo}$ amounts to $4.1{}_{-0.34}^{+0.39}\%$ compared to previously reported $2\pm 0.5\%$.

Figure 1

Beam intensity as a function of irradiation time for the $E_p=4.8\mathrm{MeV}$ activation. The beam was kept at very constant values of about 400 nA. The shown beam current is the effective current on the target corrected for released $\delta$ electrons.

Figure 2

Summing-effect analysis using a Geant4 simulation of the detector setup at a sample-detector distance of 1.3 cm. The top panel shows the simulated $\gamma$-ray histogram for the decay of ${}^{96g}\mathrm{Tc}$ including all subsequently emitted $\gamma$ rays with their respective intensities. The lower panel shows the results of the simulation when only the $\gamma$-ray transition with an energy of 778 keV is allowed. Due to the summing effects, the total peak volume is effectively smaller, when the complete decay pattern is taken into account, because the $\gamma$ rays of interest might be detected coincident with other $\gamma$ rays, causing the presence of summing peaks at the sum of both of their $\gamma$-ray energies. The simulation in each mode included the decay of ${10}^6$ nuclei.

Figure 3

Schematic illustration of the reaction mechanisms following the proton capture on ${}^{96}\mathrm{Mo}$. The metastable state in ${}^{96}\mathrm{Tc}$ can either decay via internal conversion into its ground state with a branching ratio of $f$ or it can decay via electron capture directly into ${}^{96}\mathrm{Mo}$ with a branching of $1-f$.

Figure 4

Typical $\gamma$-ray spectrum from a 6 hour offline counting after the ${}^{96}\mathrm{Mo}(p,n){}^{96}\mathrm{Tc}$ reaction using 4800 keV protons. All visible peaks originate from the EC decay of ${}^{96}\mathrm{Tc}$. The three smaller peaks at around 1600 keV are the result of true coincidence summing effects of the three peaks at around 800 keV. The summing effects have been estimated using a Geant4 [19] simulation (see Sec. 2 for details).

Figure 5

Measured absolute activity of the 812 keV line from the decay of ${}^{96g}\mathrm{Tc}$ as a function of time after the end of bombardment. The fit function given in Eq. (17) is employed to derive the number of ${}^{96g}\mathrm{Tc}$ nuclei at the end of bombardment.

Figure 6

Branching ratio $f$ that describes how many ${}^{96m}\mathrm{Tc}$ nuclei decay into the ${}^{96}\mathrm{Tc}$ ground state relative to the total amount of ${}^{96m}\mathrm{Tc}$ decays for different $\gamma$-ray intensities of the 812 keV line. The formerly reported intensity of (82 $\pm$ 3)% [21] has been revised in this work. The new measured value amounts to (81 $\pm$ 1)%. Consequently, the uncertainty of the branching ratio $f$ is governed by this uncertainty region (shown as the grey shaded region).

Figure 7

Measured cross sections of the ${}^{96}\mathrm{Mo}(p,n){}^{96m}\mathrm{Tc}$ reaction as a function of center-of-mass energy along with statistical model calculations using the Talys code version 1.95 with default parameters as well as with previously reported results from Ref. [22].

Figure 8

The same as Fig. 7 but for the total ${}^{96}\mathrm{Mo}(p,n){}^{96}\mathrm{Tc}$ cross section. Also, experimental results from Flynn et al. are shown [23].