Experiment-based determination of the excitation function for the production of ${}^{44}\mathrm{Ti}$ in proton-irradiated vanadium samples

In this paper, the excitation function utilizing the nuclear reaction ${}^{\mathrm{nat}}\mathrm{V}(p,X)$ ${}^{44}\mathrm{Ti}$ was determined. The seven investigated metallic vanadium disks were proton irradiated within an energy range of 111–954 MeV between 1995 to 1996. The experiments' cross sections were validated using two independent measurements by combining $\gamma$ spectrometry with both a low-energy germanium detector and a high-purity germanium detector. The maximum cross section was observed for energies of 145 $\pm$ 1.2 and 150.2 $\pm$ 1.2 MeV with values of 803 $\pm$ 28 and 805 $\pm$ 27 $\mu \mathrm{b}$, respectively. In this regard, it was demonstrated that our data were in good agreement with the former, however, unpublished results which were investigated over a similar energy range. Thus, combined with these earlier measurements, a consistent data set for the ${}^{\mathrm{nat}}\mathrm{V}(p,X)$ ${}^{44}\mathrm{Ti}$ excitation function from 111 to 1350 MeV is provided. Model calculations using Liège Intranuclear Cascade (INCL)/ABLA reproduce the shape of the excitation function correctly but overpredict the absolute values by factors of 2 to 3. Some considerations regarding this already earlier observed systematic overestimation of neutron-poor residues are given. The results will trigger new approaches in code development in order to improve the predictions.

Figure 1

Overview of the seven metallic vanadium disks before the dissolving process. Notably is the different appearance, which is likely caused by partial oxidation.

Figure 2

Experimental excitation function for the ${}^{44}\mathrm{Ti}$ production from proton-induced reactions as a comparison between the two data sets.

Figure 3

Further comparison of the excitation function for the ${}^{44}\mathrm{Ti}$ production with additional data in the low-energy range (taken from Ref. [14]) as well as theoretical calculations.

Figure 4

Mass distributions of the $Z=25$ isotope from the $p+\mathrm{Fe}$ reaction at proton energies (a) E($p$) of 300 MeV and (b) E($p$) of 1000 MeV. Calculations (green line) come from the INCL-ABLA model combination and experimental data from GSI for 300 MeV [33] and for 1000 MeV [34], respectively.

Figure 5

Compilation of ${}^{52}\mathrm{Fe}$ excitation function from $p+\mathrm{Co}$ reactions. Experimental compiled from [35, 36, 37, 38, 39, 40, 41] and theoretical predictions obtained using the INCL-ABLA code combination. Although (a) is the regular comparison in (b) a scale factor of 1/3 is applied to the calculation results.

Figure 6

Mass distributions of the $Z=25$ isotope from the $p+\mathrm{Fe}$ reaction at proton energy E($p$) of 300 MeV. Same as Fig. 4, (a) shows where the original excitation energy takes several new values with multiplying factors ranging from 0.5 to 1.5. In (b), the ratios to the original values are plotted. Calculations come from the INCL-ABLA model combination and experimental data from GSI [33].

Figure 7

Evolution of the production cross section of the ${}^{49}\mathrm{Mn}$ isotope from the $p+\mathrm{Fe}$ reaction at proton energy E($p$) of 300 MeV including several values of the excitation energy at the end of the intranuclear cascade. Calculations come from the INCL-ABLA model combination.

Figure 8

Excitation energies of the remnant nuclei obtained at the end of the cascade phase for reactions $p+\mathrm{V}$ with proton energies ranging from 50 to 1000 MeV. The black curve shows the mean values for all cases, whereas the blue curve shows only the cases where, at the end of the reaction, a ${}^{44}\mathrm{Ti}$ nucleus is produced (a). Furthermore, only the latter one is plotted with the X axis in logarithmic representation (b).

Figure 9

Contributions to ${}^{44}\mathrm{Ti}$ production in $p+\mathrm{V}$ reactions with more than 5%. Calculated with the INCL-ABLA combination code. “$6n2p$” means the emission of six neutrons and two protons (in fact, the possible associated emissions of charged pions are included, which obviously modifies the number of neutrons or protons, e.g., seven neutrons + one proton + one ${\pi }^{+}$ is included). In the same way, “$1d$” means five neutrons, one deuteron, one proton; “$1t$” means four neutrons, one triton, one proton; and “1α” means four neutrons and 1α .