Capture cross sections for the synthesis of new heavy nuclei using radioactive beams

We have measured the capture-fission excitation functions for the reaction of stable ${}^{39}\mathrm{K}$ and radioactive ${}^{46}\mathrm{K}$ with ${}^{181}\mathrm{Ta}$ using the ReA3 facility at the National Superconducting Cyclotron Laboratory. In addition the capture-fission excitation function for the ${}^{39}\mathrm{K}+{}^{181}\mathrm{Ta}$ reaction was measured at Australian National University . The capture cross sections for the ${}^{46}\mathrm{K}+{}^{181}\mathrm{Ta}$ reaction are larger than those for the ${}^{39}\mathrm{K}$ induced reactions in the near barrier region although the reduced excitation functions for the two reactions do not indicate any fundamental differences between the reactions. The results of the measurements are compared to modern phenomenological models and microscopic time-dependent Hartree-Fock calculations. The implications of these measurements for the synthesis of heavy nuclei at radioactive beam facilities are discussed.

Figure 1

Sample predictions of capture cross sections for reactions synthesizing heavy elements. The labels FBD, Skyrme, Zagrebaev, QMD, and DNS indicate the predictions from [2], [3], [4], [5], [6], respectively. They refer to the Fusion by Diffusion, Skyrme, Quantum Molecular Dynamics, and DiNuclear Systems models. ${\mathrm{V}}_B$ indicates the value of the Bass barrier energy [14]. The data for the ${}^{31}\mathrm{Al}+{}^{197}\mathrm{Au}$ reaction is from [15], the data for the ${}^{48}\mathrm{Ca}+{}^{154}\mathrm{Sm}$ reaction is from [16], the data for the ${}^{26}\mathrm{Mg}+{}^{248}\mathrm{Cm}$ reaction is from [17], the data for the ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ and ${}^{48}\mathrm{Ca}+{}^{248}\mathrm{Cm}$ reactions are from [18] while the data for the ${}^{64}\mathrm{Ni}+{}^{238}\mathrm{U}$ reaction is from [19].

Figure 2

The capture-fission excitation function for the ${}^{39}\mathrm{K}+{}^{181}\mathrm{Ta}$ reaction. The labels MSU and ANU refer to the results of independent experiments conducted at ReA3 and ANU. The labels Sargsyan, Zagrebaev, and Wang refer to calculations of these cross sections using [3, 4, 13], respectively. ${\mathrm{V}}_B$ denotes the position of the Bass barrier.

Figure 3

The capture-fission excitation function for the ${}^{46}\mathrm{K}+{}^{181}\mathrm{Ta}$ reaction. The labels Sargsyan, Zagrebaev, and Wang refer to calculations of these cross sections using [3, 4, 13]. The TDHF calculations are represented by upper and lower limits for the cross section. ${\mathrm{V}}_B$ denotes the value of the Bass barrier.

Figure 4

(a) A simple comparison of the capture excitation functions for the ${}^{39,46}\mathrm{K}+{}^{181}\mathrm{Ta}$ reaction. (b) The reduced excitation functions for these reactions.