Calculated fission-fragment yield systematics in the region 74 <=Z <= 94 and 90 <=N <= 150

Background: In the seminal experiment by Schmidt et al. [Nucl. Phys. A 665, 221 (2000)] in which fission-fragment charge distributions were obtained for 70 nuclides, asymmetric distributions were seen above nucleon number $A\ensuremath{\approx}226$ and symmetric ones below. Because asymmetric fission had often loosely been explained as a preference for the nucleus to always exploit the extra binding of fragments near $^{132}\mathrm{Sn}$ it was assumed that all systems below $A\ensuremath{\approx}226$ would fission symmetrically because available isotopes do not have a proton-to-neutron $Z/N$ ratio that allows division into fragments near $^{132}\mathrm{Sn}$. But the finding by Andreyev et al. [Phys. Rev. Lett. 105, 252502 (2010)] did not conform to this expectation because the compound system $^{180}\mathrm{Hg}$ was shown to fission asymmetrically. It was suggested that this was a new type of asymmetric fission, because no strong shell effects occur for any possible fragment division.Purpose: We calculate a reference database for fission-fragment mass yields for a large region of the nuclear chart comprising 987 nuclides. A particular aim is to establish whether $^{180}\mathrm{Hg}$ is part of a contiguous region of asymmetric fission, and if so, its extent, or if not, in contrast to the actinides, there are scattered smaller groups of nuclei that fission asymmetrically in this area of the nuclear chart.Methods: We use the by now well benchmarked Brownian shape-motion method and perform random walks on the previously calculated five-dimensional potential-energy surfaces. The calculated shell corrections are damped out with energy according to a prescription developed earlier.Results: We have obtained a theoretical reference database of fission-fragment mass yields for 987 nuclides. These results show an extended region of asymmetric fission with approximate extension $74\ensuremath{\le}Z\ensuremath{\le}85$ and $100\ensuremath{\le}N\ensuremath{\le}120$. The calculated yields are highly variable. We show 20 representative plots of these variable features and summarize the main aspects of our results in terms of ``nuclear-chart'' plots showing calculated degrees of asymmetry versus $N$ and $Z$.Conclusions: Experimental data in this region are rare: only ten or so yield distributions have been measured, some with very limited statistics. We agree with several measurements with higher statistics. Regions where there might be differences between our calculated results and measurements lie near the calculated transition line between symmetric and asymmetric fission. To draw more definite conclusions about the accuracy of the present implementation of the Brownian shape-motion approach in this region experimental data, with reliable statistics, for a fair number of suitably located additional nuclides are clearly needed. Because the nuclear potential-energy structure is so different in this region compared to the actinide region, additional experimental data together with fission theory studies that incorporate additional, dynamical aspects should provide much new insight.