In this article we explore the availability of radiopure tungsten and its potential as high density shield material for low background applications. For compact shield designs, conventionally, lead is used. Metallic tungsten and tungsten pseudo-alloys reach higher densities up to 19.3 gcm$^{-3}$ and do not exhibit a significant $^{210}$Pb activity, which is a typical intrinsic contamination in lead. Within several $\gamma$-ray screening campaigns we were able to identify tungsten samples with activities similar or better than 1 mBqkg$^{-1}$ in $^{232}$Th, $^{40}$K, $^{60}$Co and the second part of the $^{238}$U decay chain. In cooperation with a manufacturer we further reduced a persisting contamination in the first part of the $^{238}$U decay chain by a factor of $\sim$2.5 down to (305$\pm$30) mBqkg$^{-1}$. With Monte Carlo simulations, the construction of prototype tungsten-based setups and dedicated measurements, the shield capability of tungsten in comparison to lead was extensively studied. Specifically, the impact of cosmogenic radiation on the background at shallow depth was investigated. We showed that a 6-40% reduction (depending on the exact shield configuration) in the muon-induced neutron fluence is achievable by replacing lead with an equivalent amount of tungsten regarding the suppression of external $\gamma$-radiation. Overall, many benefits using tungsten especially for low energy applications below a few 100 keV are found. The pseudo-tungsten alloy presented in this work paves the way for several applications especially regarding background suppression in particle and astroparticle physics search programs.
Comment: 17 pages, 15 figures