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The Soreq Applied Research Accelerator Facility (SARAF) is under construction in the Soreq Nuclear Research Center at Yavne, Israel. When completed at the beginning of the next decade, SARAF will be a user facility for basic and applied nuclear physics, based on a 40 MeV, 5 mA CW proton/deuteron superconducting linear accelerator. Phase I of SARAF (SARAF-I, 4 MeV, 2 mA CW protons, 5 MeV 1 mA CW deuterons) is already in operation, generating scientific results in several fields of interest. The main ongoing program at SARAF-I is the production of 30 keV neutrons and measurement of Maxwellian Averaged Cross Sections (MACS), important for the astrophysical s-process. The world leading Maxwellian epithermal neutron yield at SARAF-I ($5\times 10^{10}$ epithermal neutrons/sec), generated by a novel Liquid-Lithium Target (LiLiT), enables improved precision of known MACSs, and new measurements of low-abundance and radioactive isotopes. Research plans for SARAF-II span several disciplines: Precision studies of beyond-Standard-Model effects by trapping light exotic radioisotopes, such as $^6$He, $^8$Li and $^{18,19,23}$Ne, in unprecedented amounts (including meaningful studies already at SARAF-I); extended nuclear astrophysics research with higher energy neutrons, including generation and studies of exotic neutron-rich isotopes relevant to the rapid (r-) process; nuclear structure of exotic isotopes; high energy neutron cross sections for basic nuclear physics and material science research, including neutron induced radiation damage; neutron based imaging and therapy; and novel radiopharmaceuticals development and production. In this paper we present a technical overview of SARAF-I and II, including a description of the accelerator and its irradiation targets; a survey of existing research programs at SARAF-I; and the research potential at the completed facility (SARAF-II)., Comment: 32 pages, 31 figures, 10 tables, submitted as an invited review to European Physics Journal A