Within the frame of Accelerator Based Boron Neutron Capture Therapy (AB-BNCT), the ⁷Li(p,n)⁷Be reaction, relatively near its energy threshold is one of the most promising, due to its high yield and low neutron energy. In this work a thick LiF target irradiated with a proton beam was studied as a neutron source. The 1.88-2.0 MeV proton beam was produced by the tandem accelerator TANDAR at CNEA's facilities in Buenos Aires. A water-filled phantom, containing a boron sample was irradiated with the resulting neutron flux. The ¹⁰B(n,αγ)⁷Li boron neutron capture reaction produces a 0.478 MeV gamma ray in 94% of the cases. The neutron yield was measured through the detection of this gamma ray using a hyperpure germanium detector with an anti-Compton shield. In addition, the thermal neutron flux was evaluated at different depths inside the phantom using bare and Cd covered gold foils. A maximum neutron thermal flux of 1.4×10⁸cm^-2s^-1mA^-1 was obtained at 4.2 cm from the phantom surface. In order to optimize the design of the neutron production target and the beam shaping assembly extensive Monte Carlo Neutron and Photon (MCNP) simulations have been performed. Neutron fields from a thick LiF and a Li metal target (with both a D₂O graphite and a Al/AlF₃ graphite moderator/reflector assembly) were evaluated along the centerline of a head and a whole body phantom. Simulations were carried out for 1.89, 2.0 and 2.3 MeV proton beams. The results show that it is more advantageous to irradiate the target with 2.3 MeV near-resonance protons, instead of very near threshold, because of the higher neutron yield at this energy. On the other hand, the Al/AlF3-graphite exhibits a more efficient performance than D₂O in terms of tumor to maximum healthy tissue. Treatment times of less than 15 min and tumor control probabilities larger than 98% are obtained for a 50 mA, 2.3 MeV proton beam. The alternative neutron-producing reaction ¹³C(d,n) is also briefly reviewed. A proposal is made to construct an electrostatic, 2.5 MeV, 50 mA proton accelerator suitable for hospital use. A combination of a Tandem and an Electrostatic Quadrupole is considered to be the best option.