Portable neutron generators are commercially available based on the d–t fusion. These devices contain a source of deuterium ions, an accelerator that accelerate the ions up to about T_d=130 keV kinetic energy and a target in which tritium nuclei are chemically bound in a metallic compound (hydride). The fusion reaction d + t → n + 4He has a maximum cross-section (5 barn) at that energy.

(1) Calculate the neutron kinetic energy [m_d =1875.6, m_t =2808.9, m_α =3727.4].

(2) Neutrons are emitted isotropically. If the neutron production rate is I=3 x 10¹⁰s^-1, what is the neutron flux at the distance R=1 m from the source?

(3) By measuring the direction and time of the α-particle the direction of the neutron and the time of its production can be ‘tagged’. The neutrons can be used to study some materials. A neutron collides with a nucleus of that material producing a characteristic, prompt γ-ray. By measuring the time interval between the α-particle and γ-ray signals one can determine the position of the nucleus along the line of flight. Calculate the resolution on the time of flight measurement necessary to locate the nucleus within Δz = 5 cm.