A curved detection slit to improve ERD energy and depth resolution

Recoil atoms detected in elastic recoil detection (ERD) experiments emerge from an initial collision area along the surface of cones of constant energy as a result of cylindrical symmetry of the elastic scattering event with respect to the incident beam. The constant energy cones therefore intercept planar slit plates placed before the detectors in conic sections. For ease of fabrication slits are typically configured as long narrow rectangles, and as a result energy resolution is adversely affected. It has been shown that the kinematic broadening caused by using rectangular slits in minimized when L ≅ 2(Wz0 tan θ0)1/2, where W is the slit width, L is the slit length, z0 is the slit-target distance and θo is the lab-frame recoil angle. The improved energy resolution which results when rectangular slits are replaced by appropriate curved slits is examined here. Formulas are given for the conic sections associated with the curved slits as a function of experimental geometry. When slit dimensions are small compared with the full extent of the conic section, slit geometry can be accurately approximated as the arc of a circle with radius Rc=z0 tan θ0. Geometry-dependent energy loss effects on the resolution are also accounted for in our treatment. The use of curved slits with L ≅ 4(Wz0 tan θ0)1/2 is shown to improve kinematic broadening by ∝ 50% as compared to optimized rectangular slits of the same area. (orig.)