Scan profiles for neutron spectrometers. I. Gaussian-profile elements by acceptance-diagram methods

`Acceptance diagrams' are a powerful graphical method of describing beam characteristics on neutron scattering instruments. Recent examples of the technique have used hypothetical rectangular‐profile beam elements, not the conventional Gaussian profiles, to clarify the description. This article develops the method for Gaussian‐profile beam elements and shows that it gives identical results to accepted techniques. Direct expressions are presented for scan profiles, their widths and intensities for both powder diffractometers and three‐axis spectrometers. This work gives some necessary background and therefore forms the first part of a discussion of the resolution effects of the new reflecting Soller collimators for neutrons.