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.