Convergence of the hyperspherical harmonic expansion for crystallographic texture

Advances in instrumentation allow a material texture to be measured as a collection of spatially resolved crystallite orientations rather than as a collection of pole figures. However, the hyperspherical harmonic expansion of a collection of spatially resolved crystallite orientations is subject to significant truncation error, resulting in ringing artifacts (spurious oscillations around sharp transitions) and false peaks in the orientation distribution function. This article finds that the ringing artifacts and the accompanying regions of negative probability density may be mitigated or removed entirely by modifying the coefficients of the hyperspherical harmonic expansion by a simple multiplicative factor. An addition theorem for the hyperspherical harmonics is derived as an intermediate result.

THREE-BODY FORCES FROM n-BODY INVERSION

Within the context of the lowest order approximation to the calculation of the n-body bound state in the Hyperspherical Harmonic Expansion Method, the hypercentral potential may be determined from n-body spectral data. Previously, we showed how the two-body force can be determined exactly from the hypercentral potential in the absence of three-body forces. In this paper, we investigate to what extent the three-body force can be determined if the two-body force is assumed to be known. For this purpose, a three-quark system is considered.