Moment Methods and Lanczos Methods

Abstract

In contrast to many of the speakers at this conference I am less interested in average properties of nuclei than in detailed spectroscopy. I will try to show, however, that the two are very closely connected and that shell-model calculations may be used to give a great deal of information not normally associated with the shell-model. Professor French has demonstrated clearly to us that the level spacing fluctuations in nuclear spectra convey very little physical information. This is true when the fluctuations are averaged over the entire spectrum but not if one’s interest is in the lowest few states, whose spacings are relatively large. If one wishes to calculate a ground state (say) accurately, that is with an error much smaller than the excitation energy of the first excited state, very high moments, µ_n, n ≈ 200, are needed. As I shall show we use such moments as a matter of course, albeit without actually calculating them; in fact I will try to show that, if at all possible, the actual calculations of moments is to be avoided like the plague.