BAYESIAN DECONVOLUTION AND ANALYSIS OF PHOTOELECTRON OR ANY OTHER SPECTRA - FERMI-LIQUID VERSUS MARGINAL FERMI-LIQUID BEHAVIOR OF THE 3D ELECTRONS IN NI

We present a simple and effective iterative deconvolution of noisy exp erimental spectra D broadened by the spectrometer function. We show th at this ''iterative Bayesian deconvolution'' is closely related to the more,complex ''Bayesian analysis,'' also known as the quantified maxi mum-entropy method. A model m of the true spectral function is needed in both cases. The Bayesian analysis is the most powerful and precise method to relate measured spectra D to the corresponding theoretical m odels m via the respective probabilities, but two grave conceptual pro blems together with two severe technical difficulties prevented widesp read application. We remove these four obstacles by (i): demonstrating analytically and also by computer simulations that the most probable deconvolution (a) over cap obtained as; a by-product from the Bayesian analysis gets closer to the true spectral function as the quality of m increases, (ii) finding it equivalent but vastly more efficient to o ptimize the parameters contained in a given;;model m by the usual leas t-squares fit between D and the convolution of m prior to the Bayesian analysis instead of using the Bayesian analysis itself for that purpo se, (iii) approximating the convolution by a summation over the energi es of the n data points only, with the normalization of the spectromet er function chosen to minimize the errors at both edges of the spectru m, and (iv) avoiding the severe convergence problems frequently encoun tered in the Bayesian analysis by a simple reformulation of the corres ponding system of pr nonlinear equations. We also apply our version of the Bayesian analysis to angle resolved photoelectron spectra taken a t normal emission from Ni(lll) close to the Fermi energy at about 12 K , using two different physical models: Compared with the marginal Ferm i liquid, the Fermi-liquid line shape turns out to bk about 10(4) time s more probable to conform with the observed structure of:the majority and minority spin peaks in the low-photon End small-binding-energy :r egion.