Development of two-dimensional fitting and application to prompt gamma-rays of californium-252 fission.

Abstract

We have developed a method for the direct two-dimensional decomposition of complex coincidence matrices in order to extract gamma-gamma coincidence intensities at the statistical limits. The algorithms written to analyze the gamma-gamma coincidence data were developed first while working on unidimensional spectra from the decay of $\sp{65}$Ni, $\sp{65}$Zn and $\sp{\rm 108m}$Ag. They were then extended to work in two dimensions in order to obtain a general method that could be used for extracting information from data sets having different dimensions. We successfully modeled the continuum and the ridges over the entire coincidence matrix. The continuum is described by the simple product of two vectors while the ridges are reproduced from a centroid based on gamma-rays in the total projection and a vector giving the height as a function of position. The peaks found by a two-dimensional zero-area transform are fitted with a Singular Value Decomposition--Levenberg Marquardt code extended to two dimensions. We applied the technique to the analysis of the coincidences involving the prompt gammas from the spontaneous fission of $\sp{252}$Cf. The information from the 20,000 coincidence peaks obtained from the fit was manipulated through a computer program. The built-in database constructed from NNDC nuclear structure data files provided access to literature schemes. A graphical interface allowed the interactive building and extension of level schemes. Newly placed transitions were checked by comparing predicted coincidences to those observed. In the even-even nuclides, models like the Variable-Moment-of-Inertia and the product of valence protons and neutrons (NpNn scheme) are used to guide placements based on systematics. We take advantage of the cross-coincidences between fission partners to determine the atomic number and mass of the nuclide in which a transition occurred. Fifty-eight level schemes from $\sp{252}$Cf fission have been constructed and seventeen of them have been extended by placing twenty-four new transitions.