A generalized least-square method with Tikonov-Miller regularization and non-negativity constraints has been developed for deconvoluting two-dimensional coincidence Doppler broadening spectroscopy ͑CDBS͒ spectra. A projected Newton algorithm is employed to solve the generalized least-square problem. The algorithm has been tested on Monte Carlo generated spectra to find the best regularization parameters for different simulated experimental conditions. Good retrieval of the underlying positron-electron momentum distributions in the low momentum region is demonstrated. The algorithm has been successfully used to deconvolute experimental CDBS data from aluminum.

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Two-dimensional angular correlation of annihilation radiation ͑2D-ACAR͒ spectra have been taken for 10 19 cm Ϫ3 phosphorus-doped Si in the as-grown state after having been subjected to 1.8 MeV electron fluences of 1ϫ10 18 and 2ϫ10 18 cm Ϫ2. Positron annihilation lifetime spectroscopy confirms, in accordance with previous works, that positrons are saturation trapping into (V Si :P) pair defect ͑E-center͒ monovacancy sites in the electron irradiated samples. In the as-grown case, the positron-electron autocorrelation functions along the ͓111͔ and ͓1-10͔ directions, obtained through Fourier transformation of the 2D-ACAR data, reveal zero-crossings that deviate only slightly from the lattice points, in a manner consistent with positron-electron correlation effects. Conversely, in the spectra of the irradiated samples, the zero-crossing points are observed to move outward further by between 0.15 and 0.50 Å. This displacement is associated with positron annihilation with electrons in localized orbitals at the defect site. An attempt is made to extract just the component of the defect's positron-electron autocorrelation function that relates to the localized defect orbitals. In doing this features are found that correspond to the expected atomic positions at the vacancy defect site suggesting that this real-space function may provide a convenient means for obtaining a mapping of localized orbitals. The observed approximate separability of positron and electron wave-function autocorrelates leads to an estimate of 0.22 eV for the positron binding energy to the E-center.

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