Here, we present a new method to evaluate the expectation value of the power spectrum of a time series. A statistical approach is adopted to define the method. After its demonstration, it is validated showing that it leads to the known properties of the power spectrum when the time series contains a periodic signal. The approach is also validated in general with numerical simulations. The method puts into evidence the importance that is played by the probability density function of the phases associated to each time stamp for a given frequency, and how this distribution can be perturbed by the uncertainties of the parameters in the pulsar ephemeris. We applied this method to solve the power spectrum in the case the first derivative of the pulsar frequency is unknown and not negligible. We also undertook the study of the most general case of a blind search, in which both the frequency and its first derivative are uncertain. We found the analytical solutions of the above cases invoking the sum of Fresnel's integrals squared.Keywords: neutron stars, gamma ray experiments P (ω) = N 0 cos(θ i ) 2 + sin(θ i ) 2 .(3.5)Since we used the mean values of cosine and sine, eq. (3.5) is the expectation value of the power spectrum at the frequency ω.

Phaseshifts, partial and total cross sections for elastic electron scattering by small sodium clusters are calculated. The non-local dynamic interaction of the extra electron with the neutral cluster is described within the many-body framework of Dyson's equation. Low-energy electron scattering resonances and the energies of bound and quasibound states are shown to be very sensitive to the non-local exchange and dynamic polarization interactions.

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