We give a precision analysis of the correlation coefficients of the
electron-energy spectrum and angular distribution of the
Beta-decay and radiative Beta-decay of the neutron with
polarized neutron and electron to order 10^(-3). The calculation of
correlation coefficients is carried out within the Standard model with
the contributions of order 10^(-3), caused by the ``weak magnetism''
and proton recoil, taken to next-to-leading order in the large
proton mass expansion, and the radiative corrections of order
"alpha/\pi ~ 10^(-3)", calculated to leading order in the large
proton mass expansion. The obtained results can be used for the
planning of experiments on the search for contributions of order
10^(-4) of interactions beyond the Standard model. The talk is based
on the results, obtained in Phys.Rev. D88, 073002 (2013) and Phys.Rev. D88, 065026(2013). It is supported by the
Austrian ``Fonds zur Förderung der Wissenschaftlichen Forschung''
(FWF) under contracts I689-N16, I862-N20 and P26781-N20 and by the
ÖAW within the New Frontiers Groups Programme, NFP 2013/09.