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A b s t r a c t . The cross-section for the reaction e+ + e-+ z1 + V , under a strong magnetic field is calculated. The rate of energy loss is also calculated. These calculations may be of great importance for astrophysical estimations in neutron stars. Lepton-Lepton-Wechselwirkung im starken MagnetfeldI n h a l t s u b e r s i c h t . Es wird der Wirkungsquerschnitt der Reaktion e+ + e--+z1 + Fsowie die Energieverlustrate in einem starken Magnetfeld berechnet. Die Ergebnisse konnen fur astrophysikalische Abschkitzungen in Neutronensternen von groSem Interesse sein.2 1 A < l , --% V --S l .

Radiation loss due to pair production by ah intense electromagnetic wave is calculated. The calculations were made in the coulomb field of the ions and in the presence of a constant strong magnetic field aligned along the z-direction. The expression obtained for the radiation loss can be used for the case of nonrelativistic electrons and positrons. These calculations may be of great importarLce for the astrophysical estimations, since the basic mechanism of the energetic losses is mainly due to pair production.

The neutrino energy loss rate is calculated due to the photoneutrino process in a hot plasma, under magnetic field.The calculations done for Iow densities and re]atively ]ow temperatures may be used for astrophysical estimations in neutron stars. IntroduetionRecent progress in the production of a strong magnetic field in the laboratory [1] has focussed interest on the study of the effect of magnetic fields on various phenomena [2]. The largest field t h a t can now be produced in the laboratory is of the order of 1 5 G, which is much smaHer than that existing in neutron stars, which ma)" be of the order of 10 ~ G [3].Canonical models for the description of the weak interaction among fermions predicts a direct interaction between electron-neut¡ pairs [4]. The effective Hamiltonian which describes the eleetron neutrino interactions is H,,---ig (~~ ~,~(1 -5 Zs)V',,)(W,, 9'~ (1 --5 y.~)%).(1) 8m',,, Such an interaction follows immediately in conventional theories in which the weak interaction is mediated by a few intermediate vector bosons [5], or when the weak coupling has the forro phenomenologically at least of current-current interaction.A Fierz transformation of the Hamiltonian of Eq. (1) yields the equivalent form Hw = _ i/___~2 [~e Y,, V'e)(~,, }'. (1 + Ys) %) + (~, Y6 Y,, 'P,)(~,, ~'. (1 + Ys) V',,)], 8 m~ (2)which exhibits more explicitly the matrix element for a neut¡241 pair to be radiated by ah electron, by means of a vector or axial rector current. The vector current is analogous to the coupling of an eleetron to a photon and Acla Physica Aeod+miae Sci+n+iar~m lt.ngori+o+ 39, 1975