The two presently available measurements of the low-energy 3H(a, ~)TLi reaction differ from each other by roughly 30% in total magnitude as well as in their determination of the branching ratios for the transition into the two final 7Li bound states. Studying the 3H(e, 7)7Li reaction in the framework of the microscopic Resonating Group Method we were able to reproduce both experimental total cross sections using different effective nucleon-nucleon interactions. However, none of the effective forces yields branching ratios compatible with the data measured by the Toronto-M/inster-collaboration. PACS: 25.55. -e; 25.70.Jj; 21.60.GxThe 3H(e, 7)7Li reaction is a main source for the 7Li production during the big bang nucleosynthesis [1]. Measurements of this reaction rate in the energy range E= 150-600 keV performed by Griffith et al.[2] are consistent with the assumption of an energy independent astrophysical S-factor for the 3H(c~, 7)7Li reaction at stellar energies with a value of S(0)=0.064keV-b [3]. This energy-independent S(E)-factor has been adopted in standard hot big bang model studies [4,5].Recently several microscopic calculations of the 3H(e, 7)VLi reaction at low energies (E < 1 MeV) have been performed in the framework of the Resonating Group Method [6][7][8] or on the basis of a microscopic potential model [9]. While these studies reproduced the experimental data of [2], they do not support the assumption of an energy-independent 3H(e, 7)7Li S-factor at low energies. In agreement with each other these calculations predict the S-factor to increase noticeably with decreasing energy resulting in S(0)~0.10keV.b [6][7][8][9]. Consequently the microscopic studies recommend a higher thermally averaged 3H(c~, 7)7Li reaction rate at astrophysically important temperatures T< 109K than the rate given by Fowler et al. [-3] resulting in a production of 7Li during the big bang which is noticeably higher than currently believed.Motivated by the theoretical predictions a Mfinster-Toronto collaboration [10] has very recently measured the 3H(~, y)VLi cross sections in the energy range E = 80-500 keV. In fact the new experimental data show the predicted increase of the S-factor towards E =0, however, they exceed the data of [-2] by roughly 30% and are also noticeably larger than the microscopically calculated cross sections [6][7][8][9]. An extrapolation of the new experimental data resulted in S (0) ~ 0.14 + 0.02 keV. b [ 10]. Without knowledge of the data of [10] Kajino investigated the dependence of the microscopically calculated 3H(c~, 7)7Li cross sections and those of its analogue reaction 3He(e, 7)TBe on the effective nucleon-nucleon interaction used in these studies [11]. As a main result he observed that the various calculations predict different energy dependences of the Sfactor in the astrophysically important energy regime. In close relation to the study of Kajino [11] we will show in the following that the experimental data of [10] are compatible with the results of the microscopic calculations if other force...