We report on a new cross-section measurement for the 3 He(α, γ ) 7 Be reaction at three medium energies of E c.m. between 1 and 3 MeV. The interest stems from the significant role played by the reaction in calculating an accurate solar neutrino flux and the primordial 7 Li abundance. The energy dependence of the astrophysical S 34 factor observed in the present work, especially above 1 MeV, highlights the need to constrain theories in order to obtain a precise extrapolated value for S 34 (0). In this context, a comparison with the recent theoretical work in a fully microscopic fermionic molecular dynamics approach and a few other representative calculations emphasize the need for further experimental as well as theoretical work to resolve the existing conflicts. The cross section of the 3 He(α, γ ) 7 Be direct capture reaction was first studied by Holmgren et al. [1], being followed by a posteriori measurements of solar fusion reactions of ever-increasing sophistication and accuracy. These measurements are driven by the need to obtain more precise information that is crucial for a critical evaluation of solar models, solar neutrino fluxes, and big-bang nucleosynthesis (BBN) [2][3][4]. Specifically, the 3 He(α, γ ) 7 Be reaction plays a key role in calculating the high-energy solar neutrino flux that probes the temperature as well as the metallicity of the solar interior [3] and in explaining the primordial 7 Li abundances [4]. In recent years, the so-called 7 Li problem has attracted a considerable amount of attention as the disagreement between the observations and the predictions of the primordial 7 Li abundances became worse resulting in a persistent discrepancy of a factor of 3. This open problem poses severe challenges to the cosmological models that have been used for predicting the primordial abundances of nuclei [4][5][6][7]. In Ref.[5], a change of ∼16% was calculated in the central value of 7 Li abundance at BBN energies by utilizing the results from an evaluation of the available data on the astrophysical S 34 factor. This work highlights the need for an accurate knowledge of this reaction rate for reliable predictions of the 7 Li abundance and therefore for any progress towards a solution.There have been a number of efforts on both the experimental and the theoretical fronts that followed Ref. [1], in particular at low energies [8][9][10][11][12][13]. A "best" result of S 34 (0) = 0.56(3) keV b was reported in Ref. [3] from an evaluation of the modern data that became available after 1998 (Ref. [14]) for the energies below 1 MeV. This improved value can be compared with the previous recommendation [14] of 0.53 (5) keV b. Such * snarasingh@gmail.com efforts also suggested that the precision could be improved if the theoretical spread in the extrapolated values is minimized. In addition, recent work of the ERNA (European recoil mass separator for nuclear astrophysics) Collaboration [15] is in conflict with the data from Ref. [8] and highlights the importance of precise measurements at medium energies, ...