Experimental determination of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mi>He</mml:mi><mml:mprescripts /><mml:none /><mml:mn>3</mml:mn></mml:mmultiscripts><mml:mo>(</mml:mo><mml:mi>α</mml:mi><mml:mo>,</mml:mo><mml:mi>γ</mml:mi><mml:mo>)</mml:mo><

The $^3$He($\alpha$,$\gamma$)$^7$Be reaction plays a major role both in the BBN producing the majority of the primordial $^7$Li, and in the pp-chain, where it is the branching point. As a few-nucleon system, this reaction is often used to validate ab-initio theoretical calculations and/or test R-matrix theory and code implementations. For the latter, experimental data in an extended energy range is of crucial importance to test the fit and extrapolation capabilities of the different codes. The $^3$He($\alpha$,$\gamma$)$^7$Be reaction cross section has been measured by several groups up to the first resonance ($E_{c.m.} \approx 3$ MeV) in the reaction. However, only one dataset exists above the $^7$Be proton separation threshold measured in a narrow energy range ($E_{c.m.} = 4.0-4.4$ MeV). In this work we extend the available experimental capture cross section database to the energy range of known $^7$Be levels. The activation method was used. The experiment was performed using a thin-window gas cell with two high-purity Al foils as entrance and exit windows. The activity of the $^7$Be nuclei implanted in the exit/catcher foil was measured by detecting the yield of the emitted $\gamma$~rays using shielded high-purity germanium detectors. New experimental $^3$He($\alpha$,$\gamma$)$^7$Be reaction cross section data were obtained for the first time in the $E_{c.m.}=4.3-8.3$ MeV energy region. The new dataset with about 0.2 MeV step covers the energy range of known levels and particle separation thresholds. No prominent structures are observer around the $^7$Be levels. The reaction cross section is slowly increasing with increasing energy. Above the $^6$Li$+p_1$ threshold, a decrease starts in the cross section trend. The overall structure of the cross section suggest a broad resonance peaking around $E_x=7.5$ MeV $^7$Be excitation energy, with a width of 8 MeV.