  The $^7$Li(p,n)$^7$Be reaction is widely used as neutron source for neutron
induced reaction cross section measurements, and for $^7$Be radioactive source
production. There are two prominent structures in the excitation function, a
narrow resonance between $E_\mathrm{p}= 2.2-2.3$ MeV, and a broad peak, around
$E_\mathrm{p}= 5$ MeV. There are tension between the experimental data sets
both in the position and the width of this latter structure, as well as in the
absolute scale of the data. In the present work the $^7$Li(p,n)$^7$Be reaction
is investigated using the activation technique, with the aim of providing
comprehensive cross section data covering the second structure and connecting
prior literature data sets. The irradiations were performed with the Atomki
cyclotron accelerator with pairs of thin foil targets, thus with precisely
controlled reaction energy in the range of E$_\mathrm{p} = 3.5-13$ MeV. After
the irradiations the activity of the samples was measured using a high-purity
germanium detector. The energy uncertainty of the new data points is much
smaller than in any of the previous works, while the cross section uncertainty
is comparable with the most precise literature data. A consistent data set was
obtained connecting the most recent and most precise literature data sets. With
the new data the absolute magnitude of the $^7$Li(p,n)$^7$Be reaction cross
section is constrained and became more precise.
