I have data that I would like to fit with Bessel function https://www.dropbox.com/s/7se9mb2epbietng/data.dat?dl=0
cylinder=NonlinearModelFit[data,(k1/q)*(BesselJ[1, q*r1]/(q*r1))^2 , {k1, r1},q, MaxIterations -> 10000] // (sol = #) &;
fitPoints = cylinder[Q] /. sol[[1]][[2]] // Table[{Q, #}, {Q, data[[All, 1]]}] & // (cylRes = #) &;
ListLogLogPlot[{data, fitPoints}, PlotRange -> All]
data in blue, fit mapped on data[[All,1]]
in orange Log/Log view
how can I fit it so that $ r_1 $ has a Gaussian distribution which would smoothen the minima? I was thinking about maybe summing up 100 Bessels with $ r_1 $ confined somehow with Gaussian, but I have no idea how to proceed.