The XENON1T experiment is searching for dark matter that scatters with xenon atoms. The experiment contains 1 tonne (1000 kg) of liquid xenon and takes data for 1 year. After analysing the 1 year dataset, the XENON1T experiment announces that it has detected 10 dark matter scattering events.

A theorist thinks that these 10 events are caused by a 100 GeV/c2 dark matter particle that has scattered with a xenon atom via the Yukawa potential V(r)=cexp(r/a0)/r where is a positive real number and a0=1.97103 fm.

If the theorist is correct, use the scattering amplitude in the first Born approximation, f()=m22d3rV(r)eiqr, to determine the value of that is consistent with the experimental data.

In the box below, please enter the numerical value of ln() (i.e. the natural logarithm of ). You should round your answer to 1 decimal place.

[You should assume that in the vicinity of the XENON1T experiment, the dark matter speed is 300 km/s (103c) and the dark matter mass density is =0.4 GeVcm3. Recall that c=0.197 GeV fm. Hint: compare the sizes of a10 and q.]