Dark matter collisions with Xe on earth

[j-lee00]

original question

Assume that the density of dark matter near the Earth is 0.3 GeV / cm3 and that the dark matter particle has a mass of 100 GeV and a velocity of 200 km/s. If the dark matter-nucleon cross section is 10^-44cm2 calculate how many events you would expect to see every year in a metre cubed volume of Xenon at room temperature.

I have worked out that

1) density of dark matter particles near Earth is 3 particles per m^3
2) the flux of the dark matter 6 * 10^5 m^-2 s^-1 passing through a m^3 of Xe
3) that there are 1.668 *10^25 particles in a m^3 of xenon

if the the cross section of dark matter 10^-44 cm^2

How do i work out the number of collisions per second?

 

[Jhero]

To calculate the number of collisions per second, we can use the following formula:

Number of collisions per second = density of dark matter particles * flux * number of particles in a cubic meter * cross section

Plugging in the values we have calculated, we get:

Number of collisions per second = 3 particles/m^3 * 6 * 10^5 m^-2 s^-1 * 1.668 * 10^25 particles/m^3 * 10^-44 cm^2

= 3 * 6 * 10^5 * 1.668 * 10^25 * 10^-44 collisions/s

= 3 * 10^6 * 1.668 * 10^-19 collisions/s

= 5.004 * 10^-13 collisions/s

Therefore, we can expect to see approximately 5.004 * 10^-13 collisions per second in a cubic meter of Xenon at room temperature. To calculate the number of collisions per year, we can multiply this value by the number of seconds in a year (3.154 * 10^7):

Number of collisions per year = 5.004 * 10^-13 collisions/s * 3.154 * 10^7 s/year

= 1.578 * 10^-5 collisions/year

Therefore, we can expect to see approximately 0.00001578 collisions per year in a cubic meter of Xenon at room temperature.