Calculating Dark Matter Events in Xenon | 100 GeV, 0.3 GeV/cm3

[Bacilla]

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.

Haven`t done anything similar and now struggling...

 

[Bacilla]

I tried to take a sqare metre box, and calculate the total area of the xenon atoms in the box, and i found out that the area is 165 000 square metres, which gives 100% impact probability. Thats not good...

 

[mgb_phys]

The cross section is the effective 'size' of the xenon atom as far as the particles hitting it are concerned. So you need to calculate the total cross section area for a cubic metre of xenon and the number of particles going through the cubic metre pers second.

edit - is that what you tried? Looks like you might have got a few powers of 10 wrong. Make sure you are working in consitent units.

 

[Bacilla]

Can i simplify that Dark matter articles are point like, and they are traveling all in one directon?

 

[-Vitaly-]

Hi, I don't know what you are talking about, but when I did molecular theory we used a simplification that the mean of square speeds of particles in one direction is 1/3 of the mean square speeds of particles in all directions.
http://img395.imageshack.us/img395/5379/clipboard01qw2.jpg

This is probably irrelevant, but anyway, goodluck :)

 

[mgb_phys]

Can i simplify that Dark matter articles are point like, and they are traveling all in one directon?

Yes - treat the dark matter particles as rays going through the Xenon.
The 'area' of the xenon comes from the cross section and th enumbe rof atoms in that volume.

 

[Bacilla]

The 'area' of the xenon comes from the cross section and th enumbe rof atoms in that volume.

If the radius of a Xe atom is 10^-10m or 100pm and there is 2.5*10^25 atoms in a cubic metre, then the area* is 900000 square metres. this means that a particle will interact with 900000 Xe atoms when crossing a metre of a gass, that doesn`t make sense to me...

*area = all atoms in the cubic metre forming a one atom thick film.

 

[mgb_phys]

The cross section area is given in the question.
It's not the physical area (which is a bit meaningless for an atom) - the capture cross section is the area * the probability of it interacting. Think of it as the cross section area the atom would have if it were guarranteed to stop an incoming particle.

 

[Bacilla]

Silly me, haven't noticed the "nucleon" part in a "dark matter-nucleon" expresion...
Now there is only 4.65*10^-3 events per year, that is a bit low i think, as you will need 215 square metres of water to observe one event per year.