Luminosity vs. number of collisions

[ferar]

Hi, I was wondering if there is any way of calculate number of collision per second for example based on luminosity. Is this possible?
I read somewhere that there are about 13 collisions per bunch, is this correct? Are there any LHC Vistar with this information?
Thanks very much.
Fernando

[Kasuha]

At present there is six collisions per bunch crossing on average in Atlas and CMS, 14 is maximum. LHCb and Alice have luminosity caps so it's less for them.
Calculating number of collisions from units currently being used (inverse nano- and picobarns) is possible but I'm not sure what the coefficient is.

[adam_jeff]

The coefficient is called the cross-section. Cross-sections can be defined for each type of collision but I guess what you're interested in is the 'total inelastic cross-section' which will give you the total number of collisions (the 'total cross-section' also includes elastic colisions, where two protons just glance off each other but don't produce anything interesting and are not detected in the experiments).
Event rate = Luminosity * cross-section
Cross section is measured in barns, that's why luminosity is defined in inverse barns.
The cross section depends on energy and so it's never been accurately measured for the LHC beams. I believe that's what the ToTEM experiment will do sometime this year. But theory and first signs from the experiments agree it's around 60 mbarns.
So this will give you the events per second. Divide by the rate of crossings (number of colliding bunches * revolution frequency) to get the collisions per crossing.

[adam_jeff]

Oh and a barn is technically a unit of area, equal to 10^-24 square cm. So the luminosity can also be given as cm-2.
For example, right now the ATLAS instantaneous luminosity is 600 * 10^30 cm-2 s-1, which is the same as 600 *10^6 inverse barns per second or 600 inverse microbarns per second.
Therefore the rate of events is 600*10^6 * 60*10^-3 = 36 000 000 events per second. There are 1042 bunches colliding in ATLAS, thereofe 1042*11245 crossings per second. So there are 36 000 000 / (1042*11245) = 3.07 collisions per crossing.

[chelle]

You may want to check my Frequencies and Densities topic. There are also some references to a spanish fan site that is quite good.

I hope you don't mind my controversial mambo jumbo too much ...