What is the coalescence factor?


by Waxbear
Tags: coalescence, factor
Waxbear
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#1
Nov8-12, 08:21 AM
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I am reading an article on experimental nuclear physics. The article is about deuteron and triton production in Pb + Pb collisions. In the article they mention the coalescence factor which is given by:

[itex]B_{A}=A\frac{2s_{A}+1}{2^{A}}R^{N}_{np}\left(\frac{h^{3}}{m_{p}\gamma V}\right)^{A-1}[/itex]

The coalescence factor has something to do with the formation of light clusters A(Z,N). So A is the mass number of the cluster, the R_np thing is the ratio of neutrons to protons participating in the collision, gamma is just the lorentz factor related to the velocity of the cluster and V is the volume of of particles at freeze-out (after hadronization, when there are no more strong interactions between the nucleons). I don't know what s_A is though. I have worked out the units for A = 2 to be:

[itex]s_{A}\cdot \frac{ev^{2}s}{m}+\frac{ev^{2}s}{m}[/itex]

But i don't know the units of s_A. I was hoping for this to turn out unit-less, since it could then be interpreted as a sort of probability of a cluster A(Z,N) to form. Now i'm not sure what it is.

I apologize if this post was supposed to go in homework. Technically it is a sort of homework question, since i am supposed to present the article as an exam tomorrow. But i figured that there was a bigger chance that someone could help me with this on the HEP board.
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Vanadium 50
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#2
Nov8-12, 08:34 AM
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It has to be unitless, since you add 1 to it.
Waxbear
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Nov8-12, 09:35 AM
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Of course, i didn't even consider that. Okay, so i guess the coalescence factor has dimensions of:

[itex]\frac{ev^{2}s}{m}[/itex]

I'm still not sure exactly sure about what the coalescence factor is though.

mfb
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Nov8-12, 11:19 AM
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What is the coalescence factor?


Where does your formula come from? I found a similar one in Coalescence and flow in ultra-relativistic heavy ion collisions (pdf, equation 6.2), but that uses (2pi)^3 in the nominator of the brackets.
I don't see how masses cancel in the equation.

A cross-section (1/m^2) or a dimensionless fraction would be a nice result, and I think c=1 is implied.
Waxbear
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#5
Nov8-12, 01:57 PM
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I probably did something wrong when i tried to find the dimensions and yes i think you are right that c = 1 is implied. I got the equation from an old article called "Deuteron and triton production with high energy sulphur and lead beams". It's from 2001, so you might not be able to find it on the internet anymore.

Yes a cross-section or a fraction would be very nice, however, i found a plot later in the article where B_2 has dimensions:

[itex]Gev^{2}c^{-3}[/itex]

Which is mass times momentum. Weird.


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