2014
DOI: 10.1103/physrevd.89.103533
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Relativisticσvrelin the calculation of relics abundances: A closer look

Abstract: We find the probability density function P(Vr) of the relativistic relative velocity for two colliding particles in a non-degenerate relativistic gas. The distribution reduces to Maxwell distribution for the relative velocity in the non-relativistic limit. We find an exact formula for the mean value Vr . The mean velocity tends to the Maxwell's value in the non-relativistic limit and to the velocity of light in the ultra-relativistic limit. At a given temperature T , when at least for one of the two particles … Show more

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Cited by 50 publications
(51 citation statements)
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“…In this simple setup the scattering rate s should be s = nσ, where it is taken into account that the relative velocity between particles is close to the speed of light (a calculation using Eq. (52) of [34] gives v rel ≈ 0.98 for our setup), and n is the particle density. From Fig.…”
Section: Elastic Box Testmentioning
confidence: 99%
“…In this simple setup the scattering rate s should be s = nσ, where it is taken into account that the relative velocity between particles is close to the speed of light (a calculation using Eq. (52) of [34] gives v rel ≈ 0.98 for our setup), and n is the particle density. From Fig.…”
Section: Elastic Box Testmentioning
confidence: 99%
“…is evaluated at T = m χ , with g * defined similarly to (123), but with (T i /T ) 4 instead of (T i /T ) 3 , such that the energy density is ρ = (π 2 /30)g * T 4 . The cross section is thermally averaged, and the v appearing there is usually considered to be the relative velocity between the annihilating particles, but there is some subtlety in this identification that becomes relevant when the annihilations are relativistic [111], which is not the case here. Since the particles are highly nonrelativistic for thermal freezeout, it is a good approximation to use Maxwell-Boltzmann statistics so that…”
Section: B Thermal Freezeoutmentioning
confidence: 99%
“…(A8). Thus, taking into account the relation between the average velocity and temperature [41,42], the velocity-averaged cross section is σv conv = σ conv v = σ conv · 2/ √ πx. Finally, we arrive at the following expression…”
Section: A Boltzmann Equationsmentioning
confidence: 99%