
#1
Oct213, 02:29 PM

P: 1

Hi,
I recently read the following article http://arxiv.org/pdf/0805.2895v4.pdf which deals with dark matter scattering and I have difficulties in deriving formula (1). The problem is the following, we have a nucleon (mass m1, velocity u1) scattering from a dark matter particle (mass m2, velocity u2) into an outgoing nucleon (mass m1, velocity v1) and a secondary dark matter particle (masse m'2, velocity v2, with m'2 = m2  Δm). And we want to know the outgoing velocity of the nucleon v1 as a function of u1 and u2. Both u1 and u2 are assumed to be small compared to c (no relativistic effects). I started with momentum and energy conservation : [itex]m_1\vec{u}_1+m_2\vec{u}_2 = m_1\vec{v}_1+m'_2\vec{v}_2[/itex] and [itex]m_1\vec{u}^2_1+m_2\vec{u}^2_2 = m_1\vec{v}^2_1+m'_2\vec{v}^2_2  2\Delta m c^2[/itex] But then I'm stuck because I get a formula like equation (1) of the article but in which the following term is missing [itex]\frac{(m_1\vec{u}_1+m_2\vec{u}_2)^2}{(m_1+m_2)(m_1+m'_2)}[/itex] and I do not know where it comes from. It looks like it is the product of the center of mass velocity before and after scattering. Did I forget something in the momentum/energy conservation equations ? More generally, how to deal with this kind of process where total mass is not conserved so that center of mass velocity is discontinuous ? Thanks in advance for your help. 


Register to reply 
Related Discussions  
Can dark matter form planets and dark matter life?  Astrophysics  13  
Dark Matter, Dark Energy, Dark Flow... ohh...  Astrophysics  12  
Energy from mattermatter annihilation (relation to Dark Matter)  High Energy, Nuclear, Particle Physics  12  
superb overview of contemporary research/observations in dark matter, dark energy  Cosmology  0  
dark matter doesn't (or what's the matter with dark matter? or pick your lame pun)  General Physics  4 