Relativistic Nuclear Reaction.

1. Oct 25, 2007

azatkgz

1. The problem statement, all variables and given/known data
Nucleus A has rest mass $$m_A$$,collides with nucleus B which has rest mass $$m_B$$.In the laboratory frame,nucleus A has energy $$E>m_Ac^2$$ and nucleus B is stationery.After the collision,a nuclear reaction takes place:
$$A+B\rightarrow C+D$$

where nucleus C has rest mass $$m_C$$ and nucleus D has rest mass $$m_D$$.Suppose that $$m_A+m_B+Q=m_C+m_D$$,where Q>0.Find the minimum value of E required for this reaction to occur.Give answer in terms of $$m_A,m_B,Q$$

2. Relevant equations
$$E^2-P^2c^2=const$$

3. The attempt at a solution

$$(E+m_Bc^2)^2-E^2+m_A^2c^4=(m_C+m_D)^2c^4=(m_A+m_B+\frac{Q}{c^2})^2c^4$$

$$E=\frac{2m_Am_Bc^4+Q^2}{2m_Ac^2}$$