Calculate the kinematic threshold energy of a proton

[tritenick]

Homework Statement

Given the reactions:
p + 9 Be --> 10B + "gamma"
p + 9 Be --> 9B + 1n
p + 9 Be --> 9Be + 1p
p + 9 Be --> 8Be + 2H
p + 9 Be --> 7Be + 3H
p + 9 Be --> 6Li + 4He

Calculate: a) Q-value
b) kinematic threshold energy of the proton
c)threshold energy of the proton for the reaction
d) minimum kinetic energy of the products

Homework Equations

The Attempt at a Solution

Attempt: I have worked out part a) for each. But am not sure what the difference between b & c are? Any ideas? For c) I thought the equation would be:
KE_threshold = -Q*(mb+mB)/(mB+mb+ma)

Thanks for any thoughts!

 

[Astronuc]

One may find a discussion of binary nuclear/particle reactions in Chapter 6.3 of Fundamentals of Nuclear Science and Engineering Third Edition by J. Kenneth Shultis, Richard E. Faw, 2017 or Second Edition, 2007.

The give problem is #2 in the third edition, and probably the second.

The minimum energy will depend on the Q-value of the reaction, which only considers the mass of the reactants and products. For Q > 0, there is no threshold, but for Q < 0, some energy, e.g., kinetic energy will be required to make the reaction happen. The minimum kinetic energy of the proton requires no scattering of the product particles, i.e.,g the lighter particle/nucleus must travel in the same direction as the larger nucleus, or in the same direction as the incident proton.

In addition, for charged particles, e.g., proton, it must overcome the Coulomb barrier with the target, which is an additional energy threshold to overcome in order to the proton and target to interaction and the reaction take place.