Nuclear diamters will a meson traverse?

[clockworks204]

nuclear diameters will a meson traverse?

Approximately how many nuclear diameters (A=100) will a (pi)⁰ meson traverse at a speed of 0.95c before it decays?

My textbook is very vague for the chapter containing this material. The only thing that is really given is that the mass is 135.0 MeV/c² and its lifetime is 0.84x10^-16s.

 

[Bob S]

If the pi-zero did not interact with the nucleus, then the decay length in the lab is

L = βγcτ

where β and γ are the relativistic Lorentz parameters, c is the speed of light, and τ is the undilated (center-of-mass) lifetime.

Bob S

 

[clockworks204]

Thank you for your reply. Can you please specify what exactly a lorentz parameter is?

 

[Bob S]

Thank you for your reply. Can you please specify what exactly a lorentz parameter is?

The velocity of the particle is v = βc, and γ= 1/sqrt(1-β²). Both β and γ are used in the Lorentz transformation from one moving relativistic reference frame to another. For the relativistic decay length L = βγcτ, the velocity is βc, and the time-dilated decay lifetime τ in the laboratory reference frame is γτ, so the decay length in the laboratory reference frame is velocity times time, or L = (βc)(γτ) = βγcτ. A complete (perhaps too mathematical) discussion of Lorentz transformations between different relativistic inertial reference frames is given in

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/ltrans.html

http://en.wikipedia.org/wiki/Lorentz_transformation

See also Section 38.1 in kinematics section in http://pdg.lbl.gov/2009/reviews/contents_sports.html

Bob S

 

[aprillove20]

Thanks Bobs for the great discussion, and the formula it very detailed. Well done.

 

[clockworks204]

I do appreciate the info