HW 7 problems/solutions

HW 7 problems/solutions - Homework 6 1 11/1/2005 Homework...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Homework 6 1 11/1/2005 Homework VII Problems: VII.1 Scattering of spinless particles: a. Calculate d σ / d * and the total cross section tot for electromagnetic lowest-order electromag- netic scattering of spin-0 bosons A and B, both with charge + e . b. How does the result change for bosons that have opposite charges? Solution: For the process a + b a’ + b’ , with m a = m a’ and m b = m b’ we have found (assuming a b ): () 2 '' 2 2 4 2 2 ' ' ' ' 24 2 44 2 2 22 4 ' ''' 1 =, with 64 ( ) In CMS variable ab a b a b a b aa bb ab a b ba a b a b d ds ig e ie p p ie p p p p p p qq ee s u pp p p pp pp s m m u m m e t m m µν νµ µ π +→ + = ⎛⎞ =+ + = + + ⎜⎟ ⎝⎠ + + = + + + = ' ' ' ' 1 1 ' 2 2 ' s: cos( ) 2 1 cos c o s 1 c o s p EE mm a s u pp p p tm p p m E p CMS πθ ββ θ θθ −− ≡= = = = = −+ + + + == = +− where β i 1 stands for E i / p for particle i . In case where all masses can be neglected, i 1 =1, the dif- ferential cross section becomes: 2 4 2 CMS, ignoring all masses 3c o s 64 1 cos de + = Ω− which can be integrated. Note that the cross section goes to infinity for 0, which is related to the infinite range of the electromagnetic interaction! In practice, we define a minimum scattering angle, which depend on our interest and on the smallest angle that can be detected by our detec- tor. Physics sets a practical limit as well: small scattering angles correspond to large impact pa- rameters; e.g. the upper limit for e p scattering would be the Bohr radius. .. From the expression it
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/22/2009 for the course PHYSICS 557 taught by Professor Michaelrijssenbeek during the Fall '05 term at SUNY Stony Brook.

Page1 / 3

HW 7 problems/solutions - Homework 6 1 11/1/2005 Homework...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online