Chapter 4 - UCSB HEP

WORK AND ENERGY
Since the scattering is elastic, v:, = Vrc.
Hence
vlo sin O
tan O1 =
v + V l, cos @
=
sin 8
(V/hc> + cos o
From Eqs. (I) and (21, V/el, = ml/mn. Therefore
sin 8
tan el =
(ml/mz) + cos o
The scattering angle @ depends on the details of the interaction, but in
generat it can assume any value. If ml < mp, it follows from Eq. (3) or
the geometric construction in sketch (a) that O1 is unrestricted. However,
the situation is quite different if ml > mn. In this case 8, is never
greater than a certain angle el,,,,. As sketch (b) shows, the maximum
value of 6, occurs when r: and vi, are both perpendicular. In this case
sin OI, = VI,/~ = mz/ml. If ml >> mt, 81,max = wn/ml and the maximum
scattering angle approaches zero.
Increasing Q
I
\ / 1
\
\ / /
\
\ /' '.
\--A'
\
\
I
I
/
.--'
0 /'
Physically, a light particle at rest cannot appreciably deflect a massive
particle. The incident particle tends to continue in its forward direction
no matter how the light target particle recoils.
Problems 4.1 Asmall blockof rnassmstartsfrom rest and slidesalonga frictionless
loop-the-loop as shown in the left-hand figure on the top of the next
page. What should be the initial height z, so that m pushes against