Chaotic scattering
Disponible también en ESPAÑOL
In particle scattering a projectile that moves toward a fixed target p, interacts with it, and leaves the region. Let us consider a particle moving in a potential V(x,y) that describes the interaction between the particle and the target. The particle initial velocity, position, and impact parameter b, can be modified, using the applet´s text fields. Finally, when the particle leaves the scattering region, we determine the direction the particle takes. This direction being caracterized by the scattering angle, and is equal to the angle that makes the velocity vector with a fixed axis.
Let us consider the repulsive potential :
V(x,y)= x2 y2 exp[-(x2+y2)]
We clearly see, that the potential has four maxima, at the coordinates (1,1) , (-1,-1) , (-1,1) , (1,-1). At these maxima the potential energy has a value of v(x,y) = 1/e^2 = Em. Later we will see that depeding of the ratio of the particle energy E to the value of Em, that is, E/Em, chaotic scattering can be obtained.
1- Lets prepare a simulation for the case in which the particle´s energy is greater than the maximum potential value Em. Select the parameters to: mass=1, vel. in x=1, vel. in y=0, initial b=-1, final b=1, delta=0.05. ¿What behavior do you see in the graphic? Remember to push the start button.
2- Lets try again with an energy smaller than Em, the parameter values are : mass=0.5, vel. in x=0.5, vel. in y=0, initial b =-1, final b=1, delta=0.05. In wich regions do you observe abrupt changes in the graphic?
3- Lets try again with the last energy, but this time lowering the b parameter values, and seting delta smaller. Say, let us select: mass=0.5, vel. in x=0.5, vel. in y=0, initial b=-0.5,final b=0.5, delta=0.005. Do you still observe abrupt changes?
4- Do your own experiments, but this time, set the potential as atractive.