Electron scattering simulation in a Hydrogen’s

S-orbital

A simulation by Pau and Aleks

11th Petnica International Summer Science Camp Physics

Mentor: Stefan Badza

ProblemHow can we know what happens inside?

How can we quantify it?

Problem Theoretical approach

Computational approach Results

Conclusions

Electron scattering simulation in a Hydrogen’s S-orbital

A new parameter: The scattering angle

Problem Theoretical approach

Computational approach Results

Conclusions

Electron scattering simulation in a Hydrogen’s S-orbital

Theoretical approach conclusionsWhile outside the sphere, force is zero

While inside the sphere, total force is given by

!

!

Acceleration at a certain distance can be derived immediately

Force given by the nucleus

Force given by the electron

cloud

Problem Theoretical approach

Computational approach Results

Conclusions

Electron scattering simulation in a Hydrogen’s S-orbital

Computational goals

Trace the particle

Plot a graph of the scattering angle as a function of impact parameter and initial energy

Problem Theoretical approach

Computational approach Results

Conclusions

Electron scattering simulation in a Hydrogen’s S-orbital

Tracing the particle (I): Inside a time loop

Problem Theoretical approach

Computational approach Results

Conclusions

AccelerationForce

Distance to center ( )

RK4

Velocity RK4

Position

Electron scattering simulation in a Hydrogen’s S-orbital

Tracing the particle (II): The 4th order Runge-Kutta method (RK4)

Problem Theoretical approach

Computational approach Results

Conclusions

Approximation method for differential equations

Better approximations than Euler’s method since the acumulated error is reduced

Electron scattering simulation in a Hydrogen’s S-orbital

Finding the scattering angle for each impact parameter

Problem Theoretical approach

Computational approach Results

Conclusions

Net force equals 0 <-> Striaght line

Second point after it leaves the sphere

First point after it

leaves the sphere

Electron scattering simulation in a Hydrogen’s S-orbital

A sea of data: To store or not to store

Problem Theoretical approach

Computational approach Results

Conclusions

AccelerationForce

Distance to center ( )

RK4

Velocity RK4

Position

x 1000

1000 x Impact Parameter 1000 x Scattering angle

>7 million calls!

x 8 Different initial velocities

Do we need to store all of it?

Which data is relevant for our purpose?

1000 x Differential cross-section

Electron scattering simulation in a Hydrogen’s S-orbital

Problem Theoretical approach

Computational approach Results

Conclusions

What to store and what to discard

Relevant data to plot

Everything is stored in a vector

We just want the last two points

Until these two the data is overwritten

every time

Electron scattering simulation in a Hydrogen’s S-orbital

Problem Theoretical approach

Computational approach Results

Conclusions

Obtained data (I)

+ initial energy

Electron scattering simulation in a Hydrogen’s S-orbital

Problem Theoretical approach

Computational approach Results

Conclusions

Obtained data (II)

+ initial energy

Electron scattering simulation in a Hydrogen’s S-orbital

Positive impact parameters lead to negative scattering angles and vice-versa

Lower impact parameter lead to higher scattering angles

As the impact parameter approaches zero, the behaviour becomes impredictable, specially in lower velocities

Problem Theoretical approach

Computational approach Results

Conclusions

ConclusionsElectron scattering simulation in a Hydrogen’s S-orbital

Thank you for your attention

Questions & Answers

Electron scattering simulation in a Hydrogen’s S-orbital