Collision Theory

Recommended Prerequisites

Quantum Mechanics.

Teaching Methods

Expository and concise teaching. The details of the calculations should be made by the students within the classes OT. Great emphasis on continuous assessment.

Learning Outcomes

- Know how to compute the differential cross section in an elastic collision process using various approximation techniques.

- To understand the relationship between the description of the collision process by the time independent theory and the description by the time dependent theory.

- Ability to address the multi-channel collision and the semiclassical approximation.

Work Placement(s)

No

Syllabus

Elastic Collisions

Time dependent formalism

Müller operators and the S operator. T-matrix operator and collision amplitudes. Calcula-tion of the cross section using wave trains. Collision of identical particles. Spin. Symme-tries and expansion in partial waves.

Independent time formalism

The G and T operators. The Lippmann-Schwinger equation. Stationary wave function and its asymptotic form. Expansion in partial waves. Regular solution and normalised solution. The method of the phase variable. Jost function. Levinson theorem. Resonances. Coulomb potential. Born approximation and Born approximation with distorted waves.

Multichannel collision

Adaptation of the concepts introduced in the elastic collision for multichannel collision. The coupled channels approximation. Optical potential.

Semiclassical formalism.

Assessment Methods

Assessment
Exam: 20.0%
Resolution Problems: 35.0%
Synthesis work: 45.0%

Bibliography

-Taylor, J.R. Scattering Theory: The Quantum Theory on Nonrelativistic Collisions, (Dover Publications, 2006). ISBN-13: 978-0486450131.

-Newton, R.G. Scattering Theory of Waves and Particles, (Dover Publications, 2003). ISBN-13: 978-0486425351.

-Sitenko, A.G. Scattering Theory, (Berlin, Springer-Verlag,1991). ISBN-13: 978-0387519531.

-Brink, D.M. Semi-Classical Methods in Nucleus-Nucleus Scattering,(Cambridge, Cambridge University Press, 1986). ISBN-13: 978-0521239400.