Diploma Projects – Examensarbeten .
Short-lived
states as bottle necks in small chemical reactions.
Collisions between atoms and molecules, weather charged or not, are vital paths in the formation of stars from interstellar clouds. The same processes appear in gas phase reactions when for example a candle or a piece of wood is burning. It is believed that these processes are not direct.
The intermediate system as well as the products may appear in different electronically excited states. These intermediate states are not unique to atomic and molecular physics. Whereas the first such ''collision complex'' in atomic and molecular physics was experimentally verified about five years ago, the equivalence in nuclear physics ( the compound nuclei ) have been studied since around 1960. While the existence thus is relatively recent, the collision complex concept originates from theoretical modeling starting about 20 years ago.
Potential energy surfaces.
In order to describe collision process we need to study how two non-relativistic atomic or molecular systems approach, react and leave each other. We need to solve the Schrödinger equation for the electronic motion while keeping the nuclei fixed. We thereby obtain eigenvalues which depend
on the nuclear geometry as well as how these electronic eigenstates interact with each other. Computer programs which solve the electronic problem and generate these electronic “potential energy surfaces” are available to us. Doing such a calculation could be part of, or an entire diploma project.
Scattering calculations.
Having a set of potential energy surfaces, from which the forces between the atoms can be derived, one can use scattering theory to determine reaction rates and in particular search for intermediate short-lived states. If you choose to work on a project you will also here use existing computer codes. You will here study the motion of the atoms within the total system. You will propagate a set of coupled Schrödinger equations from origin, where the two systems are close to each other, to a large inter-system distance where the two systems do not interact. Comparing the form of the propagated wave function you can then compute matrix elements of the so called scattering operator to get the scattering matrix. Using this matrix you can derive the probability that a certain reaction has taken place at a certain relative collision energy.
Short-lived states – resonances.
A sharp peak in a reaction probability may be a sign of a resonance. Since these states are not bound they do not correspond to real values eigenvalues of the corresponding Schrödinger equation. It can be shown that the real parts of these complex eigenvalues correspond to the energy of the system while the imaginary parts correspond to the natural width or Heisenberg energy
uncertainty of the particular state. You will be able to compute these eigenvalues if you give up the Hermiticity, by using a complex transformed Schrödinger equation.
Present and Future experiments ?
The question is now : ''Can more of these intermediate collision complexes be found experimentally?'' Well, at Stockholm University,in a collaboration between the Manne Siegbahn laboratory and the Department of Physics, we are currently building a double beam electrostatic storage ring : DESIREE. The unique feature of this ring is that the two stored, well defined ion beams are merged in a section of the ring. The two stored kinds of particles will there be able to collide and react with well defined relative kinetic energies.
Example : The mutual neutralization
of H+ + H -
One of the simplest and most fundamental ion-ion collision reactions that can be studied is
H+ + H- -> H2 -> H(n=1) + H(n). Experimental and theoretical studies were done in the 1980s.
The double beam electrostatic storage ring, DESIREE, will allow for more detailed studies and
we therefore announced a diploma project with the title “The mutual neutralization of H+ + H- .“ Michael Stenrup defended his diploma thesis in December 2006. He had there found new structures
that most likely are short-lived, resonant H2 molecules. You can find his diploma thesis by here.
Cross section for the reaction path H+ + H- -> H2 ->
H(n=1) + H(n=5). Note the sharp peaks which most likely are signatures of
short-lived H2 quantum
states. You find the report of this
diploma project here as a pdf
file.
Summary.
Understanding the details of chemical reactions fascinates us since we thereby eventually may understand the basics of life - its origin and it biological processes. If successful we may help to give experimental tools to alter the outcome of chemical reactions in life and industry. There are several diploma projects that are announced here. Every student can choose her/his example. Together we will try to predict interesting cases to eventually be studied experimentally at, for example, DESIREE.
Contact persons :
Åsa Larson e-mail : aasa@teochem.kth.se
Dr. Theoretical Chemistry Div. Phone : 08/ 5537 84 11
Dept. of Biotechology Room : 103:030
AlbaNova, KTH. Roslagstullbacken 16
Nils Elander e-mail : elander@physto.se
Prof. Molecular Physics Div. Phone : 08/ 5537 86 56
AlbaNova, Stockholm Univ. Room : C4 : 3068