Master projects
Are you following a master program with a focus on theoretical physics? Are you intrigued by the physics going on at the subatomic scale and its influence on events in cosmos? Would you like to experience to work in an active research group in this area of science? Then you should consider joining us and finishing your degree with a master project in our group.

The effective vertex in the low energy effective theory (Fermi interaction). We usually offer several opportunities for master thesis projects. You should be interested in one or several of the following topics:

Please feel free to discuss topics with any of us (see people).

For optimal learning output you should enter the project with a genuine interest in theoretical physics and a confidence in the mathematical toolbox that you have acquired. Many of our projects have a computational aspect; and consequently those projects offer an excellent opportunity to advance your skills in the computational scientific methodology. In fact, we also offer projects that are aimed at students that are more computationally inclined and who has an interest in one or several of the following topics:

We are always aiming to construct projects that are directly related to ongoing research efforts. In fact, we take great pride in the fact that many project lead all the way to a scientific publication. See examples below (master student authors in bold face):

Previous projects are listed below:

Three-Nucleon Forces Through Normal-Ordered Approximations

A three-nucleon Hamiltonian is approximated through
	normal-ordering with respect to a Fermi state.. Three-body forces have long been known to play an important role in nuclear physics. However, fully including such interactions in ab-initio methods is computationally expensive and not feasible for larger nuclei. As an alternative, approximations based on normal-ordering with respect to a Fermi state of the nucleus can be used. In this framework part of the three-body interaction can be expressed as lower order interactions, which can be included without increasing the computational complexity. This thesis provides a full derivation of the normal-ordered two-body (NO2B) approximation for closed-shell nuclei. In addition, a simple implementation of this method is described. This is then used to calculate ground states of helium-4 in small model spaces, which are compared to the corresponding calculations with full three-body forces. The results show a relative error of less than 1.5%, in line with earlier studies.

Full text: Chalmers CPL 244698
Supervisor: Christian Forssén and Andreas Ekström

by Dag Fahlin Strömberg, 2016


Three-Body Forces in Configuration-Interaction Methods for Nuclear Physics

Hamiltonian matrix with explicit three-body forces. In this thesis, three-body forces are studied and implemented in a quantum many- body configuration-interaction method. The general importance of three-body forces in physics is discussed, providing some classical examples, before focusing in particular on their appearance in modern nuclear physics. The theoretical formalism that is needed for the implementation of three-body forces in quantum many-body systems is presented, with the angular-momentum coupling of two- and three-body systems of identical particles as main focus point. The resulting software, that is written in C, is then utilized to compute the ground-state energy of the tritium (3H) and helion (3He) nuclei in finite model spaces (Nmax <= 8). Results are compared with other simulations and the difference is within an acceptable tolerance. A few suggestions for future optimization of the code, such as the utilization of hash maps, are discussed.

Full text: Chalmers CPL 241645
Supervisor: Christian Forssén and Andreas Ekström

by Tor Djärv, 2016


Dark Matter Capture by the Sun via Self-Interaction

There is compelling evidence that dark matter constitutes 85 % of the universe's total matter content. So far, this distinctly different type of particle is observed only in terms of its gravitational effects, but various detection experiments are conducted and underway. One method is indirect detection of neutrinos coming from the Sun. Under the assumption that dark matter consists of Weakly Interacting Massive Particles (WIMPs), one of the most studied dark matter particle candidates, these WIMPs would interact with atomic nuclei within the Sun and be trapped in its gravitational field. After a large enough concentration of trapped WIMPs has been amassed, they would begin annihilating with each other, producing a high-energy neutrino signal. In this thesis I study the possibility that WIMP self-interaction has a significant effect on the total capture rate and resulting neutrino signal. Potentially, an amassed concentration of WIMPs inside the Sun can itself constitute a scattering target and contribute to further captures from the galactic dark matter halo. In order to describe the kinematics of particle interaction and WIMP capture I utilize an effective field theory in the non-relativistic limit. This allows me to explore, in a model-independent way, the parameter space of interaction and the possibility for WIMP capture enhancement due to self-interaction. Upper limits to the strength of these interactions come from direct detection experiments and galaxy cluster observation and simulation. It is found that self-interaction could play a signficant role in amplifying the neutrino signal; even an amplification of several orders of magnitude is not ruled out by current limits.

Full text: Chalmers CPL 239147
Publication: arXiv:1609.04825 [astro-ph]
  JCAP 1612 (2016) no.12, 016.
Supervisor: Riccardo Catena

by Axel Widmark, 2016


Tunneling Theory for Few-Body Systems in One-Dimensional Traps

Two distinguishable fermions in a one-dimensional, open trap. In recent experiments, carried out at the University of Heidelberg, tunneling rates of ultracold distinguishable fermions out of an optomagnetical trap have been measured. The fermions interact by a tunable short-ranged interaction, and the trap is asymmetric making the trapped quantum system effectively one-dimensional. In this thesis, a method for calculating the energy levels and tunneling rates of one and two interacting particles out of a very general onedimensional potential well is devised. The method is based on expanding the Schrˆdinger equation of the system in a complex-momentum basis. This is done utilizing the so-called Berggren completeness relation. Ultimately, the basis expansion leads to a complex symmetric non-Hermitian eigenvalue problem for a large, dense matrix. The general method is applied to a system of trapped, ultracold fermionic atoms in a setup that closely resembles the Heidelberg experiments. The short-ranged interaction is modeled as a point-interaction, and the trap potential is regularized at large distances from the interesting region. The obtained energies and decay rates are contrasted to results obtained using the Wentzel-Kramers-Brillouin (WKB) approximation. Notable differences can be observed, and these may be due to insufficiency of the WKB approximation to accurately describe the system in question.

Full text: Chalmers CPL 197684
Publication: arXiv:1412.7175 [cond-mat]
  Phys. Rev. A 91, (2015), 041601(R), Rapid communication.
Supervisor: Christian Forssén and Jimmy Rotureau

by Rikard Lundmark, 2014


Fermionization in one-dimensional cold atom systems

Correlation density for weakly attractive odd-parity state of 2+1
	fermions in 1d trap. Recent developments in experimental techniques have made it possible to use magnetic fields to tune interactions between trapped cold atoms with different spin components allowing for detailed experimental investigations of the properties of quantum mechanical few-body systems. In this thesis we investigate the properties of two-component cold atoms trapped in a harmonic oscillator potential with a zero range interaction of arbitrary strength between the different species. In the limit of infinite interaction the atoms will tend to avoid each other. This is reminiscent of the Pauli principle and we will address differences and similarities to a system of identical fermions. Exact diagonalization of the Hamiltonian in a harmonic oscillator basis is used to obtain the eigenvectors and eigenvalues of the system and we also employ numerical methods borrowed from nuclear physics to generate effective interactions using unitary transformations. This method proves to be very effective for improving the convergence and the computation time is significantly decreased even for very strongly interacting systems.

Full text: Chalmers CPL 180197
Publication: arXiv:1304.2992 [cond-mat]
  New J. Phys. 16 (2014) 063003
Supervisor: Christian Forssén and Jimmy Rotureau

by Jonathan Lindgren, 2013


The Similarity Renormalization Group for three bosons in a momentum-space partial-wave basis

SRG transformation of the modified Yukawa potential in a momentum- space partal-wave basis for L=2. The Similarity Renormalization Group (SRG) flow equation is explored for systems of two and three spinless bosons in a momentum-space partial-wave basis. The two- and three-body binding energies as well as the phaseshifts are used to gauge that the transformation is unitary and to study how well the SRG decouples high- and low-energy physics. I consider four different potentials with different characteristics: Two simplied nucleon potentials and two inter-atomic helium potentials (a soft-core potential and the state-of-the-art LM2M2 potential that is fitted to a wealth of experimental data). An initial three-body force is included for two of these potentials. Even with only two-body terms in the initial hamiltonian, SRG induced many-body forces are shown to arise during the transformation. These induced forces are computed for the three-body system and their evolution is studied as a function of the flow parameter. In all cases the SRG transformed potentials display greatly improved decoupling. This is achieved with a three-body binding-energy deviation of less than 0.1% in all cases except for the soft-core helium potential.

Full text: Chalmers CPL 166975
Supervisor: Christian Forssén and Lucas Platter

by Boris Carlsson, 2012


Chiral Perturbation Theory,Weak Interactions and the Nuclear Two-body Axial Vector Current

The two Feynman diagrams that give the leading contribution to the two- body axial vector current. In this thesis I give a practical introduction to chiral perturbation theory. This is an effective field theory of pions and nucleons. It is governed by the chiral symmetry stemming from the lightness of the up- and down quarks in quantum chromodynamics. The validity region comprises energies up to the rhomeson mass. The theory is expressed as an infinite series of chiral invariant interactions, whose strengths are expressed in an infinite number of low energy constants. The interactions can be ordered and I identify the most important ones. Special care has to be taken when including nucleons in chiral perturbation theory because of the scale introduced by the nucleon mass. To facilitate straightforward calculations I work in heavy-baryon chiral perturbation theory. In this formalismthe nucleons are considered to be very heavy and the nucleon mass only appears in next-to-leading order corrections. The pions and nucleons are coupled to the charged vector bosons of the weak interactions. This interaction is determined entirely by the chiral symmetry. As an example, I compute the decay rate of charged pions. Experimental data for this observable can be used to fix one low energy constant. Finally, I compute the two-body axial vector current of nucleons in heavybaryon chiral perturbation theory with the long wavelength approximation. This current complements the leading order one-body current operator and gives the first correction to the Gamow-Teller operator from the nuclear environment. I provide both a detailed derivation and an explicit expressions for this two-body current operator.

Full text: Chalmers CPL 160376
Supervisor: Christian Forssén

Chiral Extensions of the MSSM

This thesis is based on the paper [1]. We present the construction and analysis of supersymmetric models. We begin by giving a short description of the Minimal Supersymmetric Standard Model (MSSM) and pointing out its two main problems. Motivated to resolve them we construct a class of MSSM extensions characterized by a fully chiral field content (no -terms) and no baryon or lepton number violating terms in the superpotential due to an extra U0(1) gauge symmetry. The minimal models consist of the usual matter sector with family dependent U0(1) charges, six Higgs weak doublets, and four charged singlets required to give masses to the Higgsinos, cancel anomalies and allow for commensurate charges. These models are characterized by a discrete set of solutions for the charges. The models with right handed neutrino superfields are also presented. As a different issue we briefly discuss the SUSY breaking mechanism in gauge mediation scenario, where we show how an extra gaugino ~ Z0 can be used to mediated SUSY breaking from the Hidden Sector. Analysing the models, we discuss their general features, e.g. classical vacuum, CPviolation, Electro-Weak symmetry breaking and running coupling constants. In the end we investigate the decays of Z and Z0 -bosons and study in detail experimental constraints on Flavour Changing processes.

Full text: Chalmers CPL 179157
Supervisor: Gabriele Ferretti/td>

by Denis Karateev, 2012


Three-Body Overlap Functions in Atomic Nuclei

Three-body cluster channel form factor for 6-He. We study the computation of translationally invariant overlap functions in the formalism of ab-initio No-Core Shell Model. In particular, we establish the framework for the three-body cluster overlap function and derive the explicitly the expression for the special case, when the A-body nucleus is clustered into Core+N+N. The translationally invariant expression for the two-body cluster overlap function was originally presented by Petr Navratil. That work has formed the basis for this thesis. To illustrate overlap functions, numerical calculations of the single-particle overlap between 9Be-states and 8Be-states + one neutron are performed. The calculations are done with a SRG-evolved N3LO interaction and the results are presented in this thesis.

Publication: arXiv:1309.5810 [nucl-th]
  Phys. Rev. C 89, 011303 (2014)
Supervisor: Christian Forssén

by Daniel Sääf, 2011