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A Dirac-Rmatrix approach to the determination of opacities

A Dirac-Rmatrix approach to the determination of opacities

                        Supervisor : Professor Connor Ballance (


Opacities are key ingredients in any domain where radiative transfer is important. In particular, Rosseland mean opacities play an essential role in stellar modelling. They characterize the interaction between the photons produced in the centre of stars and the surrounding plasma up to the surface of the stars. Bound-Bound  (atomic structure) transitions and bound-free(photoionisation) transitions underpin the accurate determination of such opacities, which our atomic collision group are able to calculate quite accurately. Beyond the stellar opacities for which the codes were originally developed, certain phases of kilonova modelling could benefit from the opacity of heavier elements of the periodic table, which we are now able to address.

For the stellar opacities, until 2015, there was essentially agreement between all of the theoretical opacity models, however a Sandia experiment challened that idea. The measurement at Sandia National Laboratory of the Fe opacity at 180 eV and Ne = 3.1 x10^(22) cm (-3)$ , which is in line with conditions corresponding to the base of the Solar convection zone:

Te 2.15 x 10^6 K and Ne 3.1 x 10^{22} cm(-3) measured an opacity of a factor of 2 higher than all calculations and exhibits large differences (filled windows, higher continuum)at certain photon energies (Bailey et al. 2015; Nagayama et al.2019). We shall investigate Fe as well as two other Fe-peak elements Cr and Ni.

For kilonova modelling, we shall also consider the photoionisation of a range of elements Z>70 and the associated processes of dielectronic and radiative recombination. This project does have a large computational component and some of the calculations are only possible on supercomputer architectures.

Plan of work

(1) The project shall proceed as follows. There shall be a review of the underlying Dirac R-matrix approach to photoionisation and dielectronic recombination. The student will familiarize themselves with theory as implemented within a large suite of parallel codes.

(2) The student will be responsible for carrying out the majority of the Ni and Cr photoionisation calculations and dielectronic recombination calculations.

(3) In terms of kilonova modelling, new observations may require us to quickly pivot to model  new species as they are observed.


It would be beneficial if the prospective student has had an entry-level quantum mechanical course.

There is the intent that the student would develop , with guidance,  their own photoionisation models. Therefore, some basic understanding of numerical methods with either Matlab, C++ , Fortran or their more modern equivalents would be desirable. However, more important is an interest in the topic as these skill-sets can be acquired during the project.

Aims and objectives of the project

(1)To provide the student with a ability to update the data underpinning stellar opacities. To take first principle atomic structure calculations through to photoionisation and recombination collisional models and finally through to their implementation within an opacity code. To present results at workshops or a conference environment.

(2) There is a strong computational aspect, therefore an interest in computational modelling, and in particular utilizing powerful parallel supercomputers is required.

(3) The PhD. student shall have to respond to observational requests for data at quite short time-frames,  depending on whether new kilonova observations are  forthcoming.

(4) To acquire good programming and numerical skills valuable for graduate level work, which are also marketable skills within the workplace.

For further information, contact


(1) Bailey J. E. et al., 2015, Nature, 517, 56

(2) Nagayama T. et al., 2019, Phys. Rev. Lett., 122, 235001