Tuesday, 8 June 2021

Papers 064304 and 064305

By something of a coincidence, I have two papers appearing consecutively in Physical Review C this month.  An unplanned coincidence because one was submitted in April, accepted in May and published in June, while the other was submitted in January, accepted in April, and published in June.  

The older (published last Friday) paper also has a longer history:  It is work done by my PhD student Matthew Barton.  Matthew finished his PhD in 2018 and this paper was part of it.  His thesis was on the use of the time-dependent density matrix (TDDM) method to look at beyond mean-field aspects of nuclear dynamics with a goal (initially) of understanding fission processes.  Previous implementations of the (rather computationally intensive) TDDM method involved a few approximations which we thought we could overcome.  Although we did sort-of overcome them, we only did partially, in the sense that the result was too time-consuming to apply to fission.  One of the approximations we got rid of was to not assume that an uncorrelated ground state was good enough to start studies of collective motion from.  It seemed sensible, especially with fission as a goal, to start from as close to the right state as possible. 

This means running the time-dependent calculation in such a way as to turn on part of the interaction at the beginning of the simulation time so that the generation of the starting point ground state for the 'real' calculation occurs as the nuclear interaction is turned on.  It uses the Gell-Mann Low theorem to build up the ground state correlations.  In the end just this part of the calculation was quite a heroic effort and had not been done before in the same level of consistency we had done it.  Even though it was a sub-project of Matthew's thesis, we thought it worth publishing, and eventually got round to writing it up in time for a submission at the beginning of this year.

The paper is published as Matthew Barton, Paul Stevenson, and Arnau Rios, Phys. Rev. C 103, 064304 (2021) doi: 10.1103/PhysRevC.103.064304

Here's a figure from the paper showing the Gell-Mann Low theorem in action, turning on the correlation part of the formalism to build up a more complicated wave function and finding a lower energy state than the inial configuration which was itself a variational minimum within the space of uncorrelated wave functions

The newer paper's history (or at least my involvement with it) dates back to October last year when my colleague at Surrey, (Emeritus) Prof Phil Walker got in touch to ask me a question about state mixing and how it might change the wave functions of K-isomers.  State mixing is a bit like the correlations of the TDDM paper above, in the sense that we are trying to 'mix' or 'correlate' some functions that we have calcualted based on a model to make them more like nature has them.  Nature has already done the mixing or correlation.  As a statement, I cringe slightly when I write things like that, as if there is something somehow natural that they should be thought of as uncorrelated and nature then mixes them.  It's a language we use in nuclear physics, and in physics in general, that implies an event - states are mixed, symmetry is broken etc, when the action of mixing or breaking is only done in our theories so that we better reproduce what nature is.  Anyway - there is some logic to thinking this way, because sometimes natures produces unmixed states or unbroken symmetries and we can use those as a way to understand the more complicated cases. 

In the case of this paper we have some excited state of nuclei which either look like quite pure simple wave function which can be written down as 'unmixed' configuration, but that get mixed with other ones if there is a chance near-degeneracy between states with the same quantum numbers.  Then the wave functions of each state gets mixed together.   The effects of two state mixing is widely understood (by afficionados) to mix together the values of angular momentum projection (known as K in the context of nuclear isomers), changing the decay rates of the states compared to if there were no mixing.  Phil had come to me to see if I could help him understand whether a three-way mixing might be causing what appeared to be quite an anomalous decay rate for a particular isomeric state in Ta-179.  I helped by doing the three-state mixing calculation, but Phil did all the "understanding".  Anyway, his hunch was right, and the calcualtion should this really nicely. 

Here's a picture of the effect of the extra mixing caused by the third state:


The paper is P. M. Walker and P. D. Stevenson, Phys. Rev. C 103, 064305 (2021) doi: 10.1103/PhysRevC.103.064305

I owe my current position to Phil Walker, by the way, as it was he who first employed me as a post-doc at Surrey.  Thanks Phil!  Glad to still be collaborating with you.