A theory for all nuclei, ever?

NOTE: Apologies for the length of this blog, but the talk was quite an epic.

My hobby: going to physics talks by both members of a classic physics textbook authoring double act. It's my equvalent of autograph hunting. Today I complete the Ring and Schuck collection I started four years ago when I saw Peter Schuck talk at Orsay.

I've also completed the Hawking and Ellis set (Large Scale Structure of Space-Time). I think that might be it for two-authored texts. I must try and see Walter "must beat Landau" Greiner sometime, which automatically covers about 411 textbooks.

Anyone else seen any interesting textbook authors? Anyone else care?

15.03 So Peter Ring is talking on "Density Functional Theory in Nuclear Physics". And he's off.

15.04 Goal: a theory that covers the whole nuclide chart. Simples.

15.04 A lot of astrophysicists' needs are flashed up for about two seconds. I didn't catch any, but I can come up with a few...

15.04 Ab-initio scales: >1GeV QCD, 200MeV for nucloeon and pion Lagrangian, 100keV density dependent effective nuclear forces > DFT!

15.06 Ring has set off at a furious pace. The familiar phenomenology of the bare nucleon-nucleon interaction comes and goes like a Mercedes at Hockenheim.

15.07 Nuclei are very small apparently. Try telling that to a friend of mine who was mugged by one walking back from the pub one night.

15.08 He means relative to the scale of the uncertainty relation; in comparison, molecular physics has a similar potential, but it is able to sit in the bottom of the attractive well since that well sits at distances much larger than those at which uncertainty becomes a problem.

15.09 Crikey.

15.10 Hohenberg-Kohn theorem - the remarkable theorem that the exact energy of a quantum mechanical many body system is a universal function of the local density. From this we can embark on the project of constructing such a functional for nuclear physics.

15.13 For a many body system in an external field, local density is a functional of potential, and we Legendre transform to get potential as a functional of density. The Legendre transform is explained with reference to transforming between thermodynamic variables, the most familiar use of such transforms.

15.15 This is breathless stuff. Can he keep up the pace, or has he come out of the gates too quickly? Stay tuned....

15.16 Hohenberg-Kohn gave a proof for the existence of their universal functional, but didn't tell us how to calculate it. Spoilsports.

15.18 the HK functional can be decomposed into the direct interaction part (the Hartree term), the non-interacting part and the exchange term (Fock term).

15.19 Thomas-Fermi approx. is a local density approx. - take density to be locally constant, and the non-interacting term is analytical. Usually gradient terms in density are added to make it work better. Still, shell effects are not included.

15.21 Kohn-Sham theory: Kohn is not done yet; together with the unfortunately named Sham, he added an auxiliary potential, which, in the Schrodinger equation, would give the exact density (which includes shell effects). Crazy, but nice!

15.23 By the way, the equations on the slides are color-coded: potentials and densities in red, wavefunctions and kinetic energy densities in blue, the rest black.

15.25 I think of wavefunctions as having a melancholy shade of azure.

15.26 We arrive at a Hartree-Fock like scheme. Except it's exact not an approximation to the ground state. Actually the Fock term isn't explicit - it's somewhere hiding in the local approximation. It's shy.

15.27 Condensed matter physicists rejoice: for Coulomb forces one now has the exact functional.

15.28 I catch something about going to the supermarket to purchase functionals. I usually find them between the pet food and paper towels.

15.30 Amusingly, the paper towels in the convenience store opposite the hotel have the brand name "Snob".

15.31 DFT in nuclei: We have Skyrmes, Gogny and RMF. We have spin, isospin, relativistic and pairing degrees of freedom. AND we have to perform all calcuations while suspended upside down over a crocodile infested pool while half-starved lions are projected towards us by catapult.

15.34 The slide with the catapulting lions was quite amusing.

15.35 Virtues of DFTs: self-consistency - deformations, shells, whether valence or not, universality (applicability over the whole nuclear chart) and taste good with or without whipped cream.

15.36 He's talking about Skyrmes, something I'm actually very familiar with. Now he's finished and moved on to relativistic mean field theory. Oh well, easy come easy go.

15.37 RMF has many advatages, not least among them covariance, connection to underlying theories (chiral theories, for example), more apparently physical coupling constants, self-consistent inclusion of spin-orbit term and a rather nice line in jaunty hats.

15.41 I was working on the beach the other day and employed the no-sea approximation. I almost drowned.

15.42 For a small fee, I'm available for weddings and bar-mitzvahs.

15.43 Let's compare a point-coupling RMF model with ab-initio. Excellent agreement with Baldo's results. (Baldo is a nuclear theorist, not the nickname of a follically challenged physicist). But it is sometimes necessary to fit to microscopic results.

15.44 Now it's time for the "running out of time so lets show 279 graphs in 3 minutes" part of the talk.

15.45 It was only two minutes. Now we're on to time-dependence. The Runge-Gross theorem is the time-dependent version of Kohn-Sham. Or Hohnberg-Kohn. Or Even Hohnberg-Sham. I'm losing track. Some nice slides of giant resonances in tin, (My master's thesis was on giant resonances in Argon isotopes using time-dependent Hartree-Fock, so I'm wallowing in nostalgia right now).

15.50 Interesting results for spin-isopsin resonances and beta decay. I would say more, but next time I look up he's covering supernova neutrino flux. Aaaargh!

15.52 Conclsion: DFT is VERY successful, though we're far from a microscopic derivation. Uncertainties are, among other things, the isospin dependence of the parameters (e.g. large isospin asymmetries?) and tensor forces.

15.53 The isospin dependence is raised as a problem in rare isoptopes for n or p-rich nuclei.

15.56 Interestingly, Ring says he doesn't understand the spin-orbit emergence from the simple Walecka RMF model.

15.58 Deriving the mean-field parameters from microscopic, or at least some hybrid microscopic-nuclear matter model, is ongoing.

16.04 And we're done. Breathe.