**INT DFT Workshop Home Page**

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The workshop
Towards a Universal Density Functional for the Nucleus,
took place at the Institute for Nuclear Theory in
Seattle on September 26-30, 2005, during the first week of
the fall INT program
Nuclear Structure Near the Limits of
Stability (INT-05-3).
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Below you may find:
List of Participants,
List of Talks,
Workshop Schedule, and
Homework Problems.
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This workshop brought together experts working on
different aspects of density functional theory, which are
important in developing a universal density functional for
nuclei. The main topics of the meeting included:
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- systematic improvements of density functionals (gradient terms, many-body contributions,... )
- matching to microscopic nuclear forces, chiral contributions
- pairing in density functional theory
- including correlations beyond mean-field
- reliable extrapolations to weakly-bound, n/p-rich nuclei
- constraints on density functionals from effective action theory
- understanding restoration of broken symmetries in density functional theory
- role of continuum in density functional theory for weakly-bound/open systems

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Our workshop was the third in a series of meetings, after
the 2004 workshop on
Relativistic Density Functional Theory for Nuclear Structure
at the INT and 2003 workshop on
Density Functional Theory in Nuclear Structure
at ECT*, Trento.
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Jacek, Achim, and Dario
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- Jacek Dobaczewski (Jacek.Dobaczewski@fuw.edu.pl)
- Achim Schwenk (schwenk@indiana.edu )
- Dario Vretenar (vretenar@phy.hr )

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- Naftali Auerbach
- Michael Bender
- Karim Bennaceur
- Jean-Francois Berger
- Anirban Bhattacharyya
- Scott Bogner
- Piotr Borycki
- Thomas Duguet
- Paolo Finelli
- Christian Fuchs
- Dick Furnstahl
- Charles Horowitz
- Dean Lee
- Horst Lenske
- Thomas Lesinski
- Masayuki Matsuo
- Witek Nazarewicz
- John Negele
- Nils Paar
- Thomas Papenbrock
- Michael Pearson
- Peter Ring
- Luis Robledo
- Tomas Rodriguez
- Vincent Rotival
- Brian Serot
- Amritanshu Shukla
- Janusz Skalski
- Mario Stoitsov
- Jianmin Tao
- Masayuki Yamagami

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- Naftali Auerbach:
*Nuclear Structure and Neutrino-Nucleus Interactions* - Michael Bender:
*Going beyond the mean-field: configuration mixing of symmetry-restored mean-field states* - Karim Bennaceur:
*Pairing schemes for HFB calculations: Results and discussions* - Jean-Francois Berger:
*The Gogny force: recent improvements; towards a new parameterization* - Anirban Bhattacharyya:
*Incorporating Spin-Orbit in Kohn-Sham DFT* - Scott Bogner:
*Simplifying the Nuclear Many-Body Problem with Low Momentum Interactions* - Thomas Duguet:
*Pairing schemes for HFB calculations of nuclei: Formal aspects* - Paolo Finelli:
*Relativistic nuclear energy density functional constrained by low-energy QCD* - Christian Fuchs:
*Isospin dependence of the mean field from relativistic Brueckner-Hartree-Fock* - Dick Furnstahl:
*Density Functional Theory from Effective Actions* - Charles Horowitz:
*Cluster formation in low density nuclear matter and the virial expansion: implications for density functionals* - Dean Lee:
*Lattice simulations of cold dilute neutron matter* - Horst Lenske:
*ab initio DFT for Nucleons and Hyperons* - Thomas Lesinski:
*Fitting the parameters of a Skyrme-type interaction using a microscopic effective interaction in the pairing channel* - Masayuki Matsuo:
*Small neutron Cooper pair at low density: BCS-BEC crossover and interactions* - Witek Nazarewicz:
*(i) Nuclear DFT and Maximum-Spin States, (ii) Microscopic Leptodermous Expansion* - John Negele:
*Density Functional Theory for Nuclei: Old Ideas and New Questions* - Nils Paar:
*Collective excitations in atomic nuclei based on density functionals and correlated nucleon-nucleon interactions* - Thomas Papenbrock:
*Density functional theory for fermions in the unitary regime* - Michael Pearson:
*HFB mass models* - Peter Ring:
*Covariant density functional theory for excited states in nuclei* - Luis Robledo:
*Beyond mean field calculation with the density dependent Gogny force* - Tomas Rodriguez:
*Correlations Beyond the Mean Field: Towards Variation After Projection Solutions* - Brian Serot:
*Electromagnetic Interactions in a Chiral Effective Lagrangian for Nuclei* - Janusz Skalski:
*Fusion (fission) barriers from self-consistent calculations as a DF test* - Mario Stoitsov:
*Density Functional Theory and Symmetry Restoration in Nuclei* - Jianmin Tao:
*Nonempirical Construction of a Meta-GGA Density Functional and Useful Extensions* - Masayuki Yamagami:
*Continuum effects for many-body correlations in nuclei close to the neutron drip line*

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Over the lunch at the Little Thai restaurant, and after having an
overdose of iced water, the organizers of the workshop joined forces with
Witek Nazarewicz to formulate three simple (to formulate) problems pertaining
to the subjects presented and discussed during the workshop.
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We challenge every participant, and also every living soul for that matter,
to answer one or all of the questions posed below. Answers are due before
or at the next DFT workshop, wherever and whenever it takes place. They will
be evaluated by the panel composed of us four, naturally. All evaluations
are final and not subject to appeal. The winner(s) will be awarded one
bottle of champaign per each problem solved; the quality of champaign will
be commensurate with the quality of provided solutions.
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*Problem No. 1*What is the ground state of infinite, spin-symmetric nuclear matter (protons and neutrons) at low densities, interacting with 2- and 3-body contacts? The scattering length in the 2-body T=1 channel is infinite. The strength of the 3-body contact must ensure saturation with increasing isoscalar density. The resulting density functional must be isospin invariant, and clusterisation must be considered. The parameter space of the system are: (i) the isoscalar and isovector average densities, (ii) the scattering length in the 2-body T=0 channel, and (iii) the strength of the 3-body contact (as long as it provides saturation).

*Problem No. 2*How can one replace in a nuclear density functional: (i) dependence on momentum by dependence on density, or (ii) dependence on density by dependence on momentum? The fact of life that nuclei are finite systems composed of protons and neutrons must not be ignored, forgotten, disregarded, neglected, or otherwise assumed irrelevant. The consequences of the proposed replacements must be considered in the context of (i) constructing functionals from first principles (e.g., how to replace the Fermi momentum for the density), (ii) conserving symmetries (e.g., how to construct an isospin-invariant density functional from microscopic results for asymmetric matter), and (iii) restoring broken symmetries.

*Problem No. 3*Can we formulate a DFT for symmetry-restored states? The aim is to obtain the laboratory ground-state energy for a system which breaks a symmetry in the intrinsic frame. Degeneracy of symmetry-breaking states with respect to shifts by symmetry operators must not be forgotten. A restriction of solution to gauge-symmetry breaking, related to particle-number mixing is acceptable. Solutions based on projection methods may be considered only if they avoid known drawbacks.

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PS. If you need to google these problems use adajawi.
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Last modified: October 4, 2005