INT Workshop, University of Washington
Pairing degrees of freedom in nuclei and the nuclear medium
Nov. 14-17 2005
The purpose of this four-day workshop is to consolidate our knowledge of the pairing interaction and pairing effects in nuclei.
The themes of the four days are:

Monday, Nov. 14
The interaction.
--Effective interactions from two-particle potentials or T-matrices.
--Role of medium polarization
--Constraints from symmetries

Tuesday Nov. 15
Nuclear structure applications
--Computational methods.

--global surveys
--excitations

Wednesday Nov. 16
Astrophysical Context.
--Proton and neutron pairing.
--vortices
--Pasta phase of nuclear matter.
--Transport at positive neutron chemical potential.

Thursday Nov. 17
Summary and Discussion.
Near-term and far-term open problems, homework problems

George Bertsch and Aurel Bulgac
Tentative schedule, speakers and titles
Monday
 Tuesday
 Wednesday
 Thursday
  9:30 am - 10:15 am
 Chasman
10:15 am - 11:00 am
 Macchiavelli
11:00 am - 11:30 am
 break
11:30 am - 12:15 pm
 Furnstahl
 12:15 pm - 2:00 pm
 break
 2:00 pm - 2:45 pm
 Vigezzi
 2:45 pm - 3:30 pm
 Frauendorf
 3:30 pm - 4:00 pm
 break
 4:00 pm - 4:45 pm
 Zelevinsky

9:30 am - 10:15 am Afanasjev
10:15 am - 11:00 am Sagawa
11:00 am - 11:30 am break
11:30 am - 12:15 pm Tajima
12:15 pm - 2:00 pm break
 2:00 pm - 2:45 pm Duguet/Bender
2:45 pm - 3:30 pm Civitarese
 3:30 pm - 4:00 pm break
 4:00 pm - 4:45 pm Barranco

9:30 am - 10:15 am Schulze
10:15 am - 11:00 am Pizzochero
11:00 am - 11:30 am break
11:30 am - 12:15 pm Clark
12:15 pm - 2:00 pm break
 2:00 pm - 2:45 pm Lombardo
 2:45 pm - 3:30 pm Wyss
 3:30 pm - 4:00 pm break
 4:00 pm - 4:45 pm Ring

10:00 am - 11:00 am
 Brink
11:00 am -11:30 am
break
11:30 am - 12:15 pm
 Discussions
12:15 pm -  2:00 pm
 break
  2:00 pm - 4:00 pm
Discussions



Speakers and Titles
Anatoli  Afanasjev      
Cranking relativistic Hartree-Bogoliubov theory: pairing in rotating nuclei and the problem of proton-neutron pairing
Francisco Barranco
 Quantum calculation of vortices in the inner crust of neutron stars
Michael Bender
 Correcting for self-pairing and poles in particle-Number projected Hartree-Fock-Bogolyubov method. II Results
David Brink
  His thoughts about the nuclear pairing and the workshop
Osvaldo Civitarese
  QRPA and np-pairing
Richard Chasman Neutron-proton pairing in nuclei
John Clark Nucleonic pairing and phase transitions inside neutron stars
Thomas Duguet 
Correcting for self-pairing and poles in particle-number projected Hartree-Fock-Bogolyubov method. I Formal aspects
Stefan Frauendorf
 Isovector proton-neutron pairing
Dick Furnstahl DFT pairing from effective actions
Umberto Lombardo
 Screening of pairing in the nuclear and neutron matter
Augusto Macchiavelli   
The (3He,p) reaction to study T=0 and T=1 pairing in N=Z nuclei
Pierre Pizzochero
Glitches and vortex pinning in superfluid pulsars
Peter Ring Pairing in covariant density functional theory
Hiroyuki Sagawa    
Pairing correlations in nuclei on the neutron drip line
Hans-Josef Schultze   
Pairing gaps in neutron stars
Naoki Tajima
 Canonical basis HFB method - drip lines and beyond
Enrico Vigezzi
Medium polarization effects and pairing interaction in finite nuclei
Ramon Wyss
 Nuclear symmetry energy
Vladimir Zelevinsky Less known aspects of nuclear pairing


The transparencies for most of the talks are vailable online.


Homework problems


In the presentations and the discussions of the Fall INT program and workshops, the idea came up that it would be useful to have a simple model Hamiltonian that could be used as a testing ground for theories and calculational approximations. The two component trapped Fermi (TCFG) gas in the unitary limit seems ideal for this purpose. Not only is it well-defined and challenging, but it is very relevant to experimental atomic trap physics, besides been of interest as well to the case of low density neutron matter.  The Hamiltonian  includes, besides the kinetic energy for the two Fermion species, a contact interaction, with a strength chosen so as to reproduce a specified value of the scattering length. 


1)  Consider at the beginning two cases in a harmonic trap, N=8 and N=20. Calculate the ground state  energy in units of the trap frequency, the spectrum of the excited states, and the density distribution at the unitary point (where the scattering length is infinite) and in a region around the unitary point, when the scattering length is still much larger than the interparticle separation. Having exact  results for these systems one can then compare them with DFT results, assess the role of derivative corrections, and also assess the range of validity of other theoretical schemes.             
 
2)  A number of ground state and excited states properties of the homogeneous TCFG in the unitary regime have been established in rather accurate  fully non-perturbative calculations (Green Function Monte Carlo, Diffusion Monte Carlo,  Auxiliary Field Monte Carlo calculations, respectively). One should test various approximate theoretical methods used so far to compute in particular pairing properties of neutron matter against  these accurate numerical results.
           
                       GFB and AB