1. Microscopic Model for Dilute Alpha-Gas State from a Theoretical Point of View
Akihiro Tohsaki
Suzuki Coop.
RCNP, Osaka University
International symposium on frontiers in nuclear physics
Novemver 1st-3rd

2. Collaborators Yasuro Funaki Riken Hisashi Horiuchi RCNP
Gerd Röpke U. Rostock
Peter Schuck　　　　　　Orsay
Taiichi Yamada Kantogakuin U.
Followed by my recent article: Frontiers of Physics 6 pp (2011)

3. Introduction and motivations
12 years from Rab island (Croatia) meeting: 1999
The starting year of study on the microscopic α-condensation
wave function.
11 years from my stumbling against such a complicated problem: 2000
10th anniversary of the first publication in PRL about this problem: 2011 　
A.Tohsaki, H.Horiuchi, P.Schuck and G.Röpke PRL 87, (2001).　　　　　　　　　　　
I should talk about the properties of the wave function via microscopic exchange kernels 　
I think that it is one of the best wave functions for describing the α-condensation.　　　　　　　　　　　　　
I think that there are many secrets in this wave function.
Therefore, it may be my duty to talk about how to manipulate this model.

5. Starting points of the model and its properties
Completeｌｙ microscopic：　
full considerations of the statistics of the nucleons.
the introduction of the effective inter-nucleon force.
the complete treatment of the Coulomb interaction
　　　　　→0　　　　h.o. shell model wave function
　　　　　→∞　　　free α-gas wave function
The number of the variational parameters is independent of that of α-particles but always 1.
All the α-particles belong to the same (0s)-orbit.
( deformation of the orbit is also available. By Funaki et al.)
The orbit is self-consistently determined by the competition between the nuclear attraction and the Coulomb repulsion.

6. wave function　

7. An example: 3α-particle system
Three α-particles belong to the same (0s)-orbit.
We employ my effective inter-nucleon force. Include 3body force with
Finite range terms: reproduce α-α elastic phase shift
Phys. Rev. C 49, 1814(1994)

12. Results of examples
Gas-like state for 2α-5α with F1 force

13. ２α

14. ３α

20. How to derive Norm kernel

21. How to manipulate the model? We employ only the following formula!
　　　　　　　　　　　　symmetric matrix：　determinant is real number
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　？　Also easy

27. Behavior of the norm kernel ？

32. Deformed condensation

36. The present status
The relative distances between α-clusters are implicit.
Only the orbit radius is a variational parameter
The ground and excited stated are described simultaneously.
Norm kernel is expressed by the superposition of connected springs.
One-body operator is an external force for one nucleons.
Two-body operator is an external force for two nucleons.