Marianne Dufour. Microscopic Cluster Models. Université de Strasbourg - IPHC. f S. f B. R. H Y = E Y = A f B f S g (r). Pierre Descouvemont. Université libre de Bruxelles. This seminar is devoted to:
Microscopic Cluster Models based on the combination of the Generator-Coordinate-Method and of the Microscopic R-matrix method.
They are very efficient tools to study the nuclear many-body problem.
Generator Coordinate and Microscopic R-Matrix Methods
Nowadays, it is commonly accepted that stellar energy is due to nuclear reactions occurring in the core (Eddington 1920) and that stellar nucleosynthesis can explain all the nuclei with A>=12 and one part with A<12.
At human scale, stellar temperatures are very high
At nuclear scale, a star is a very cold medium
Besides, deeper investigations of the stellar plasma show that:
Reactions can be studied in principle in accelerators on earth.
BUT, energies are (very) low …
Repulsive Coulomb interaction
Short range nuclear attractive interaction
Resonant/non resonant reaction
Charge induced nuclear reactions in the center of the stars can only proceed because the nuclei penetrate the repulsive Coulomb barrier that separates them. Since the stellar energies are significantly lower, the cross sections drop rapidly to very small values.
Needs for radioactive nuclei, very exotic nuclei, etc …
Theoretical investigations are necessary
The system of the two nuclei must be treated as a system of nucleons in interaction.
Reaction between Nucleons: 12N + 4N
16 Nucleons in interaction
The Pauli Principle must be exactly treated.
The system of A nucleons must be antisymmetrized.
In such a context, microscopic cluster models appear to be very efficient tools to handle the A nucleon problem.
D. Brink, Proc. Int. School, E. Fermi 36, Varenna, Academic Press NY 1966.
Lecture Notes In Physics 818, Clusters in Nuclei, Editor: C. Beck, Springer (Vol.1 (2010), Vol.2, Vol.3)
Microscopic Cluster Models – Basic idea
Cluster= Harmonic Oscillator Potential
8 Nucleons = a + a
Localizes the HO orbitals
Two cluster model
D. Brink, Proc. Int. School. E. Fermi 36, Varenna, Academic Press NY 1966
Here only s clusters
R = set of generator coordinates
P. Descouvemont, D. Baye, Rep. Prog., Phys. 73 (2010) 036301.
P. Descouvemont, M. Dufour, Microscopic Cluster Models, Lecture Notes
in Physics, Springer T2 (2011) (Ed. C. Beck).
Here, we consider a reaction between two nuclei (1) and (2) with respectively A1 and A2 nucleons.
Schematic representation of a Two-Cluster GCM-Basis State
All the quantum numbers are exactly treated
r = a = Channel Radius
To increase the number of cluster: multicluster model
(Technical difficulties also increased: Projections, implementation of the interactions, …)
Increase the number of major shells of the HO
Kalpachieva et al. 2000
Lecouey et al. 2009