exotic nuclei structure and reaction noyaux exotiques ... - IPN - IN2P3

Alpha particle condensation in nuclear systems
IPNO Participation: P. Schuck
Collaboration : RCNP,Osaka, Japan ; Universitaet Rostock; Germany; RIKEN, Tokyo; Japan ; Kanto
Gakuin University, Yokohama, Japan
Nous avons maintenant bien établi que le deuxième état 0+ dans le 12 C à 7.65 MeV est un état à trois particules
alpha qui sont en interaction faible. C'est donc un gaz à trois alpha ou en d'autres termes un
condensat de particules alpha. L'occupation de l'onde S est de 70% ce qui justifie bien le terme
'condensat'. Nous reproduisons le facteur de forme inélastique expérimental avec une très bonne précision
sans paramètre ajustable ce qui nous fait penser que notre description est bonne. Une fois accepté qu'un
tel état existe dans le 12 C il n'y a qu'un pas à supposer que de tels états existent aussi dans d'autres
noyaux n alpha plus lourds, comme 16 O, 20 Ne, etc. Dans 16 O, un calcul récent indique que l’état 0+ à 15.1
MeV est un condensat à quatre particules α.
It is well known that at least lighter nuclei show
under certain circumstances a pronounced cluster
structure. One of the most prominent clusters is
the alpha particle with its unusual high binding
energy per particle for such a light element. That
nuclei have such a rich cluster structures has to do
with the fact that there are four different fermions
with almost equal mutual attraction. In a mean field
picture two protons and two neutrons can be put
into the lowest S-state whereas in a hypothetical
tetra-neutron two out of the four neutrons have to
be put into the energetically very costly P-state.
Unfortunately most of other fermionic systems çhave
only at most two different species. It is evident
that clusters of more than two constituents are
theoretically very difficult to be described microscopically.
For example the second 0+ state in 12 C, the
famous 'Hoyle' state of astrophysics at 7.65 MeV,
is completely absent in a large scale shell model
calculation of the modern kind (it comes somewhere
around 21 MeV!!). On the other hand we describe
this state with a microscopic 12 nucleon wavefunction
of the alpha condensate type without adjustable
parameter with very good precision. This
wavefunction consists out of three center of mass
Gaussians with width parameter B and three intrinsic
alpha particle wavefunctions, also Gaussians
but with width parameter b. The whole wave function
is explicitly antisymmetrised among the protons
and neutrons. The two parameters B and b
are used as Generator Coordinates and with a suitable
Hamiltonian the corresponding Schroedinger
equation is solved.
Energy of the Hoyle state as well as transition probabilities
and form factors are in very good
agreement with the experimental data. We obtain a
volume of this state which is 3 or 4 times as large
as the corresponding ground state. The effective
bosonic occupation of the lowest S-state of the
alpha particles is obtained as 70% which indicates
that this state can be considered to very good approximation
as a weakly interacting condensate of
three alpha particles. Our calculation shows that
analogous states should exist also in heavier N
alpha nuclei like 16 O, 20 Ne, 24 Mg, etc with 4, 5, 6,...
condensed alphas. Recent extensive so-called
OCM-type calculation for the 0+ spectrum of 16 O
explains the whole spectrum of the 6 lowest states.
The 6-th state at 15.1 MeV is predicted to be of 4 α
condensate structure [1].
A dedicated experiment to detect α-particle
condensed states with Chimeria Catania by B. Borderie
and M.F. Rivet et al. is in final stage of analysis
with exciting results. Experiments have been
started to look for the 4 alpha condensate in 16 O.
We also have made calculations in infinite nuclear
matter which show that at low densities where the
alpha particles do not yet overlap, alpha particle
condensation is favored and that the critical temperature
is as high as 6 MeV [2]. During the collapse
of massive stars nuclear matter may go through
stages where it contains a lot of alpha particles.
Their possible condensation may influence pressure
and equation of state of the matter and thus the
collapse scenario. It is believed that the outer tail
of a neutron star contains a lot of alpha particles.
Also there the condensation phenomenon can occur.
References:
[1] Y. Funaki, T. Yamada, H. Horiuchi, G. Roepke,
P. Schuck, A. Tohsaki, Phys. Rev. Lett. 101(2008)
082502
[2] T.Sogo, R. Lazauskas,G.Roepke,P.Schuck,
Phys. Rev. C79 (2009) 051801
74