New insight on the chain states and bose einstein condensate in the light nuclei
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NEW INSIGHT ON THE CHAIN STATES AND BOSE-EINSTEIN CONDENSATE IN THE LIGHT NUCLEI. K.A. Gridnev, S. Yu. Torilov, W. Greiner. Saint-Petersburg State University. Light self-conjugated nuclei. Structure (Two possibilities). α. α. α. α. α. nucleons. α. α. α. α. 8. Be. D.

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NEW INSIGHT ON THE CHAIN STATES AND BOSE-EINSTEIN CONDENSATE IN THE LIGHT NUCLEI

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New insight on the chain states and bose einstein condensate in the light nuclei

NEW INSIGHT ON THE CHAIN STATES AND BOSE-EINSTEIN CONDENSATE IN THE LIGHT NUCLEI

K.A. Gridnev, S. Yu. Torilov, W. Greiner

Saint-Petersburg State University


New insight on the chain states and bose einstein condensate in the light nuclei

Light self-conjugated nuclei

Structure

(Two possibilities)

α

α

α

α

α

nucleons

α

α

α

α


New insight on the chain states and bose einstein condensate in the light nuclei

8

Be

D

Θ= const.

ρ

ρ

ρ

p

tot

n

P. Arumugan, et al.

Phys. Rev. C71

064308 (2005)


New insight on the chain states and bose einstein condensate in the light nuclei

<T> ~ number of kinds of Jacobi coordinates

<V> ~ number of bonds

Binding energy ~ <T> + <V>

(H. Horiuchi, K. Ikeda, Cluster model of the nuclei)

Binding energy

Binding energy


New insight on the chain states and bose einstein condensate in the light nuclei

E

Bind

MeV

20

15

10

5

L.R. Hafstad, E. Teller, Phys. Rev. 54 (1938) 681

2

4

6

8

N

Bonds


New insight on the chain states and bose einstein condensate in the light nuclei

Spin-isospin alpha-like combinations of nucleons in nuclei

D

Alpha-particle


New insight on the chain states and bose einstein condensate in the light nuclei

Energy levels of an harmonic-oscillator potential

for prolate deformation

P. Ring, P. Schuk

“The nuclear many-body problem”


New insight on the chain states and bose einstein condensate in the light nuclei

Chain configurations in light nuclei

2

Efr – fragmentation energy

Eb – binding energy of the configuration


New insight on the chain states and bose einstein condensate in the light nuclei

The breaking up of bonds

1 Bond ~ 3 MeV

3 Bonds ~ 9 MeV

+

< 4 Bonds + 5 Bonds > ~ 13.5 MeV


New insight on the chain states and bose einstein condensate in the light nuclei

Shell-model calculations with Strutinsky corrections


New insight on the chain states and bose einstein condensate in the light nuclei

Classification of the alpha-particle states in 20Ne


New insight on the chain states and bose einstein condensate in the light nuclei

Radial density distribution of 8Be

ρ [fm-3]

R


New insight on the chain states and bose einstein condensate in the light nuclei

Bose-Einstein Condensation description

A)

Nonlinear Schrödinger equation – Gross-Pitaevskii equation

(K. A. Gridnev et al., Cond . Matter. Theor. 15, Nova Science, Ney-York, 2000)

B)

Linear Schrödinger equation

(S. Mishra, P. Pfeifer, J. Phys. A40 (2007) F243)

  • Conditions for BEC

  • No nodes

  • The same value of momentum for every α’s

  • λα~ D

  • ρnucl ~ ⅓ρ0


New insight on the chain states and bose einstein condensate in the light nuclei

Folding potential

“Nucleons-clusters” phase transition

(Brink )

Alpha-particles density distribution

(Hofstadter)

Alpha-alpha interaction

(Yamada, Schuck

Phys. Rev. C69 (2004) 024309 )

One-particle energy


New insight on the chain states and bose einstein condensate in the light nuclei

Cluster density distribution

12

C

Nucleons

Phase transition

(ρ ~ 1/3ρ0)

BEC


New insight on the chain states and bose einstein condensate in the light nuclei

The solution of the Schrödinger equation with

a folding potential for 12C,16O and 20Ne

EBEC=ESch (Nα-1)


New insight on the chain states and bose einstein condensate in the light nuclei

Results


New insight on the chain states and bose einstein condensate in the light nuclei

Conclusion

Though we do not think that the model here presented is good enough to give a detailed account of experimental facts, we believe that it is not worse than the Hartree model.

L.R. Hafstad, E. Teller, Phys. Rev. v54 (1938) 681

BEC is a new state of the nuclear matter. It manifests itself

for high excitations and small values of the alpha’s momentum in

the momentum space.


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