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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

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

slide2

Light self-conjugated nuclei

Structure

(Two possibilities)

α

α

α

α

α

nucleons

α

α

α

α

slide3

8

Be

D

Θ= const.

ρ

ρ

ρ

p

tot

n

P. Arumugan, et al.

Phys. Rev. C71

064308 (2005)

slide4

<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

slide5

E

Bind

MeV

20

15

10

5

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

2

4

6

8

N

Bonds

slide8

Energy levels of an harmonic-oscillator potential

for prolate deformation

P. Ring, P. Schuk

“The nuclear many-body problem”

slide9

Chain configurations in light nuclei

2

Efr – fragmentation energy

Eb – binding energy of the configuration

slide10

The breaking up of bonds

1 Bond ~ 3 MeV

3 Bonds ~ 9 MeV

+

< 4 Bonds + 5 Bonds > ~ 13.5 MeV

slide14

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
slide15

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

slide16

Cluster density distribution

12

C

Nucleons

Phase transition

(ρ ~ 1/3ρ0)

BEC

slide17

The solution of the Schrödinger equation with

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

EBEC=ESch (Nα-1)

slide20

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.