Measurement of GMR in unstable nuclei
and the determination of
nuclear matter incompressibility
E. Khan
K∞
J.Li et al, PRC78(2008)064303
E. Khan PRC80(2009)011307(R)
G. Colo et al, PRC70(2004)024307
Is the method
well defined ?
Z.Y. Ma et al, NPA686(2001)173
J.P. Blaizot, Phys. Rep.64(1980)171
Determination of K∞
Microscopic
(CHF)
Sn Pairing
Relativistic
data
Microscopic
(RPA)
Pairing effects on the incompressibility
Exp.
E. Khan, J. Margueron, G. Colo, K. Hagino, H. Sagawa, PRC82(2010)024322
Nuclear incompressibility vs. pairing
112-132Sn
isotopes,
SkM* , CHFB
• Cooper pairs favor compressibility
• Incompressibility of superfluid nuclear matter: K∞(Δ) ?
E. Khan, PRC80(2009)011307;057302
Density dependence of the incompressiblity
Saturation density: ρ0 = 0.16 fm-3
<ρ> = 0.12 ± 0.04 fm-3
The mean value of the density in a nuclei
is NOT the saturation density
• K(ρ) is probed when measuring
the GMR in a nucleus : not only K∞
• K(ρ): large variations around ρ0
Why K∞ ?
• Liquid drop expansion not valid (Blaizot) for incompressibilities
• EOS: K(ρ) more relevant than K∞
Give up K∞ as a specific experimental point (used in the design of the functionals)
Measure K(ρ): needs for GMR measurements on several nuclei
Measurement of the GMR in unstable nuclei
56Ni
@ 50 MeV/A (GANIL - SISSI)
5.104 pps
July 2005
68Ni
@ 50 MeV/A (GANIL - LISE)
105 pps
Sept 2010
Ionisation
Drift
chamber
chamber
Au foil
56Ni
Si wall
Moving flap
CsI wall
Diamond
(5.104 pps)
50 A.MeV
+ contaminants
Beam shield
MAYA
recoiling d kinematics
Results
56Ni
excitation
energy spectrum
GMR+GQR
C. Monrozeau et al., PRL100(2008)042501
Preliminary results on 68Ni
M. Vandebrouck, PhD
Solving puzzles ?
• GMR in nuclei (KA) are probing K(ρ) (variation of several ten’s of MeV)
• This may explains:
• Puzzle1: different K∞ values obtained within the same nuclei between R (260 MeV) and NR (230 MeV) models
K∞ is not the only part of the functional probed by the GMR measurement.
K at different ρ are also involved. A compensation between K∞ and different density dependencies
allows to reproduce the same data
R
Κ(ρ)
NR
ρSn ρPb ρ0
Κ(ρ)
• Puzzle2: different K∞ values obtained within the same model
between Pb and Sn nuclei
ρ
∂3E/∂ρ3 =?
Pb data
Sn data
Nuclei have different density fluctuations around ρ0 (skin, …).
Only a functional with the correct K(ρ) may allow to describe both data.
ρSn ρPb ρ0
ρ
Conclusions
• Role of density dependence and pairing in the determination of the incompressibility
• Interpretation: K(ρ) is probed when measuring the GMR in a nucleus : not only K∞
and Ksym (in progress)
• Need for several measurements (isotopic chain) : mapping of K(ρ,δ) through the
GMR using a microscopic method
Importance to follow up the Sn chain, especially until doubly magic 132Sn
GMR measurements on Pb isotopic chain (unstable nuclei)
Collaboration (Exp)
C.Monrozeau1, E.Khan1, Y. Blumenfeld1, C-E.Demonchy3,W. Mittig5, P.Roussel-Chomaz5
D.Beaumel1, M.Caamaño2,D.Cortina-Gil2,J.P. Ebran1, N.Frascaria1, U.Garg4, M.Gelin5,
A.Gillibert6, D.Gupta1, N. Keeley6, F.Maréchal7, A.Obertelli6, J-A.Scarpaci1
1 Institut
de Physique Nucléaire (IN2P3/CNRS), 91406 Orsay Cedex, France
2 Univ. Santiago de Compostela, E-15706 Santiago de Compostela, Spain
3 Univ. of Liverpool, Dep. of Physics, Olivier Lodge Lab., Liverpool L69 7ZE, U.K.
4 Univ. of Notre-Dame, Dep. of Physics, Notre Dame, IN 46556 USA
5 GANIL (DSM/CEA, IN2P3/CNRS), BP 5027, 14076 Caen Cedex 5, France
6 CEA/DSM/DAPNIA/SPhN, Saclay, 91191 Gif-sur-Yvette Cedex, France
7 Institut de Recherches Subatomiques (IN2P3/CNRS), BP 28, 67037 Strasbourg, France
Collaboration (Exp)