Halo Nuclei

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Halo Nuclei
Helmholtz International Summer School "Nuclear
Theory and Astrophysical Application"
S. N. Ershov
Joint Institute for Nuclear Research
new structural dripline phenomenon with
clusterization into an ordinary core nucleus
and a veil of halo nucleons forming very
dilute neutron matter
HALO
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Nuclear scale 10-22 sec
Width 1 ev 10-16 sec
Life time for radioactive nuclei gt 10-12
sec
b decays define the life time of the most
radioactive nuclei
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Neutron halo nuclei
weakly bound systems with large extension and
space granularity
Halo
( 6He, 11Li, 11Be, 14Be, 17B, )
none of the constituent two-body subsystems are
bound
Borromean system is bound
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Peculiarities of halo nuclei the example of 11Li
(i) weakly bound the two-neutron separation
energy (300 KeV) is about 10
times less than the energy of the first excited
state in 9Li .
(ii) large size interaction cross section of
11Li is about 30 larger than for 9Li
This is very unusual for strongly interacting
systems held together by short-range
interactions
Interaction radii
E / A 790 MeV, light targets
I. Tanihata et al., Phys. Rev. Lett., 55 (1985)
2676
(iii) very narrow momentum distributions,
compared to stable nuclei, of both neutrons and
9Li
measured in high energy
fragmentation reactions of 11Li .
No narrow fragment distributions in breakup on
other fragments, say 8Li or 8He
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(iv) Relations between interaction and neutron
removal cross sections ( mb ) at 790 MeV/A
sI (ACxn) sI (C) s-xn
Strong evidence for the well defined clusterizatio
n into the core and two neutrons
Tanihata I. et al. PRL, 55 (1987) 2670 PL,
B289 (1992) 263
(v) Electromagnetic dissociation cross
sections per unit charge are orders of
magnitude
larger
than for stable nuclei
halo
stable
T. Kobayashi, Proc. 1st Int. Conf. On Radiactive
Nuclear Beams, 1990.
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Soft Excitation Modes
(peculiarities of low energy halo continuum)
specific nuclear property of extremely
neutron-rich nuclei
Large EMD cross sections
M. Zinser et al., Nucl. Phys. A619 (1997) 151
excitations of soft modes with different
multipolarity collective excitations
versus direct transition from weakly bound to
continuum states
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(vi) Ground state properties of 11Li and 9Li
Schmidt limit 3.71 n.m.
Previous peculiarities cannot arise from large
deformations core is not significantly perturbed
by the two valence neutrons
Nuclear charge radii by laser spectroccopy
R. Sanches et al., PRL 96 (2006) 033002 L.B. Wang
et al., PRL 93 (2004) 142501
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(vii) The three-body system 11Li (9Li n
n) is Borromean neither the two
neutron nor the core-neutron subsytems
are bound
Three-body correlations are the most
important due to them the system becomes bound.
The Borromean rings, the heraldic symbol of the
Princes of Borromeo, are carved in the stone of
their castle in Lake Maggiore in northern Italy.
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Stable nuclei
Unstable nuclei
N / Z 0.6 - 4
N / Z 1 - 1.5
eS 0 - 40 MeV
eS 6 - 8 MeV
decoupling of proton and neutron
distributions
r0 0.16 fm -3
proton and neutrons homogeneously mixed, no
decoupling of proton and neutron distributions
neutron halos and neutron skins
Prerequisite of the halo formation
low angular momentum motion for halo
particles and few-body dynamics
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Peculiarities of halo
elastic scattering some inclusive
observables (reaction cross sections, )
nuclear reactions (transition properties)
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The T-set of Jacobin coordinates (
)
The hyperspherical coordnates r,
T - basis
r is the rotation, translation and permutation
invariant variable
Y - basis
Volume element in the 6-dimensional space
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The kinetic energy operator T has the separable
form
is a square of the 6-dimensional hyperorbital
momentum
Eigenfunctions of are the homogeneous
harmonic polynomials
are hyperspherical harmonics or K-harmonics.
They give a complete set of orthogonal functions
in
the 6-dimensional space on unit hypersphere
are the Jacobi polynomials,
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(positive), if K even - (negative), if K
- odd
The parity of HH depends only on
The three equivalent sets of Jacobi coordinates
are connected by transformation (kinematic
rotation)
Quantum numbers K, L, M dont change under a
kinematic rotation. HH are transformed in a
simple way and the parity is also conserved.
Reynal-Revai coefficients
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The three-body bound-state and continuum wave
functions (within cluster representation)
The Schrodinger 3-body equation
where the kinetic energy operator
and the interaction
The bound state wave function (E lt 0 )
- spin function of two nucleons
The continuum wave function (E gt 0 )
is the hypermomentum conjugated to r
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The HH expansion of the 6-dimensional plane wave
Normalization condition for bound state wave
function
Normalization condition for continuum wave
function
After projecting onto the hyperangular part of
the wave function the Schrodinger equation is
reduced to a set of coupled equations
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a general behaviour of three-body effective
potential if the two-body potentials are
short-range potentials
if E lt 0
if E gt 0
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Correlation density for the ground state of 6He
cigar-like configuration dineutron
configuration
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Three-body halo fragmentation reactions
Cross section
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Reaction amplitude Tfi (prior representation)
a
1
halo ground state wave function target ground
state wave function distorted wave for relative
projectile-target motion exact scattering wave
function NN - interaction between projectile
and target nucleons optical potential in initial
channel
ky
kx
2
C
kf
A

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Reaction amplitude Tfi (prior representation)

• Kinematically complete experiments
• sensitivity to 3-body correlations (halo)
• selection of halo excitation energy
• variety of observables
• elastic inelastic breakup

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Model assumptions
Transition densities
effective interactions ( NN N-core )
Method of hyperspherical harmonics 3-body
bound and continuum states
binding energy electromagnetic moments electromagn
etic formfactors geometrical properties density
distributions . . . . . . .
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Model assumptions
One-step process
no consistency with nuclear structure
interactions
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Halo scattering on nuclei
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Continuum Spectroscopy
Y-system
T-system
Excitation Energy
Orbital angular momenta
Spin of the fragments
Hypermoment
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ABC of the three-body correlations
Permutation of identical particles must not
produce an effect on observables. Manifestation
depends on the coordinate system where
correlations are defined.
Neutron permutation changes
1. Angular correlation is symmetric relative
2. Energy correlation ? no effect
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ABC of the three-body correlations
Energy correlations of elementary modes 2
excitations with the hypermoment K 2
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Realistic calculations mixing of configurations
T system
n
n
x
For low-lying states only a few elementary
modes
Y system
Energy correlations for 2 resonance in 6He
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Energy and angular fragment correlations
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assume 4? -measurements of fragments
T. Aumann, Eur. Phys. J. A 26 (2005) 441
"The angular range for fragments and neutrons
covered by the detectors corresponds to a 4?
measurement of the breakup in the rest frame of
the projectile for fragment neutron relative
energies up to 5.5 MeV (at 500 MeV/nucleon beam
energy)".
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CONCLUSIONS

• The remarkable discovery of new type of nuclear
  structure at driplines, HALO, have been made with
  radioactive nuclear beams.
• The theoretical description of dripline nuclei is
  an exciting challenge. The coupling between bound
  states and the continuum asks for a strong
  interplay between various aspects of nuclear
  structure and reaction theory.
• Development of new experimental techniques for
  production and /or detection of radioactive beams
  is the way to unexplored

TERRA INCOGNITA
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Special thanks to B.V. Danilin J.S. Vaagen