PowerPointPrsentation

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Dinuclear system model in
nuclear structure and reactions
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The two lectures are divided up into
I. Dinuclear effects in nuclear spectra and
fission II. Fusion and quasifission with the
dinuclear system model
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First lecture
I. Dinuclear effects in nuclear spectra and
fission
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Contents
1. Introduction 2. The dinuclear system model 3.
Alternating parity bands 4. Normal- and
superdeformed bands 5. Hyperdeformation in heavy
ion collisions 6. Rotational structure of 238U 7.
Binary and ternary fission 8. Summary
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Work of G. G. Adamian, N. V. Antonenko,
R. V. Jolos, Yu. V. Palchikov,
T. M. Shneidman Joint Institute for Nuclear
Research, Dubna Collaboration with N.
Minkov Institute for Nuclear Research and Energy,
Sofia
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1. Introduction

• A dinuclear system or nuclear molecule is a
  cluster configuration of two (or more) nuclei
  which touch each other and keep their
  individuality, e.g. 8Be a a.
• First evidence for nuclear molecules in
  scattering of 12C on 12C and 16O on 16O by
  Bromley, Kuehner and Almqvist (Phys. Rev. Lett.
  4 (1960) 365) importance for element synthesis
  in astrophysics.
• Dinuclear system concept was introduced by V. V.
  Volkov (Dubna).

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The dinuclear system has two main degrees of
freedom

• Relative motion of nuclei formation
  of dinuclear system in heavy ion collisions,
  molecular resonances,
  decay of dinuclear
  system fission, quasifission, emission of
  clusters
  
  
  
• Transfer of nucleons between nuclei change
  of mass and charge asymmetries between the
  clusters

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Mass asymmetry coordinate
A2
A1
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Applications of dinuclear system model

• Nuclear structure phenomena normal-, super- and
  hyperdeformed bands, alternating parity bands
• Fusion to superheavy nuclei, incomplete fusion
• Quasifission, no compound nucleus is formed
• Fission

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Aim of lecture Consideration of nuclear
structure effects and fission due to the dynamics
in the relative motion, mass and charge transfer
and rotation of deformed clusters in a
dinuclear configuration
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2. The dinuclear system model

• The degrees of freedom of this model are
• internuclear motion ( R )
• mass asymmetry motion ( h )
• deformations (vibrations) of clusters
• rotation (rotation-oscillations) of clusters
• single-particle motion

Let us first consider some selected aspects of
the dinuclear system model.
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2.1 Deformation
Dinuclear configuration describes quadrupole- and
octupole-like deformations and extreme
deformations as super- and hyperdeformations. Mult
ipole moments of dinuclear system
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Comparison with deformation of axially deformed
nucleus described by shape parameters
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152Dy
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• Dinuclear system model is used in various ranges
  of h
• h0 - 0.3 large quadrupole deformation,
  hyperdeformed states
• h0.6 - 0.8 quadrupole and octupole
  deformations are similar, superdeformed states
• h1 linear increase of deformations, parity
  splitting

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2.2 Potential and moments of inertia
Clusterisation is most stable in minima of
potential U as a function of ?. Minima by
shell effects, e.g. magic clusters. Potential
energy of dinuclear system B1, B2, B0 are
negative binding energies of the clusters and the
united (?1) nucleus. V(R,?,I) is the
nucleus-nucleus potential. Example 152Dy
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152Dy
50Ti102Ru
26Mg126Xe
?
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Moment of inertia of DNS
moments of inertia of DNS clusters
For small angular momenta
For large angular momenta and large deformations
Exp. Moments of inertia of superdeformed states
are about 85 of rigid body limit.
Example 152Dy
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? 0.34 50Ti102Ru, Hyperdeformed properties
U20 MeV
above g.s., about estimated energy of L0
HD-state of 152Dy, ?(calc)131 MeV-1,
?(est)130 MeV-1, ?2(calc)1.3, ?2(est)?0.9.

? 0.66 26Mg126Xe, Superdeformed properties
?(calc)104 MeV-1, ?(exp)853 MeV-1,
Q2(calc)24 eb (?20.9), Q2(exp) 183 eb
Similar ? 0.71 22Ne130Ba 26Mg126Xe and
22Ne130Ba have SD properties.
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2.4 Mass asymmetry motion
For nuclear structure studies we assume h as a
continuous coordinate and solve a Schrödinger
equation in mass asymmetry.
Wave function yI(h) contains different cluster
configurations. At higher excitation energies
statistical treatment of mass transfer.
Diffusion in h is calculated with
Fokker-Planck or master equations.
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3. Alternating parity bands
Ra, Th and U have positive and negative parity
states which do not form an undisturbed
rotational band. Negative parity states are
shifted up. This is named parity splitting.
5-
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3-
4
1-
2
0
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Parity splitting is explained by
reflection-asymmetric shapes and is describable
with octupole deformations. Here we show that it
can be described by an asymmetric mass
clusterization. Configuration with
alpha-clustering can have the largest binding
energy. AZ (A-4)(Z-2) a -
particle
a
a
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Ba
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_
splitting
oscillations in h
Lower state has positive parity, higher state
negative parity. Energy difference depending on
nuclear spin is parity splitting.
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potential
wavefunctions
Positive parity
Negative parity
x
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238U
236U
234U
232U
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-
223Ra
-
-
-

-

-



3/2
(I,K-) (I,K)
3/2
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225Ra
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4. Normal- and superdeformed iiiiibands
Here application of dinuclear model to structure
of 60Zn, 194Hg and 194Pb a) Cluster structure of
60Zn 1. 60Zn 56Nia, tresh. 2.7 MeV above
g.s. Assumption g.s. band contains a-component.
2. 60Zn 52Fe8Be, tresh. 10.8 MeV above g.s.


/
48Cr12C, tresh. 11.2 MeV above g.s. Extrapolated
head of superdef. band 7.5 MeV Assumption
superdeformed band contains 8Be-component.
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Unified description of g.s. and sd bands by
dynamics in mass asymmetry coordinate. b)
Potential U(h , I) for 60Zn
mono-nucleus (h1,-1) U(I0) 0 MeV
56Nia
- 4.5 MeV 52Fe8Be
5.1 MeV 48Cr12C
9.0 MeV Stepwise potential
because of large scale in h. Barrier width is
fixed by 3- state (3.504 MeV).
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60Zn I0
xh-1 for hgt0 x h1 for hlt0

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60Zn
8Be
I0
a
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I8
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c) Spectra and E2(DI2)-transitions
Experimentally observed lowest level
of sd band 8 I(12sd 10gs)/I(12sd
10sd) 0.42 calc.
aa
0.54 exp. I(10sd 8gs)/I(10sd 8sd)
0.63 calc. aa
0.60
exp.
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60Zn
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60Zn
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5. Hyperdeformed states in heavy ion collisions
Dinuclear states can be excited in heavy ion
collisions. The question arises whether these
states are hyperdeformed states. Shell model
calculations of Cwiok et al. show that
hyperdeformed states correspond to touching
nuclei. Possibility to form hyperdeformed states
in heavy ion collisions.
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Hyperdeformed states can be quasibound states of
the dinuclear system.
V(R)
quasibound states
R
Rm
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Investigation of the systems
One to three quasibound states with
Energy values at L0, quadrupole moments and
moments of inertia of quasibound configurations
are close to those estimated for hyperdeformed
states.
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80
L0
80
L0
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Optimum conditions
Decay of the dinuclear system by g-transitions to
lower L-values in coincidence with quasifission
of dinuclear system (lifetime against
quasifission 10-16 s). Estimated cross section
for formation of HD-system is about 1 mb. Heavy
ion experiments with coincidences of g-rays and
quasifission could verify the cluster
interpretation of HD-states.
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6. Rotational structure of 238U
Description of nuclear structure with dinuclear
model for large mass asymmetries Heavy cluster
with quadrupole deformation light spherical
cluster, e.g. a - particle
z1
z
A2
A1
R
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Coordinates
a) Polar angles from the space-fixed z-axis
defining the body-fixed symmetry
x axis of heavy cluster
x defining the direction of R
e is the angle between R and the body-fixed
symmetry axis of heavy cluster.
b) Mass asymmetry coordinate with positive x
values only
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space-fixed axis
z
sym. axis of heavy cluster
z1
q1 , ?1
e
q2 , ?2
z
mol. axis
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Hamiltonian
Moments of inertia
Potential
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If C0 is small approximately two x
independent rotators If C0 is
large restriction to small e, x
bending oscillations
Wave function
Heavy cluster is rotationally symmetric
J10,2,4... Parity of states (-1)J2 Example
238U
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238U
First excited state of mass asymmetry motion
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Bending oscillations of heavy nucleus around the
molecular(R) axis with small angle e
Moment of inertia of bending motion
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Approximate eigenenergies
Oscillator energy of bending mode
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K2
n1 bending mode
K1
238U ( 234Tha)
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7. Binary and ternary fission

• Binary fission
• The fissioning nucleus with A and Z is described
  at the scission point as a dinuclear system with
  two fission fragments in contact.

Characteristics of DNS
mass and charge numbers deform. parameters
(ratios of axes)
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b
U
b a/b
a
lt3MeV
scission point at
Rmin Rb R
potential energy
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Total kinetic energy (TKE)
excitation energy
SSn8 MeV is excitation energy in neutron
induced fission S0 in spontaneous
fission deformation energy Edef , difference to
ground state
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Relative primary (before evaporation of neutrons)
yields of fission fragments
with
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Examples Potential for neutron-induced fission
of 235U leading to 104Mo 132Sn and 104Zr
132Te Kinetic energy and mass distributions of
spontaneous fission of 258Fm and 258No
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104Mo 132Sn
104Zr 132Te bimodal fission
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258Fm
258No
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b) Ternary fission
Ternary system consists of two prolate
ellipsoidal fragments and a light charged
particle (LCP) in between. LCP has one or several
alpha-particles and neutrons from one or both
binary fragments. Ternary system can not directly
formed from the compound nucleus because of a
potential barrier between binary and ternary
fission valleys.
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• Calculation procedure
• Relative probabilities for the formation of
  different binary systems
• Relative probabilities of ternary system,
  normalized to unity for each binary system

Examples ternary fission of 252Cf, induced
ternary fission of 56Ni (32S 24Mg).
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252Cf
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56Ni
12C
8Be
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• 8. Summary
• The concept of the dinuclear system describes
  nuclear structure phenomena connected with
  cluster structures, the fusion of heavy nuclei to
  superheavy nuclei, the quasifission and fission.
• The dynamics of the dinuclear system has two
  main degrees of freedom the
  relative motion of the nuclei and the mass
  asymmetry degree of freedom.

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• Parity splitting is interpreted by oscillations
  with even and odd parities in a potential with
  minima at the a-cluster fragmentation.
• Normal- and superdeformed bands can be explained
  by the dynamics in the mass (or charge) asymmetry
  coordinate.
• Hyperdeformed states can be seen as quasibound,
  molecular states in the internuclear potential.

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• Mass asymmetry motion and bending oscillations of
  the heavy cluster in very mass asymmetric
  dinuclear systems are used to interpret the
  structure of 238U.
• Relative probabilities for binary and ternary
  fission can be statistically calculated with the
  potential depending on mass asymmetry and
  deformation.
• Further studies on mass asymmetry motion and
  rotation in the dinuclear system model are
  necessary.

D.G.