Dinuclear system model in nuclear structure and reactions. The two lectures are divided up into. I. Dinuclear effects in nuclear spectra and fission II. Fusion and quasifission with the dinuclear system model. First lecture.
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Dinuclear system model in nuclear structure and reactions
The two lectures are divided up into structure and reactions
I. Dinuclear effects in nuclear spectra and fission
II. Fusion and quasifission with the dinuclear system model
First lecture structure and reactions
I. Dinuclear effects in nuclear spectra and fission
Contents structure and reactions
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
Work of structure and reactions
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
1. structure and reactionsIntroduction
The dinuclear system has two main degrees of freedom: structure and reactions
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 nucleonsbetween nuclei: change of mass and charge asymmetries between the clusters
Applications of dinuclear system model structure and reactions
Aim of lecture: structure and reactions
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
2. structure and reactionsThe dinuclear system model
Let us first consider some selected aspects of the dinuclear system model.
2.1 structure and reactionsDeformation
Dinuclear configuration describes quadrupole and octupolelike deformations and extreme deformations as super and hyperdeformations.
Multipole moments of dinuclear system:
Comparison with deformation of axially deformed nucleus described by shape parameters:
152 described by shape parameters:Dy
2.2 described by shape parameters: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, B0are negative binding energies of the clusters and the united (=1) nucleus. V(R,,I) is the nucleusnucleus potential.
Example: 152Dy
Moment described by shape parameters: 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
described by shape parameters:= 0.34: 50Ti+102Ru,
Hyperdeformed properties: U=20 MeV above g.s., about estimated energy of L=0 HDstate of 152Dy, (calc)=131 MeV1, (est)=130 MeV1, 2(calc)=1.3, 2(est)0.9.
= 0.66:26Mg+126Xe,
Superdeformed properties:
(calc)=104 MeV1, (exp)=85±3 MeV1, Q2(calc)=24 eb (2=0.9), Q2(exp)= 18±3 eb
Similar: = 0.71:22Ne+130Ba
26Mg+126Xe and 22Ne+130Ba have SD properties.
2.4 described by shape parameters: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 hiscalculated with FokkerPlanck or master equations.
3. described by shape parameters: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
6+
3
4+
1
2+
0+
Parity splitting is explained by reflectionasymmetric shapes and is describable with octupole deformations.
Here we show that it can be described by an asymmetric mass clusterization.
Configuration with alphaclustering can have the largest binding energy.
AZ (A4)(Z2) + a  particle
a
a
Ba shapes and is describable with octupole deformations.
_ shapes and is describable with octupole deformations.
+
splitting
oscillations in h
Lower state has positive parity, higher state negative parity. Energy difference depending on nuclear spin is parity splitting.
potential shapes and is describable with octupole deformations.
wavefunctions
Positive parity
Negative parity
x
 shapes and is describable with octupole deformations.
223Ra



+

+

+
+
+
3/2
(I,K) (I,K+)
3/2
225 shapes and is describable with octupole deformations.Ra
4. shapes and is describable with octupole deformations.Normal and superdeformed iiiiibands
Here: application of dinuclear model to structure of 60Zn,194Hg and 194Pb
a) Cluster structure of 60Zn
1. 60Zn56Ni+a, tresh. 2.7 MeV above g.s. Assumption: g.s. band contains acomponent.
2. 60Zn52Fe+8Be, tresh. 10.8 MeV above g.s. / 48Cr+12C, tresh. 11.2 MeV above g.s.
Extrapolated head of superdef. band: 7.5 MeV
Assumption: superdeformed band contains 8Becomponent.
Unified description shapes and is describable with octupole deformations.of g.s. and sd bands by dynamics in mass asymmetry coordinate.
b) Potential U(h , I) for 60Zn
mononucleus (h=1,1) U(I=0) = 0 MeV 56Ni+a  4.5 MeV 52Fe+8Be 5.1 MeV 48Cr+12C 9.0 MeV
Stepwise potential because of large scale in h. Barrier width is fixed by 3 state (3.504 MeV).
I=8 shapes and is describable with octupole deformations.
c) Spectra and E2( shapes and is describable with octupole deformations.DI=2)transitions
Experimentally observed lowest level of sd band: 8+
I(12+sd 10+gs)/I(12+sd 10+sd) = 0.42 calc. aa = 0.54 exp.
I(10+sd 8+gs)/I(10+sd 8+sd) = 0.63 calc. aa = 0.60 exp.
60 shapes and is describable with octupole deformations.Zn
60 shapes and is describable with octupole deformations.Zn
5. shapes and is describable with octupole deformations.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.
Investigation of the systems: dinuclear system.
One to three quasibound states with
Energy values at L=0, quadrupole moments and moments of inertia of quasibound configurations are close to those estimated for hyperdeformed states.
Optimum dinuclear system.conditions:
Decay of the dinuclear system by gtransitions to lower Lvalues in coincidence with quasifission of dinuclear system (lifetime against quasifission 1016 s).
Estimated cross section for formation of HDsystem is about 1 mb.
Heavy ion experiments with coincidences of grays and quasifission could verify the cluster interpretation of HDstates.
6. dinuclear system.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‘
A1
A2
R
Coordinates: dinuclear system.
a) Polar angles from the spacefixed zaxis
: defining the bodyfixed symmetry x axis of heavy cluster x : defining the direction of R
eis the angle between R and the bodyfixed symmetry axis of heavy cluster.
b) Mass asymmetry coordinate with positive x values only:
If C dinuclear system.0is small: approximately two x independent rotators
If C0 is large: restriction to small e, x bending oscillations
Wave function:
Heavy cluster is rotationally symmetric: J1=0,2,4...
Parity of states: (1)J2
Example: 238U
238 dinuclear system.U
First excited state of mass asymmetry motion
Bending oscillations of heavy nucleus around the molecular( dinuclear system.R) axis with small angle e
Moment of inertia of bending motion
Approximate eigenenergies dinuclear system.
Oscillator energy of bending mode
7. dinuclear system.Binary and ternary fission
Characteristics of DNS:
mass and charge numbers:
deform. parameters: (ratios of axes)
Total kinetic energy (TKE): dinuclear system.
excitation energy:
S=Sn~8 MeV is excitation energy in neutron induced fission
S=0 in spontaneous fission
deformation energy Edef , difference to ground state
Relative primary (before evaporation of neutrons) yields of fission fragments:
with .
Examples:
Potential for neutroninduced fission of 235U leading to 104Mo + 132Sn and 104Zr + 132Te
Kinetic energy and mass distributions of spontaneous fission of 258Fm and 258No
258 fission fragments:Fm
258No
b) Ternary fission fission fragments:
Ternary system consists of two prolate ellipsoidal fragments and a light charged particle (LCP) in between.
LCP has one or several alphaparticles 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.
Examples:
ternary fission of 252Cf,
induced ternary fission of 56Ni (32S + 24Mg).
252 fission fragments:Cf
D.G.