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Dinuclear system model in nuclear structure and reactions

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

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  1. Dinuclear system model in nuclear structure and reactions

  2. The two lectures are divided up into I. Dinuclear effects in nuclear spectra and fission II. Fusion and quasifission with the dinuclear system model

  3. First lecture I. Dinuclear effects in nuclear spectra and fission

  4. 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

  5. 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

  6. 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).

  7. 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 nucleonsbetween nuclei: change of mass and charge asymmetries between the clusters

  8. Mass asymmetry coordinate A2 A1

  9. 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

  10. 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

  11. 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.

  12. 2.1 Deformation Dinuclear configuration describes quadrupole- and octupole-like deformations and extreme deformations as super- and hyperdeformations. Multipole moments of dinuclear system:

  13. Comparison with deformation of axially deformed nucleus described by shape parameters:

  14. 152Dy

  15. Dinuclear system model is used in various ranges of h: • h=0 - 0.3: large quadrupole deformation, hyperdeformed states • h=0.6 - 0.8: quadrupole and octupole deformations are similar, superdeformed states • h~1: linear increase of deformations, parity splitting

  16. 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, B0are negative binding energies of the clusters and the united (||=1) nucleus. V(R,,I) is the nucleus-nucleus potential. Example: 152Dy

  17. 152Dy 50Ti+102Ru 26Mg+126Xe 

  18. 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

  19.  = 0.34: 50Ti+102Ru, Hyperdeformed properties: U=20 MeV above g.s., about estimated energy of L=0 HD-state of 152Dy, (calc)=131 MeV-1, (est)=130 MeV-1, 2(calc)=1.3, 2(est)0.9.  = 0.66:26Mg+126Xe, Superdeformed properties: (calc)=104 MeV-1, (exp)=85±3 MeV-1, 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.

  20. 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 hiscalculated with Fokker-Planck or master equations.

  21. 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- 6+ 3- 4+ 1- 2+ 0+

  22. 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

  23. Ba

  24. _ + splitting oscillations in h Lower state has positive parity, higher state negative parity. Energy difference depending on nuclear spin is parity splitting.

  25. potential wavefunctions Positive parity Negative parity x

  26. 238U 236U 234U 232U

  27. - 223Ra - - - + - + - + + + 3/2 (I,K-) (I,K+) 3/2

  28. 225Ra

  29. 4. 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 a-component. 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 8Be-component.

  30. Unified description of g.s. and sd bands by dynamics in mass asymmetry coordinate. b) Potential U(h , I) for 60Zn mono-nucleus (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).

  31. 60Zn I=0 x=h-1 for h>0 x= h+1 for h<0

  32. 60Zn 8Be I=0 a

  33. I=8

  34. c) Spectra and E2(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.

  35. 60Zn

  36. 60Zn

  37. 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.

  38. Hyperdeformed states can be quasibound states of the dinuclear system. V(R) quasibound states Rm R

  39. Investigation of the systems: 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.

  40. 80 L=0 80 L=0

  41. Optimumconditions: 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.

  42. 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‘ A1 A2 R

  43. 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 eis 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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