1. NUCLEAR STRUCTURE PHENOMENOLOGICAL MODELS
From molecules to atomic nuclei. Standard model
Basic concepts of nuclear physics. Units
Properties of nucleons
Liquid drop model
Surface vibration and rotation
MICROSCOPIC MODELS
Nuclear force
Nuclear mean field
Shell model
Second quantisation in the mean field
Residual interaction. Collective excitations
Collective model. Nilsson model

2. From molecules to atomic nuclei
10-15m=1fm

4. Standard model

5. Basic concepts of nuclear physics
nucleon: proton or neutron
nuclide: nucleus uniquely specified by
number of protons (Z) and neutrons (N)
mass number: A=Z+N
isotopes: nuclides with the same Z
ex: 235U and 238U
isotones: nuclides with the same N
ex: 2H, 3He
isobars: nuclides with the same A
atomic mass unit: 1u=1/12 m(12C)
= kg=931.5 MeV/c2

6. Basic physical observables in nuclei
Electric quadrupole momentum
Angular momentum
Magnetic dipole momentum
Parity
Energy levels
Decay rates

7. Electric
quadrupole
moment

10. Magnetic
dipole
moment

13. Units used in nuclear physics
Length
1 fm =10-15 m
Energy
1 MeV = 106 eV
1 eV = 1, J
Basic constants
MN=938,90 MeV/c2
ħc=197,33 MeV fm
e2=ħc/137=1,44 MeV fm

14. Properties of nucleons
proton
neutron
mass =
MeV/c2 =
MeV/c2
charge +1
spin
1/2
magnetic moment μN μN
parity

15. Nuclear chart stability of nuclei

16. Limits of stable nuclei exotic nuclei

17. Nuclear size from electron scattering experiments

18. Binding energy
Mass defect

19. Example

21. Binding energy/nucleon: B/A

22. Liquid drop model Weizsäcker semiempirical formula (1935)

25. Symmetry energy

28. Liquid drop energy versus (Z,N)

29. Surface vibration and rotation Deformation parameters of the nuclear surface

31. Vibrational states

32. Rotational states

34. Total spin I and its projections to laboratory (M) and intrinsic (K) systemsΩ

35. Parameters in the intrinsic system
Ω is the rotation angle

36. β & γ vibrations of a deformed shape

37. Rotational-vibrational model Rotational bands
built on top of the
vibrational band head

38. Sakai-Sheline rule vibrational states → rotational bands

39. Nuclear force

40. Deuteron: the simplest nuclear system

41. Deuteron spin & magnetic moment

52. Electromagnetic versus strong field

53. Yukawa potential

54. Shell model

55. Nuclear mean field: the selfconsistent single particle potential created by all nucleons

56. Mean field potential for protons and neutrons

57. Spin-orbit interaction

58. Example

59. Shell model magic numbers appear due to the spin-orbit interaction

60. Spherical shell model scheme

61. The last nucleon of an odd-even (even-odd) nucleus determines the nuclear properties (spin, quadrupole and magnetic moments)

64. Schmidt limits for magnetic moments

66. Schmidt limits for quadupole moments

67. creation/annihilation
Second quantisation in the mean field Each spherical level is filled by 2j+1 nucleons with different projections
creation/annihilation
operators for
nucleons (fermions)
Fermi level
Ground state is a Slater determinant
obeying the Pauli exclusion principle

68. Particle (croses) and hole (open circles) states
p-h excitation:

69. (p,2p) reaction in the shell model

71. Residual interaction among nucleons in the mean field
Multipole expansion
l=0 : pairing
l=2 : quadrupole-quadrupole

72. Quasiparticle Hamiltonian approximation Ground state =BCS vacuum
Particle-particle (p-p) short-range interaction describes pairing correlations
Quasiparticle
approximation
Hamiltonian
Ground state =BCS vacuum

73. Occupation probabilities Gap parameter
Normal system
Superfluid system
Fermi level

74. Proton gap versus Z

75. Particle-hole (p-h) long-range interaction describes collective excitations: 1) low-lying surface vibrations 2) giant resonance of protons against neutrons
Hamiltonian
p-h excitation p h

76. Distribution of collective excitations for various multipolarities versus energy
Giant
resonance
Low-lying
vibrational state

77. Collective model

78. Nilsson model of single particle states in the deformed intrinsic system
Single particle energy versus deformation
Deformed Hamiltonian

79. DECAY PROCESSES Alpha decay, cluster emission Beta decay Gamma decay
Fission and fusion

80. Nuclear decay modes

81. Decay law
Decay width
Γ=ħλ

82. Narrow decaying resonance (Γ is small) is a quasi-stationary process

83. Decay rate (activity)

85. Alpha decay

87. The first probabilistic interpretation
G. Gamow "Zur Quantentheorie des Atomkernes" (On the quantum theory of the atomic nucleus), Zeitschrift für Physik, vol. 51, (1928).
The first probabilistic interpretation
of the wave function
Rext ↓
Internal region External region

88. Quantum penetration explains Geiger-Nuttall law for α and cluster decays (C, O, Ne, Mg, Si)
Coulomb parameter

89. Beta decay

93. Fermi & Gamow-Teller transitions

95. Gamma decay

96. Parity rules for gamma transitions

97. Decay operators in second quantisation: gamma transitions beta transitions

98. Fission & fusion

99. Fission - liquid drop model

100. Energy release for various processes

101. Strutinsky shell-model correction The double humped barrier determines the occurrence of superhevy nuclei
Density of levels
liquid drop
shell model

102. Superheavy nuclei are formed by fusion and detected by alpha decay chains

103. Fusion energy

104. The Sun