Introduction to Nuclear Physics

1. Introduction to Nuclear Physics 1/3 S.PÉRU

2. The nucleus a complex system ? • What is the heaviest nucleus ? • How many nuclei do exist ? • What about the shapes of the nuclei ?

3. The nucleus : a complex system I) Some features about the nucleus discovery radius, shape binding energy nucleon-nucleon interaction stability and life time nuclear reactions applications I) Some features about the nucleus discovery radius, shape binding energy nucleon-nucleon interaction stability and life time nuclear reactions applications II) Modeling of the nucleus liquid drop shell model mean field III) Examples of recent studies figures of merit of mean field approaches exotic nuclei isomers shape coexistence IV) Toward a microscopic description of the fission process

4. screen Target Au source  particles The discovery of the nucleus The structure of the atom was first probed by the Rutherford experiment in 1909. A beam of  particles generated by the radioactive decay of radium was directed onto a sheet of a very thin gold foil. The unexpected results demonstrated the existence of the atomic nuclei.

5. Before this exp. people thought that  particles should all be deflected by at most • a few degrees. • But some  ‘s were deflected through angles much larger than 90 degrees !! • The results suggest that the greater part of the mass of the atom was concentrated into a very small region. • Atoms are almost empty except a hard scattering center: the atomic nuclei

6. Some questions about the Rutherford experiment •  Why a thin target ? • What about electrons ? • Why in the vacuum ? • How can we determine the size of the atomic nucleus from this experiment ?

7. At the distance « a0 » from the center of the nucleus, when the  particle go back : Coulomb repulsion = kinetic energy of the  particle The size of the gold nucleus is 2.8 10-14 m Some tracks about the Rutherford experiment  Why a thin target ? To be sure that the projectile do interact with only one nucleus What about electrons ? Electrons do not affect the trajectory of the projectile which is much heavier Why in the vacuum ? In the air, the slowing down of the beam and of the scattered  make the analysis more complicated and can even stop the particles before detection. • How can we determine the size of the atomic nucleus from this experiment ?

8. ? What is the nucleus of the atom ? The nucleus contains A nucleons : A = Z protons + N neutrons Nucleons are hadron particles (particles governed by the strong interaction) Nucleons are baryons (made of 3 quarks) protons (uud) are positive charged particles 2000 times heavier than electrons. Mpc2 = 938.272 MeV Mec2 = 0.511 MeV neutrons (udd) are electric neutral particles with mass comparable to the proton one. Mnc2 = 939.565 MeV electron proton neutron neutron proton proton Nucleons are fermions, as well as electrons. A nucleus is characterized by its mass number A and its atomic number Z. It is written AZX.

9. ? What is the nucleus of the atom ? The nucleus contains A nucleons : A = Z protons + Nneutrons The nucleus is a bound system : its mass is lower than the mass of its components. There is a « missing mass » connected to the binding energy by the famous Einstein formula : ? Nuclear interaction Nuclear interaction

10. features of the nucleus : the scale of a nucleus A nucleus is almost 100000 times smaller than an atom ATOM NUCLEUS NUCLEON (10-9 m) (10-14 m) (10-15 m) Do all the nuclei have the same radius ?

11. features of the nucleus : radius R(fm) Radii are extracted from elastic scattering of  particles on different targets. R = 1.25 x A1/3 (fm) 1fm = 10-15 m The radius increases with A1/3 The volume increases with the number of particles

12. features of the nucleus : shape Ground–state nuclear deformation predicted with the Hartree-Fock-Bogoliubov approach with the Gogny force www-phynu.cea.fr Nuclei are predicted to be either: spherical prolate or oblate

13. features of the nucleus : shape, density 208Pb

14. features of the nucleus: binding energy A nucleus is a bound system i.e. its mass is lower than the mass of its components. (if not the nucleus would release its excess of energy by spontaneously evolving to a state of lower energy composed of free particles) Mass ~ Energy ~ Instability « free » nucleons ≈ A× 1000 MeV B(A,Z) ≈ A× 8 MeV nucleus : M(A,Z) ≈ A× (1000 - 8) MeV Z N ... ... Nucleus ... ... A=Z+N B(A,Z) M(A,Z) = N Mn + Z Mp –B(A,Z) Stable bound system for B > 0 Note : B is the “missing mass” Matomic(A,Z)=A (1amu) + Δm Δm = «mass excess » Δm= 0 for 126C => 1 amu = 931,500 MeV

15. Binding energy: nucleon-nucleon potential VNN 1 GeV pp s p r 1 2 3 Distance between the nucleons (fm) -50 MeV «hard core» attractive part The nucleon-nucleon interaction is still unknown nowadays !!! Phenomenological parameterization of the interaction ; THIS IS ONE OF THE MOST IMPORTANT PROBLEM NOWADAYS

16. Nuclear interaction is repulsive for small distances and attractive for large ones, it’s a binding interaction. Coulomb interaction is repulsive for protons. Binding energy: nuclear interaction N=Z Z coulomb repulsion Stability valley Stability valley N=Z Symmetry N

17. features of the nucleus : binding energy fission Binding energy per nucleon: B(A,Z)/A≈ 8 MeV fusion

18. features of the nucleus: stability The most stable nuclei ITER project Nuclear power plant

19. features of the nucleus: stability ....free... ... nucleons... Mass (MeV) ... ... ... ... ... ... B(D)+B(T) 10.71 D T B(Ra) 1731.626 ≈1800 B(4He)+n 28.30 B(Rn)+B(4He) 1736.492 ≈2 × 1000 Q=17.60 22688Ra A 4He Q=4.871 QF≈200 22286Rn A/2 A/2 4He Α radioactivity fusion fission

20. features of the nucleus: separation energy Separation energies For one neutron: S(n) =M(A-1,N-1,Z)+mn –M(A,N,Z) S(n)=B(A,N,Z)-B(A-1,N-1,Z) For one proton S(p) =B(A,N,Z)-B(A-1,N,Z-1) Two-neutron separation energy: S(2n)=B(A,N,Z)-B(A-2,N-2,Z) α particle S(α) = B(A,N,Z)-[B(A-4,N-2,Z-2)+B(α)] Mass (MeV) B(A-1,Z,N-1)+ mn B(A,N,Z) A-1 n S(n) A=Z+N S(n) = separation energy of one neutron in the A nucleus

21. The nucleus contains A nucleons: A = Z protons + N neutrons Nucleons are spin one-half particles, they are fermions. Even-even or odd-odd nuclei are whole spin systems. Even-odd and odd-even nuclei are half-whole spin systems. features of the nucleus: spin J=0 J=+1/2 J=1 neutron neutron J=-1/2 J=0

22. features of the nucleus: nuclear life times A few nuclei are stable : their lifetimes are infinite (comparable to the lifetime of the proton 1033 years.) The others are unstable : they transform into more stable nuclei Exponential decay Half –life T defined as the time for which the number of remaining nuclei is half of its the initial value.

23. Different types of radioactivity Protons b- n b+,e p a Neutrons

25. Total versus partial life times (29 h) 22689Ac e (170 h) b- (35 h) a (55 y) 22690Th 22688Ra 22287Fr

26. Examples: half lives Life times span many orders of magnitude: Nitrogen 16 T1/2 = 7.13 s Oxygen 15 = 2.037 mn Radium 224 = 3.62 d Carbon 14 = 5730 y Molybdenum 100 = 1019 y Tellurium 124 = 2.2 1028 y

27. Nuclear reactions How do we study a nucleus ? A B b a A + a b+B A(a,b)B Photonuclear reaction A(γ,b)B Radiative capture A(a,γ)B Elastic scattering A(a,a)A Inelastic scattering A(a,a’)A* A*=excited state

28. The reaction energy: Q value How do we study a nucleus ? A(b,d)C C A d b B(b)+B(A) B(C)+B(d) Q = B(C) +B(d) - (B(A) + B(b)) Q is a constant, a feature of each reaction. Q>0 exoergic Q=0 cold (elastic scattering) Q<0 endoergic: the minimum energy of the incident particle needed is the threshold energy

29. How do we experimentally study a nucleus ? I ) Elastic and inelastic scattering Excitation energy (MeV) e- ,e+ p n Heavy ions ........ Momentum transferred II ) Transferex : (p,n), (d,p) … … R(fm)

30. How do we experimentally study a nucleus ? III) Gamma spectroscopy 1) To excite the nucleus 2) To observe its decay

31. Number of detected photons Energy in MeV

32. Example of a level scheme The barcode of a nucleus

33. 148Sm 160Gd

34. Odd nuclei 61Ni

35. Some applications of Nuclear Science Nuclear physics makes indeed many essential contributions to  Energy production *Electricity generation * fission : research on * new generations of power plants, new fuel cycles * reduction by transmutation of the long – term impact of the nuclear wastes produced (ADS or GEN IV reactors) * fusion for the far future : (ITER project)  Medicine *diagnostic * detection of the decay of radioactive isotopes SPECT Single Photon Emission Computer Tomography PET Positron Emission Tomography * IRM Imaging by Magnetic Resonance *therapy (proton-, hadron-therapy …)

36. Some applications of Nuclear Science (2)  Art and archaeology * datation * identification of constituent materials (ex : AGLAE Accélérateur Grand Louvre pour l’Analyse Elémentaire)  Environmental studies * ex : observation of modification of ocean circulation patterns (measurement of 129I /127I in seawater as a function of depth and distance to the coast)  … From NuPECC long Range Plan 2004

37. Some features of the nuclei : Summary • The existence of the atomic nuclei : the Rutherford experiment in 1909 • The nucleon-nucleon interaction is not precisely known. • Many nuclei are predicted but not observed up to now • Most of them are neutron rich, and are supposed to have played a role • during the nucleosynthesis. • Nuclei are characterized by their level scheme : their barcode. • Many applications of the nuclear physics