Nuclear PhysicsAn introduction Brief history Binding energy Semi empirical mass formula or the Liquid drop model Radioactivity Nuclear energy & some applications
Why Study Nuclear Physics? To understand origin of different nuclei ◦ Big bang: H, He and Li ◦ Stars: elements up to Fe ◦ Supernova: heavy elements We are all made of stardust Applications are plenty ◦ Energy (Fission, fusion, transmutation) ◦ Medicine (Radiotherapy, MRI) ◦ Instrumentation (e.g. spectroscopy) ◦ Devices (e.g. Smoke detector) ◦ Radioactive dating
Basics The number of protons inside the nucleus is designated by Z and is known as the Atomic Number The number of neutrons inside the nucleus is designated by N and is known as the Neutron Number The mass number, A, is the sum of the atomic number and the neutron number A = Z + N The mass number is an integer and is only approximately equal to the atomic weight of a element A nuclide is a single nuclear species having a specific Z A Z EN and N. The notation that is used to designate the nuclides is Nuclei with same Z, but differing N Isotopes Nuclei with same N, but differing Z Isotones Nuclei with same A Isobars
Basic properties Size ◦ Most nuclei are nearly spherical, with the radius being given by1/3 fm R 1.2 A Density ◦ The nucleus has approximately constant density ~ 1017 kg/m3 Binding energy ◦ When you measure the mass of an atom you find that it is less than the sum of its parts BE Z M H N M N M ( A, Z ) c2 ◦ The difference is known as the binding energy and is given by
Models of the nucleus No fundamental theory that can explain all observed properties of the nucleus exists Several models developed to explain some of the observed properties Liquid Drop Model–Nucleons are treated as molecules in a liquid Shell Model–Similar to central field approximation in atomic structure
Liquid drop modelBethe-Wiezsacker mass formula (1935)Assumptions Each nucleon in interacting solely with its nearest neighbours Equivalent to atoms in a solid or molecules in liquid which move freely while maintaining fixed intermolecular distance Vibrations in solid would be too high for stability Nucleus ~ charged liquid dropWe may consider different effects term-wiseVolume term Bulk binding energy volume EV aV A Ev R3 = (r0 A1/3)3
Surface term Surface area = 4 r 2 4 (r0 A 1/ 3 )2 4 r02 A 2/ 3 Surface energy aS A 2/ 3Coulomb term The work done to bring together Z protons from infinity e V 4 0r For Z ( Z 1) / 2 pairs of protons Z ( Z 1) Z ( Z 1)e2 1 EC V 2 8 0 r AV 1/ 3 Z ( Z 1) r A EC aC A1/ 3
Asymmetry term Neutron and proton states with Neutrons Protons same spacing . Crosses represent initially occupied states in ground state. If three protons were turned into neutrons the extra energy required would be 3 3 . In general if there are N Z excess protons over neutrons the extra energy is [(N Z)/2]2 . relative to Z = N. (N Z )2E Asym aa A 1/A
Pairing term Like Cooper pair formation, the nucleons also can pair Some energy is spent in binding the pairs BE(Nucleus with paired nucleons) > BE(Nucleus with unpaired nucleons) BE (even-Z , odd-N ) BE (even-Z , even-N ) BE (odd-Z , odd-N ) BE (odd-Z , even-N )= +ve 0 -ve Its observed that this effect smaller for larger A Phenomenological fit to A dependence EPair 1/A1/3 E Pair ap 1/ 3 A
e=even o=odd + 33.5 MeV (e-e) ap= 0 MeV (o-e or e-o) av=14.1 MeV ac=0.595 MeV - 33.5 MeV (o-o) 2 2 2 3 Z (N Z )EBind av A as A ac 1 aa ap 1/ 3 A 3 A A as=13.0 MeV aa=19.0 MeV BE ( N , Z ) Constraint for most stable isotope N Z Const.
Present scenario 2900 nuclei till year 2000 3090 till August 2008 3000 more to be discovered
Classification of Decays -decay: • emission of Helium nucleus • ZZ-2Protons • NN-2 • AA-4 EC --decay • emission of e- and • ZZ+1 • NN-1 • A=const +-decay • emission of e+ and • ZZ-1 • NN+1 Neutrons • A=const Electron Capture (EC) • absorbtion of e- and emiss -decay • ZZ-1 • emission of • NN+1 • Z,N,A all const • A=const 21
Spin 1 1 3 S s( s 1) 1 2 2 2 1 ms 2Magnetic Moment e 27 Nuclear magneton N 5.051 10 J/T 2m p Proton pz 2.793 N pz has same direction as S Neutron nz 1.913 N nz is opposite to S Magnetic energy U m z B, E 2 z B Nuclear Zeeman effect
Practical Applications Nuclear fission for energy generation. ◦ No greenhouse gasses ◦ Safety and storage of radioactive material. Nuclear fusion ◦ No safety issue (not a bomb) ◦ Less radioactive material but still some technical difficulties. Nuclear transmutation of radioactive waste with neutrons. ◦ Turn long lived isotopes stable or short lived.
Medical Applications Radiotherapy for cancer ◦ Kill cancer cells. ◦ Used for 100 years but can be improved by better delivery and dosimetery ◦ Heavy ion beams can give more localised energy deposition. Medical Imaging ◦ MRI (Nuclear magnetic resonance) ◦ X-rays (better detectors lower doses) ◦ Many others…
Other Applications Radioactive Dating ◦ C14/C12 gives ages for dead plants/animals/people. ◦ Rb/Sr gives age of earth as 4.5 Gyr. Element analysis ◦ Forenesic (eg date As in hair). ◦ Biology (eg elements in blood cells) ◦ Archaeology (eg provenance via isotope ratios).
Carbon Dating C14 produced by Cosmic rays (mainly neutrons) at the top of the atmosphere. ◦ n N14 p C14 C14 mixes in atmosphere and absorbed by plants/trees constant ratio C14 / C12 . Ratio decreases when plant dies. t1/2=5700 years. Either ◦ Rate of C14 radioactive decays ◦ Count C14 atoms in sample by Accelerator Mass Spectrometer. Which is better? Why won’t this work in the future?