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(1)NUCLEAR & PARTICLE PHYSICS B. Sc. Part III (Hons.) Paper: VI University of Calcutta. A course guided by Dr. P. Mandal Department of Physics, St. Paul’s C. M. College.

(2) Syllabus Nuclear & Particle Physics I 1. Bulk properties of nuclei Nuclear mass, charge, size, binding energy, spin and magnetic moment. Isobars, isotopes and isotones; mass spectrometer (Bainbridge) 2. Nuclear structure Nature of forces between nucleons, nuclear stability and nuclear binding, the liquid drop model (descriptive) and the Bethe-Weizsacker mass formula, application to stability considerations, extreme single particle shell model (qualitative discussion with emphasis on phenomenology with examples).

(3) Syllabus Nuclear & Particle Physics I 3. Unstable nuclei (a) Alpha decay : alpha particle spectra – velocity and energy of alpha particles, Geiger-Nuttal law (b) Beta decay : nature of beta ray spectra, the neutrino, energy levels and decay schemes, positron emission and electron capture, selection rules, beta absorption and range of beta particles, Kurie plot (c) Gamma decay : gamma ray spectra and nuclear energy levels, isomeric states. Gamma absorption in matter – photoelectric process, Compton scattering, pair production (qualitative).

(4) Syllabus Nuclear & Particle Physics II 1. Nuclear reactions Conservation principles in nuclear reactions. Q-values and thresholds, nuclear reaction cross-sections, examples of different types of reactions and their characteristics. Bohr’s postulate of compound nuclear reaction, Ghoshal’s experiment 2. Nuclear fission and fusion Discovery and characteristics, explanation in terms of liquid drop model, fission products and energy release, spontaneous and induced fission, transuranic elements. Chain reaction and basic principle of nuclear reactors. Nuclear fusion: energetics in terms of liquid drop model.

(5) Syllabus Nuclear & Particle Physics II 3. Elementary Particles (a) Four basic interactions in nature and their relative strengths, examples of different types of interactions. Quantum numbers – mass, charge, spin, isotopic spin, intrinsic parity, hypercharge. Charge conjugation. Conservation laws (b) Classifications of elementary particles – hadrons and leptons, baryons and mesons, elementary ideas about quark structure of hadrons – octet and decuplet families.

(6) Syllabus Nuclear & Particle Physics II 4. Particle Accelerator and Detector Cyclotron – basic theory, synchrotron, GM counter 5. Nuclear Astrophysics Primordial nucleosynthesis, energy production in stars, pp chain, CNO cycle. Production of elements (qualitative discussion).

(7) References 1. Nuclear Physics – S. N. Ghoshal (S. Chand Chand)) 2. Introductory Nuclear Physics – David Halliday (John Wiley & Sons) 3. Introductory Nuclear Physics – K. S. Krane (John Wiley & Sons) 4. An Introduction to Nuclear Physics – Cottingham & Greenwood (Cambridge University Press) 5. Nuclear Physics – I. Kaplan (Narosa) 6. Modern Atomic and Nuclear Physics – A. B. Gupta (Books & Allied) 7. Theory and Problems of Modern Physics – R. Gautreau (Schaum’s Series).

(8) Visit https://www.youtube.com/watch?v=josqjcH79PE to view NP-TEL lectures delivered by Prof. H. C. Verma. Visit https://sites.google.com/site/stpcmcpintumandal/home/teaching to download my lecture slides (in protected pdf).

(9) Some Physical Constants. Introductory Nuclear Physics, Halliday, 2nd ed., Pg. 8.

(10) Nuclear Physics: Historical Review Year. Contributor. Contribution. 1803. John Dalton. Atomic theory: Matters constituted with ‘elementary particle’ called atom. 1869. Dimtri Mendeleev. Periodic table: Arrangement of different elements in groups. 1895. Wilhelm Rontgen. Discovery of X – rays. 1896. Henri Becquerel. Discovery of radioactivity. 1897. J. J. Thomson. Discovery of electron. Measurement of charge and mass of the electron. 1903. Rutherford & Soddy. Suggestion that radioactive decay results in new atomic species. 1908 – 1913. Geiger & Marsden. Rutherford’s α – scattering experiment. 1932. Chadwick. Discovery of neutron.

(11) Bulk properties of nuclei Rutherford’s α-scattering experiment:. https://www.youtube.com/watch?v=5pZj0u_XMbc.

(12) Rutherford’s α-scattering experiment “It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you. On consideration, I realized that this scattering backward must be the result of a single collision, and when I made calculations I saw that it was impossible to get anything of that order of magnitude unless you took a system in which the greater part of the mass of the atom was concentrated in a minute nucleus. It was then that I had the idea of an atom with a minute massive centre, carrying a charge.”. – Rutherford.

(13) Rutherford’s α-scattering experiment Outcomes: (1) Most of the atomic volume is free – does not contain mass. Mass of atom concentrated within a very small region – the nucleus (2) Radius of nucleus ~ 10-15 m (1 fermi). Atomic radius ~ 10-10 m (1 Å).

(14) Mass & Energy Units Unified mass unit (u) : The unit of atomic mass is defined to be one – twelfth of the mass of C12 atom – mass of C12 atom taken to be 12 units exactly. 1 12 × 10−3 − 27 1u = × = 1 . 660566 × 10 kg 23 12 6.023 × 10 Electron – volt unit (eV) : Atomic energy is expressed in eV unit & nuclear energy is expressed in MeV unit. 1eV = 1.6 × 10−19 J. 1MeV = 106 eV. Mass – energy equivalence: E = mc2 1.660566 × 10−27 × 9 × 1016 1u = = 931.502 MeV −13 1.6 × 10.

(15) Constituents of Atoms Constituents. Discovery. Rest Mass kg. u. Mev/c2. Charge. Spin. Electron. Thomson (1897). 9.11×10-31. 0.00055. 0.511. -1. 1/2. Proton. Goldstein (1917). 1.673×10-27 1.007276. 938.27. +1. 1/2. Neutron. Chadwick (1932). 1.675×10-27 1.008665. 939.57. 0. 1/2.

(16) TERMINOLOGIES Name. Definition. Examples. Nuclide. A nuclear species. …... Nucleon. Proton, Neutron. …... Radionuclide. A radioactive nuclide. 235U, 222Ra. Isotopes. Several nuclides with same Z. 16O, 17O, 18O. Isotones. Several nuclides with same N. 23Na, 24Mg. Isobars. Several nuclides with same A. 40Ar, 40K, 40Ca. Introductory Nuclear Physics, Halliday, 2nd ed., Pg. 8.

(17) TERMINOLOGIES Name. Definition. Examples. Mirror Nuclei. Pair of isobaric nuclei with their. 11B, 12C. proton and neutron number. 13N, 13C. interchanged Isodiaphere. Same difference between Z and N. Isomer. Same N, Z but different energy. 38K, 40Ca. Introductory Nuclear Physics, Halliday, 2nd ed., Pg. 8.

(18) Nuclear Binding Energy Definition: The nucleons are tightly bound within the nucleus. Energy must be supplied adequately to detach a nucleon from the nucleus. The minimum energy required to separate all Z protons & N neutrons from a nucleus is called the nuclear binding energy. Conversely, if we start with Z protons & N neutrons at rest , all completely separated from each other, and bring them together to form the nucleus of mass number A = Z + N, then the energy evolved is equal to the nuclear binding energy.

(19) Nuclear Binding Energy Origin: The source of nuclear energy is the mass of its constituents. While formation of the nucleus, a part of the mass of nucleons gets converted into energy.. M n ( A, Z ) < Zm p + Nmn Measured nuclear mass. Mass of proton. Mass of neutron.

(20) Nuclear Binding Energy ∆M = Zm p + Nmn − M n ( A, Z ). = Zm p + Nmn − [M ( A, Z ) − Zme ] = Z (m p + me ) + Nmn − M ( A, Z ) = ZM H + Nmn − M ( A, Z ). E B = ∆Mc 2 = [ZM H + Nmn − M ( A, Z )]c 2 EB in general, increases with A. The strength of binding is determined by not the total binding energy but the binding energy per nucleon – binding fraction. EB ZM H + Nmn − M ( A, Z ) = fB = A A. Masses are expressed in MeV, we have dropped c2.

(21) Mass Defect Precision measurement of atomic masses (measured in the unified mass unit) shows that these are very close to whole numbers, actually equal to the mass number A. For C12, the atomic mass is exactly 12 u However, for all other atoms, the measured atomic mass, though closed to the corresponding mass number (integer), differ slightly from later For example, atomic mass of He4 is 4.002603 u, atomic mass of O16 is 15.994915 u.

(22) Mass Defect The departure of the measured atomic mass M(A, Z) from the mass number A is known as mass defect (∆M’). ∆M ' = M ( A, Z ) − A Mass defect per nucleon is known as packing fraction (f). ∆M ' M ( A, Z ) f = = −1 A A M ( A, Z ) = A(1 + f ).

(23) Mass Defect & Packing Fraction. M (A, Z) > A or < A i.e. f can be either positive or negative.

(24) Mass Defect & Packing Fraction f varies in a systematic manner with the mass number A f is positive for very light nuclei (A < 20) f becomes negative for A > 20 f attains a minimum at A ~ 60 f rises slowly for higher A and becomes positive again for A > 180.

(25) Binding Fraction Systematic variation of f with A can be understood from nuclear binding fraction (fB = EB/A) versus A plot. fB is very small for very light nuclei and rises rapidly for with A attaining a value ~ 8 MeV/nucleon for A > 20 fB rises slowly above A > 20 and attains a maximum of 8.7 MeV for A ~ 56. For higher A it decreases slowly.

(26) Binding Fraction Very slight variation in fB is observed for 20 < A < 180 – fB is approximately constant in this range of A having mean value ~ 8.5 MeV For very heavy nuclei (A > 180) fB decreases monotonically with the increase of A. For the heaviest nuclei, fB ~ 7.5 MeV/nucleon For very light nuclei, there are rapid fluctuations in the values of fB. In particular, peaks in the binding fraction curves are observed for even – even nuclei He4, Be8, C12, O16 etc., for which A = 4n where n is an integer. Similar, but less prominent peaks are observed at the values of Z or N equal to 20, 28, 50, 82, 126. These are known as magic numbers & corresponding nuclei are called magic nuclei (to be discussed in detail in Nuclear Models) Appearance of peaks shows greater stability of the corresponding nuclei relative to neighbourhood nuclei.

(27) Binding Fraction & Packing Fraction The nature of binding fraction curve is complementary to the nature of the packing fraction curve.. EB = ZM H + Nmn − M ( A, Z ) = Z (1 + f H ) + N (1 + f n ) − A(1 + f ) M H = 1 + f H. = ( Z + N ) + Zf H + Nf n − A − Af. M n = 1 + fn. = Zf H + Nf n − ∆M. ∆M f = A. EB Zf H + Nf n ∆M fB = = − A A A Zf H + Nf n = −f A f B + f ≈ const.. fH = 0.007825 u f n= 0.008665 u fH ≈ f n For lighter nuclei Z≈N≈A/2.

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