Nuclear_Physics_Lecture_13.pdf

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(1)Nuclear Astrophysics Nuclear Astrophysics is an interdisciplinary branch of physics that involves close linkage amongst various subfields of nuclear physics and astrophysics, with significant emphasis in areas such as stellar modeling, measurement and theoretical. estimation. of. nuclear. reaction. rates,. cosmology,. gamma. ray, optical and X-ray astronomy, and extending our knowledge about nuclear lifetimes and masses. In general terms, nuclear astrophysics aims to understand the origin of the chemical elements and the energy generation in stars Syllabus Primordial nucleosynthesis, energy production in stars, pp chain, CNO cycle. Production of elements (qualitative discussion).

(2) Energy Production in Stars The stars are releasing energy years after years. For example, the Sun releases energy @ 4×1026 J/s for at least 4×109 years. The Sun has a mass 2×1030 kg and hence on an average it releases 2×10– 4 J/kg.s. Naturally it produces energy must be larger than this figure What is the source of this huge energy? Neither chemical reactions nor gravitational energy changes can account for this huge production of energy in stars. For example, if the Sun consisted of carbon and oxygen only and the solar energy were generated due to the burning of carbon, then all of it would burn up in only 1500 years! This leaves nuclear energy as the only possible source of solar (and stellar) energy.

(3) Energy Production in Stars The Sun is known to be mainly made up of hydrogen & helium (90% in total) in almost equal proportion. If by some series of nuclear reactions, four hydrogen nuclei combine to produce one helium nucleus, the energy release in each fusion. E = 4 M H − M He = 4 × 1.007825 − 4.002603 u = 0.028697 u = 26.73 MeV = 4.28 × 10 −12 J Each kg of hydrogen contains about 6×1026 protons, the energy content of such a source will be about 2.4×1015 J/kg. If the source releases energy @ 2×10– 4 J/kg.s, it can continue for 1012 years!.

(4) Energy Production in Stars Atkinson & Houtermans (1928) first suggested that successive capture of four protons by some light nuclei could produce α – particle and release energy at this rate. Two thermonuclear reaction cycles (proton – proton chain & carbon – nitrogen – oxygen cycle) have been suggested that explain the energy production in starts.

(5) p – p Chain 1. H +1H →2 H + β + + ν e + 0.42 MeV. 1. H + 2 H →3 He + γ + 5.5 MeV. 3. He + 3 He→4 He + 21 H + 12.8 MeV. Each of first two reactions must occur twice for every third reaction to take place. 41 H → 4 He + 2 β + + 2ν e + 2γ + 24.64 MeV.

(6) C – N – O Cycle 12. C+1H →13 N + γ + 1.95 MeV 13. N →13 C + β + + υ e + 2.22 MeV. 13. C+1H →14 N + γ + 7.54 MeV. 14. N +1H →15 O + γ + 7.35 MeV 15. 15. O→15 N + β + + υ e + 2.7 MeV. N +1H →12 C+ 4 He + 4.96 MeV. 12. C + 41 H →12 C+ 4 He + 2 β + + 2ν e + γ + 26.72 MeV.

(7) p – p Chain Reaction Vs. C – N – O Cycle C – N – O cycle is a catalytic cycle unlike the p – p chain. The net result of C – N – O cycle is the fusion of four protons to produce one 4He nucleus in the presence of 12C, which must be present, but is not destroyed in the cycle. Thus 12C acts as a catalyst in C – N – O cycle. C – N – O cycle is dominant in stars that are more than 1.3 times as massive as the Sun. For less massive stars (comparable to the solar mass or less), p – p chain dominates. p – p chain reaction starts at temperatures around 4×106 K, making it the dominant energy source in smaller stars. A self-maintaining CNO chain starts at approximately 15×106 K, but its energy output rises much more rapidly with increasing temperatures. It starts becoming the dominant source of energy at approximately 17×106 K. The Sun has a core temperature of around 15.7×106 K, and only 1.7% of 4He nuclei produced in the Sun is born in the CNO cycle.

(8) Nucleosynthesis Nucleosynthesis is the process that creates new atomic nuclei from preexisting nucleons, primarily protons and neutrons The lighter elements like hydrogen, helium have greater abundances in Sun and in other stars The relative abundances rapidly decrease with increase in mass number (A) of the element and become almost constant for A > 100 There are local variations as well. For example, natural abundance of deuterium is around 0.015% These abundances are in no way correlated with the chemical properties of the elements On the other hand, there is a clear correlation between the cosmic abundances of the elements and their nuclear properties.

(9) Nucleosynthesis. Elements. Stars. Sun. Earth’s crust. Stony meteorites. Hydrogen. 11.4. 11.5. 8.3. 6.9. Helium. 10.2. 10.2. 0. 0. Iron. 6.7. 7.2. 7.2. 7.6. Mismatch for lighter nuclei is due to different gravitational strength !.

(10) Nucleosynthesis How different elements could have been cooked (synthesized) within stars in the course of stellar evolution? Thermonuclear fusion of lighter nuclei occurs in stars having temperature ~ 107 K. For example p – p chain produces 4He nucleus after fusion of four protons (hydrogen nuclei) When hydrogen is used up to a large extent, this fusion will stop. Gravitational contraction takes place and temperature is raised At higher temperature (~2×108 K), the helium nuclei begin to fuse 4 He + 4 He→8 Be 8. Be+ 4 He→12 C + γ. 12. C+ 4 He→16 O + γ. 16. O + 4 He→20 Ne + γ.

(11) Nucleosynthesis When most of helium is used up, helium fusion will stop. Gravitational contraction takes place again which raises the temperature At higher temperature (~109 K), photo-nuclear reactions like 16O,. 20Ne. (γ, α). produces α – particles with Q = -4.73 MeV. These α – particles can produce (α, γ) reactions to synthesize heavier nuclei (α – process) 20. Ne + 4 He→ 24 Mg + γ. At more higher temperature fusion of heavier nuclei take place to produce more heavier nuclei like 56Fe (Z = 26), 56Ni (Z = 28).

(12) Nucleosynthesis Neutron capture reaction: Production of odd – A nuclei. Rapid or R - process. Slow or S - process. 56 26. Fe+ 01n→57 26 Fe. 57 26. 58 Fe+ 01n→26 Fe. 58 26. Fe+ 01n→59 26 Fe. 59 26. Fe→59 Co + β + υe 27. 59 26. Fe→59 Co + β + υe 27. 59 27. 1 0. 60 27. Co+ n→ Co.

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