Thermodynamics of the nucleus
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1 Thermodynamics of the nucleus Hilde-Therese Nyhus 1. October, 8 Hilde-Therese Nyhus Thermodynamics of the nucleus
2 Owerview 1 Link between level density and thermodynamics Definition of level density Level density and state density 3 Hilde-Therese Nyhus Thermodynamics of the nucleus
3 Definition of level density Level density and state density The link between the level density and thermodynamics The level density gives the number of levels as a function of excitation energy of the nucleus. -1 Level density ρ (E (MeV Preliminary Oslo data Known levels ack-shifted Fermi gas ρ from neutron res. data 163 Preliminary Excitation energy E (MeV Excitation energy E (MeV Hilde-Therese Nyhus Thermodynamics of the nucleus 3
4 Definition of level density Level density and state density The link between the level density and thermodynamics The density of states is proportional to the density of levels plus a spin dependent factor: Ω(E I + 1 ρ(e (1 The spin distribution is apprximated by a Gaussian, with mean value: I + 1 = πσ ( where, σ E 1/ (3 The spin dependency is weak. We define: Ω(E = ρ(e/ρ ( Hilde-Therese Nyhus Thermodynamics of the nucleus
5 The micro-canonical or canonical ensamble? The nuclear force has a short range and the nucleus does not normally share its excitation energy with its surroundings Isolated system Isolated system - Gives results which is not observed in stable microscopic systems (C v, T < System in contact with a heat bath - What heat bath? Hilde-Therese Nyhus Thermodynamics of the nucleus 5
6 Microcanonical ensemble Entropy S(E =k ln Ω = k ln ρ(e ρ = k (ln ρ(e + S (5 S = ln ρ We obtain S by applying the 3. law of thermodynamics; As T the entropy S Hilde-Therese Nyhus Thermodynamics of the nucleus 6
7 Micro-canonical entropy Entropy S (k Entropy difference ΔS (k Preliminary Excitation energy E (MeV Extensive with respect to number of quasi-particles: S = ns 1 S 1 1.8k (6 Hilde-Therese Nyhus Thermodynamics of the nucleus 7
8 Micro-canonical entropy Entropy S (k Entropy difference ΔS (k Preliminary Excitation energy E (MeV Extensive with respect to number of quasi-particles: S = ns 1 S 1 1.8k (6 Macroscopic entropy scales with the size of the system. Hilde-Therese Nyhus Thermodynamics of the nucleus 7
9 Micro-canonical entropy Entropy S (k Entropy difference ΔS (k Preliminary Excitation energy E (MeV Extensive with respect to number of quasi-particles: S = ns 1 S 1 1.8k (6 Macroscopic entropy scales with the size of the system. The Fermi gas does not give entropy that is extensive wrt the number of quasi-particles. Hilde-Therese Nyhus Thermodynamics of the nucleus 7
10 Temperature Heat capacity T = C v = ( δs 1 δe V ( δt δe V (7 (8 Hilde-Therese Nyhus Thermodynamics of the nucleus 8
11 Micro-canonical temperature and heat capacity Temperature T (kev Preliminary 16 Preliminary (k v Heat capacity C Excitation energy E (MeV Excitation energy E (MeV Hilde-Therese Nyhus Thermodynamics of the nucleus 9
12 The partition function Z(T = ω(e i e E i /k T ω(e i = δe i ρ(e i i= Entropy Energy «δf S(T = δt V «δ(f /T E = T T V (9 ( Heat capacity C V = «δ E δt (11 V Hilde-Therese Nyhus Thermodynamics of the nucleus
13 Link between level density and thermodynamics Entropy S (k 5 15 Energy <E> (MeV 5 v Heat capacity C (k The characteristic S-shape of the heat capacity is a signature of phase transition Prelim Temperature T (MeV Hilde-Therese Nyhus Thermodynamics of the nucleus 11
14 Two different physical systems which produce different results, and which indicate different phase transitions in different regions. The canonical ensemble display average properties single quasi-particle effects does not show. The importance of pair breaking does not come to light. The results obtained have to be interpreted in another way than in macroscopic systems. Hilde-Therese Nyhus Thermodynamics of the nucleus 1
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