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Semi Empirical Binding Energy Formula Part 2
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Semi empirical binding energy formula part2 (pairing energy)

SHIVAM PARASHAR
Science freak and a keen observer . I admires physics and planes. I race untill I win !

U
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  1. 0 Hence, we hau N-At, Z-A-v 2 2. N-Z-29 v = N-Z 2 becomes 2 (N-z? BE


  2. (2) PAIRING1 ENERGY The, Nucleus Neutons tPuotons Have atemdency- to bai Why ? Having opposite spm im Seme quomtum amgulax Momemtum 0 Dueto baium, ENERGY domes down


  3. um-cuon nucleus BET odd-odd mucleus BE


  4. Pairing Energy This term accounts for the fact that a pair of like nucleons is more strongly bound than is a pair of unlike nucleons. When like nucleons have equal and opposite spins they can exist in the same spatial quantum state This situation is shown in fig (a) in a kind of classical manner. The particles essentially spend more time in each other's presence and the strong interaction between them is more effective the binding is stronger. If on the other and the spins are not anti-parallel as shown in fig (b) then the pair only interact at two points on their (classical) orbits. interaction energy is not so strong. There is no real "theory" for this effect, but clearly the bigger the nucleus the less important. Empirically. +34MMelN,Z -odd -odd 3/4 A-odd -34MelN.Z-even- even


  5. Stable Nuclides Two protons or neutrons occupy a quantum state, due to their 12 spirn. pairing of nucleons Pairing nucleons stabilises nuclides, leading to a large number of stable nuclides with even Z and N Effect of Paring Nucleons No stable isotopes for Z- 43 or 61 # of stable No stable isotones with N 19, 31 35, 39, 61, 89 even even even odd odd evein odd odd stable nuclides 166 57 53 *4 More stable isotopes for even Z than odd Z and for even N than odd N Elements with even Z are more abundant than those with odd Z of comparable mass. total280 *They are: 2D1, 6Li3, 1 B5, & 14N7


  6. So Se -Em uical Binding enna Founnda AYs 4%


  7. Contribution of different terms in BE/A 16 15 14 13 12 Volume + Surface 10 +Coulomb 8 7 + Asymm 0 30 60 90 120 150 180 210 240 270