Introduction to Reactor Physics and Analysis
Introduction to Reactor Physics and Analysis PHGN 590
Colorado School of Mines
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This 9 page Class Notes was uploaded by Donato Hoeger Jr. on Monday October 5, 2015. The Class Notes belongs to PHGN 590 at Colorado School of Mines taught by Staff in Fall. Since its upload, it has received 22 views. For similar materials see /class/219611/phgn-590-colorado-school-of-mines in Engineering Physics at Colorado School of Mines.
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Date Created: 10/05/15
Nuclear Fundamentals Lesson 2 Agra I Semiempirical Mass Formula II Radioactivity How can we understand the systematics of the binding energetics of nuclei Nuclear binding due to nearest neighbor force only short range Nuclear saturatio gt Volume term BEVolume aV A Overcounting at surface gt Surface term BESurface aS AZ3 Coulomb repulsion of protons gt Coulomb term Long range coulomb repulsion means every pair of protons contributes to the energy Coulomb force falls like 1R a A39 3 39 z BECoulomb 30 z A13 ZlQL wiga Pauli exclusion principle gt Symmetry term 3 grim ii H WW llHllll ng L i protons neutrons nentrens Energy preferred V NOT preferred Q B 2 EHSymmetry a g Spinpairing preferred gt Pair term Energy preferred NOT preferred e 2 5 5 eveneven 3W O evenodd M 0444 5 oddodd L Semiempirical mass formula summary BE av A as A23asymNZ2A391 1V 2 13 acmA Spair LQML B Volume aV a 15 16 MeV list MeV Surface aS a 13 18 MeV 15925 Mail Symmetry a m 19 23 MeV 23235 Mar 33 Coulomb aC a 06 07 MEN 0 Mar Pair 4 a 111 MeV 20 MM semieggirt calm NW Semiempirical Mass Formula The nuclear binding energy is defined by BE Z Mproton N Mneutron MAZ I Note the assumptionof the relativistic equivalence of mass and energy Emcquot2 which allows one to measure mass in MeV I The mass of any stable nucleus can be calculated from the mass excess which is listed in Appendix C of Meyerhof By convention the ATOMIC mass excesses are tabulated instead of the NUCLEAR mass excess Thus the mass of any ATOM including the electrons is given by MatomAZ AMassExcess u where u is the atomic mass unit u93149432 MeV 1994 number The semiempirical mass formula Meyerhof Eq2127 without the shell term is In6 BEAZ avol A asurf A 23ac zz11v13 asym A 2 Z2A delta1ModA2 1 Modz2 ModAz2 A12 Note the use of ModA2 etc to satisfy the pairing condition Meyerhof p 41 I Typical values for the constants in MeV In2 constavolgt158asurfgt18asymgt235acgt72deltagt11 0ut2 avol gt 158 asurf gt 18 asym gt 235 ac gt 072 delta gt 11 semi Miricalma I Example 1 binding energy of Gold197 A197 Z79 hde Print NIBE 197 791 const MeV 155925 MeV Using appendix C of Meyerhof BE Z Mhyd N MneutAO33448 u 155889 MeV I Example 2 binding energy of Tungsten180 A180 Z74 mum Print NBE 180 741 const MeV 144844 MeV Using appendix C of Meyerhof BE Z Mhyd N MneutA05503 u 144571 MeV I Example 3 binding energy of Vanadium50 A50 Z23 h M Print NBE 50 231 const MeV 4 3 7 7 3 5 MeV Using appendix C of Meyerhof BE Z Mhyd N MneutA0 u 43462 MeV
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