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Binding Energy

Binding Energy. 3.3 Binding Energy. The binding energy of a nucleus is the energy required to separate all of the constituent nucleons from the nucleus so that they are all unbound and free particles. This implies that -. And, of course, the mass-energy --

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Binding Energy

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  1. Binding Energy

  2. 3.3 Binding Energy • The binding energy of a nucleus is the energy required to separate all of the constituent nucleons from the nucleus so that they are all unbound and free particles. • This implies that -

  3. And, of course, the mass-energy -- • is the nuclear mass (no electrons) • BE defined as -- • BE is always > 0.

  4. To calculate the BE, we do not know nuclear masses. Therefore, use isotopic masses -- http://www.physics.valpo.edu/physLinks/atomicNuclearLinks.html

  5. To calculate isotopic masses from  --

  6. Separation Energies & Systematic Studies • Table 3.1 - Can you see any pattern(s)? • Figure 3.16 - Describe significant features • Consider the physics that might give rise to Figure 3.16 -- can we develop a model that would describe Figure 3.16?

  7. Semi-empirical BE equation • Consistent with short-range force; nearly contact interaction. • But nucleons on surface are less strongly bound - • Surface unbinding -

  8. Semi-empirical BE equation • Coulomb force from all protons -- • This effect can be calculated exactly from electrostatics - • Coulomb unbinding -

  9. Semi-empirical BE equation • Systematic studies show that the line of stability moves from Z = N to N > Z Why? • Coulomb force demands this -- but -- • The asymmetry introduces a nuclear force unbinding -- See next slide Empirical

  10. Semi-empirical BE equation Z = N Z < N For Z < N, there is an increased energy equal to -- Energy jump for each proton # of protons p n p n

  11. Semi-empirical BE equation • Systematic studies show like nucleons want to pair and in pairs are more stable (lower energy) than unpaired. • Therefore, we add (ad hoc) a pairing energy --

  12. Semi-empirical BE equation • Combined equation for total BE is -- • Systematic BE data are fit with this function giving - • Using these values of the parameters, one can then calculateBE for any nuclide (Z,A).

  13. Semi-empirical mass equation • The isotopic mass of any nucleus can be calculated using the definition of the BE - but calculating the BE from the semi-empirical equation: • And, at constant A, one can find the value of Z at which the mass is a minimum (Zmin) - (3.30) • One can also calculate theseparation energies.

  14. Semi-empirical mass equation • BE(Z) is a parabolic function of Z at constant A (isobar!) • This curve has a maximum stability against decay. • The corresponding has a minimum at stability. • One curve if A is odd; two curves if A is even. (?) • Separation between the curves is -- 2 • With this semi-empirical model, one can --- • Calculate Q (energy) for decay schemes (, , , , p, n, fission) • Q > 0  decay is possible • Q < 0  decay is not possible • Put semi-empirical mass equation into Excel and calculate all of the masses in an isobar for a range of Z values. http://www.physics.valpo.edu/physLinks/atomicNuclearLinks.html

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