Binding Energy 3 3 Binding Energy The binding
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 -- • is the nuclear mass (no electrons) • BE defined as -- • BE is always > 0.
• To calculate the BE, we do not know nuclear masses. Therefore, use isotopic masses -- http: //www. physics. valpo. edu/phys. Links/atomic. Nuclear. Links. html
• To calculate isotopic masses from --
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?
Semi-empirical BE equation • Consistent with short-range force; nearly contact interaction. • But nucleons on surface are less strongly bound - • Surface unbinding -
Semi-empirical BE equation • Coulomb force from all protons - • This effect can be calculated exactly from electrostatics - • Coulomb unbinding -
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
Semi-empirical BE equation Z=N Z<N For Z < N, there is an increased energy equal to -- Energy jump for each proton p n # of protons
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 --
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 calculate BE for any nuclide (Z, A).
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 the separation energies.
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/phys. Links/atomic. Nuclear. Links. html
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