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.

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Presentation transcript:

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 --

To calculate isotopic masses from  --

Separation Energies & Systematic Studies Table Can you see any pattern(s)? Figure Describe significant features Consider the physics that might give rise to Figure 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 pnpn Z < N For Z < N, there is an increased energy equal to -- Energy jump for each proton # 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 (Z min ) - (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.