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5-Liquid drop model and SEMF (Liquid Drop model (Describes nuceus as a…
5-Liquid drop model and SEMF
Liquid Drop model
Describes nuceus as a drop of nuclear fluid
Spherical
incompressible
Short range force
Like intermolecular force
Matches the radius
+ve Surface tension energy
Assumes fluid is not rotating
Attractive at similar separations to their size, repulsive at very short separations
Evenly distributed charge throughout drop
Gets 3 terms
Different terms in liquid drop
Surface energy
Allows for assumption that the outer nucleons are less bound
Greatest effect on small nuclei (more nucleons near the surface)
Electrostatic Energy
From positively repelling nuclei
Assume even distribution of protons in spherical nucleus
Use charge density and electrostatic potential
Bends down curve at higher A, giving a peak in B/A curve
Volume
Main term
only +ve term
Associated with the short range force pulling the nuclei together
Constant (proportional to A)
Extra terms in semf
Asymmetry
Asymmetric wavefunctions
Nuclei more stable if there are roughly the equal numbers of neutrons and protons
Assume spacing between energy levels is constant and proportional to the volume
Pairing
From pauli exclusion principle
Favourable to have pairs of opposite spin identical nuclei
So if both in pairs, +ve, if both not, -ve
At this stage they come from observation of data
SEMF
Advantages
Still an approximation
Good fit to BE curve
Predictions for energy release in nuclear decay
Allows existence of nuclear fission
Does not explain spikes in BE curve, nuclei shapes, spin, parity and magnetic moment