Lecture 2N

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Lecture 2N
Measuring the size of the nucleus Inelastic
electron scattering
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Diffraction round an objectVCE stuff
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Diffraction round an objectthe nucleus
Rutherford (Coulomb) scattering
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Inelastic electron scattering
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Inelastic electron scattering (in principle)
a thin target containing the nuclei
A source of high-energy (gt100MeV)
electrons. Electron LINAC
A means of measuring the angle and energy of the
elastically scattered electrons Magnetic
spectrometer
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What is an electron linear accelerator?
A means of transferring EM power to accelerate
electrons
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Electron magnetic spectrometer
Need to be able to change angle Need to measure
energy of scattered electrons. (We want only
elastically scattered electrons)
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Inelastic electron scattering
The momentum transferred to the nucleus is q ki
- kf
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Inelastic electron scattering
What is V(r) ?
and is the fourier transform of ?(r)
Form factor
Thus from experimentally measured angular
dependence of F(q) it is possible to determine
?(r).
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Inelastic electron scattering
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Inelastic electron scattering
At a given Ee, the angle of the first minimum
increases as the size (atomic number A) decreases
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Nuclear charge density distributions
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Nucleon density distributions
nucleon density is essentially the same for all
nuclei.
Nucleons do not congregate in the centre of the
nucleus, they tightly pack.
Ro 1.23 fm from electron scattering. (Ro might
be considered the radius of a nucleon)
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Nucleon density distributions
Ro 1.23 fm
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• Nucleons do not bunch up in the centre of the
  nucleus.
• That is the nucleon density is approx. constant

Conclusion The nuclear force has a short-range
attractive potential, with a strong repulsive
core.
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Chart of stable nuclei
For heavier nuclei NgtZ
For light nuclei NZ
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Distribution of A N and Z for stable nuclei
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Nuclear Binding Energies
1 atomic mass unit (amu) 1/12th of the mass of
an ATOM of 12C
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Measuring nuclear masses The mass spectrometer
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Binding energy of 12C
6 p _at_ 1.0072766 6.0436596 amu
6 n _at_ 1.0086654 6.0519924 amu
6 e _at_ 0.0005486 0.0032916 amu
Sum of parts 12.0989436 amu!!! compare
12.00000 amu (mass of 12C atom)
About 1 of the mass of components has
disappeared.
The 6 protons and 6 neutrons are bound with an
energy of 96 MeV.
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Binding energy versus fundamentality
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Separation energy S.
Sn m(A-1, Z) mn - m(A, Z)
consider 40Ca m(40Ca) 39.962591 amu m(39Ca)
38.970718 amu m (n) 1.008665 amu
39.979383 amu
  so Sn 0.016792 amu (x 931.480 MeV/c2)
15.64 MeV
This is also the threshold energy for the
photoneutron reaction   40Ca ? ? 39Ca
n
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Neutron Separation Energies for Ca Isotopes
isotope Neutron No.
Sn(MeV) (97) 40Ca 20 15.7 (7x104
yr) 41Ca 21 8.4 (0.64) 42Ca 22 11.5 (0.15
) 43Ca 23 7.0 (2.1) 44Ca 24 11.1 (3
yr) 45Ca 25 7.4 (3.3) 46Ca 26 10.4 (5
day) 47Ca 27 7.3 (0.19) 48Ca 28 9.9 (10
min) 49Ca 29 5.1
Ave 7.5 MeV Ave 10.7 MeV
? pairing energy 3.2 MeV
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Current summary of properties of the Nuclear Force