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Measurement of nuclear radius

Measurement of nuclear radius. Four methods outlined for charge matter radius: Diffraction scattering Atomic x-rays Muonic x-rays Mirror Nuclides. Measurement of nuclear radius. Three methods outlined for nuclear matter radius: Rutherford scattering Alpha particle decay -mesic x-rays.

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Measurement of nuclear radius

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  1. Measurement of nuclear radius • Four methods outlined for charge matter radius: • Diffraction scattering • Atomic x-rays • Muonic x-rays • Mirror Nuclides

  2. Measurement of nuclear radius • Three methods outlined for nuclear matter radius: • Rutherford scattering • Alpha particle decay • -mesic x-rays

  3. Diffraction scattering • q = momentum transfer

  4. Diffraction scattering • Measure the scattering intensity as a function of  to infer the distribution of charge in the nucleus,

  5. Diffraction scattering • Measure the scattering intensity as a function of  to infer the distribution of charge in the nucleus • is the inverse Fourier transform of • is known as the form factor for the scattering. • c.f. Figure 3.4; what is learned from this?

  6. Diffraction scattering • Density of electric charge in the nucleus is ≈ constant

  7. Diffraction scattering • The charge distribution does not have a sharp boundary • Edge of nucleus is diffuse - “skin” • Depth of the skin ≈ 2.3 f • RMS radius is calculated from the charge distribution and, neglecting the skin, it is easy to show

  8. Atomic X-rays • Assumethe nucleus is uniform charged sphere. • Potential V is obtained in two regions: • Inside the sphere • Outside the sphere

  9. Atomic X-rays • For an electron in a given state, its energy depends on - • Assume does not change appreciably if Vpt Vsphere • Then, E = Esphere - Ept • Assume can be giving (3.12)

  10. Atomic X-rays • E between sphere and point nucleus for • Compare this E to measurement and we have R. • Problem! • We will need two measurements to get R -- • Consider a 2p 1s transition for (Z,A) and (Z,A’) where A’ = (A-1) or (A+1) ; what x-ray does this give?

  11. Atomic X-rays • Assume that the first term will be ≈ 0. Why? • Then, use E1s from (3.13) for each E1s term. Why?

  12. Atomic X-rays • This x-ray energy difference is called the“isotope shift” • We assumed that R = Ro A1/3. Is there any authentication? • How good does your spectrometer have to be to see the effect? • We assumed we could use hydrogen-line 1s wavefunctions Are these good enough to get good results? • Can you use optical transitions instead of x-ray transitions?

  13. Muonic X-rays • Compare this process with atomic (electronic) x-rays: • Similarities • Differences • Advantages • Disadvantages • What is ao? • Pauli Exclusion principle for muons, electrons?

  14. Coulomb Energy Differences • Calaulate theCoulomb energyof the charge distribution directly Considermirror nuclides: MeasureEC; How? AssumeR is same for both nuclides. Why?

  15. Measurement of nuclear radius • Three methods outlined for nuclear matter radius: • Rutherford scattering • Alpha particle decay • -mesic x-rays

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