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

Diffraction scattering q = momentum transfer

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

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?

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

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

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

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)

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?

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

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?

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

Coulomb Energy Differences Calaulate the Coulomb energy of the charge distribution directly Consider mirror nuclides: Measure EC; How? Assume R is same for both nuclides. Why?

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