The neutrino must have a spin of 1 2 .

Question

An Erbium-166 nucleus contains 68 protons. The atomic mass of a neutral Erbium-166 atom is 165.930u, where u = 931.5 MeV/c². In this question you may use that the mass of a proton is 938.27 MeV/c², the mass of a neutron is 939.57 MeV/e² and the mass of an electron is 0.511 MeV/c². i. Calculate the nuclear binding energy per nucleon, giving your answer in units of MeV. ii. Electrons with an energy of 0.5 GeV are scattered off the nucleus. Estimate the scattering angle of the first minimum in the resulting diffraction pattern. iii. Briefly comment on whether or not you expect this nucleus to be spherical, and what consequence this has for excited states of the nucleus in the collective model.

Answer 1

Question

Chapter 13, Problem 17Q

To determine

The neutrino must have a spin of 12.

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An Erbium-166 nucleus contains 68 protons. The atomic mass of a neutral Erbium-166 atom is 165.930u, where u = 931.5 MeV/c². In this question you may use that the mass of a proton is 938.27 MeV/c², the mass of a neutron is 939.57 MeV/e² and the mass of an electron is 0.511 MeV/c². i. Calculate the nuclear binding energy per nucleon, giving your answer in units of MeV. ii. Electrons with an energy of 0.5 GeV are scattered off the nucleus. Estimate the scattering angle of the first minimum in the resulting diffraction pattern. iii. Briefly comment on whether or not you expect this nucleus to be spherical, and what consequence this has for excited states of the nucleus in the collective model.

(a) (b) (c) 1. Consider a system with two spin ½ particles in a four-dimensional basis |s₁m₁₂m₂ >: 1 1 1 1 2'2'2'2 (d) |4₁ >= |4₁₂ >= |4₁ >= |4₁₂ >= >= xi xi 1 1 1 -1 1 -1 1 1 2' 2 '2'2 >= x+xz where x and x are the eigenspinors of the operator Ŝ₂. The indices 1 and 2 refer to particle 1 and particle 2, respectively. In addition, 1 -1 1-1 2' 2 '2 Xi x > = X₁ X₂ S₁ is the spin operator of particle 1. $₂ is the spin operator of particle 2. Ŝ is the total spin operator: S = S₁ + S₂. Find the matrix representations of S1z, Szz, S2, and $2 in the four-dimensional basis |Yn >. Hint: make a table. Find the matrix representations of the total spin operators S² and S₂ in the basis |Yn >. Find the normalized eigenspinors and eigenvalues of $² and Ŝ₂. Congratulations: you just derived the Clebsch Gordon coefficients in a way that is different from the method used in Griffiths. Explain! Indicate degeneracies. Using the eigenspinors of Ŝ² and $₂ representations of Ŝ² and S₂ as your new basis, write…

What is the magnitude of the repulsive electrostatic force between two protons in a nucleus? Consider the distance between the centers of the protons to be 3.5 x 10^-13 m.If these protons were released from rest, Calculate the magnitude of their initial acceleration?