Quadrupole moments in the shell model

Assignment Help Physics
Reference no: EM13884

1. The ground state of  543_Quadrupole moments in the shell model.pnghas jΠ = 3/2-1 The first excited state at 67.4 keV has jΠ = 1/2-1 and the second excited state at 283.0 keV has List the possible γ -ray transitions between these levels and give their type. Estimate the half-life of the state jΠ = 1/2- using the Weisskopf approximation. How does this compare to the  measured half-life of 23 ps?

2. Quadrupole moments in the shell model. We will calculate an estimate of the quadrupole moment for the special case of a single proton moving in an orbital around a closed shell spherical core. So the only contribution to the quadrupole moment is from this single proton. We will also assume that the proton moves in an orbital with j = l + 1/2 . The space wave function of the proton is

1282_Quadrupole moments in the shell model2.png

where Y is the spherical harmonic, and R is the radial part of the wave function. They are normalized. i.e.

1691_Quadrupole moments in the shell model3.png

(a) Since s mj = m1 + m2, what must m1 and ms be if mj = j? 

(b) Show that the quadrupole moment, when m = j, is given by

1934_Quadrupole moments in the shell model4.png

To do this start with the quadrupole moment given by 193_Quadrupole moments in the shell model5.png.

Write the quadrupole moment operator in terms of Y20 and use the integral,

1747_Quadrupole moments in the shell model6.png

(c) Apply this result to the ground state of 2379_Quadrupole moments in the shell model7.png, which has jΠ = 7/2-1. Write the configuration for this ground state and confirm that the condition of j = l + ½ holds. Estimate (r2) using r = 1.2 A1/2 . Compare your result to the measured quadrupole moment of -0.156 ± 0.003 b.

(d) Apply this result to the ground state of 917F, which has jΠ = 5/2+. Compare your result to the measured quadrupole moment of 5.8 ± 0.4 fm2.

Reference no: EM13884


Write a Review

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd