Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

Ask Physics Expert

problem1) The ground state of 6128Ni has  jπ=3/2‾ . The first excited state at 67.4 keV has jπ=5/2‾ and the second excited state at 283.0 keV hasjπ=1/2‾ . List the possible γ-ray transitions between these levels and give their type. Estimate the half-life of the jπ=1/2‾state using the Weisskopf approximation. How does this compare to the measured half-life of 23 ps?
Quewstion2) Quadrupole moments in the shell model. We will find out 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 + ½ . The space wave function of the proton is

Ψj,mj= R(r) Yl,m(Θ,φ)

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

∫Y*l,ml Yl,ml dΩ=1 & R*Rr2 dr=1
a) Since mj = ml ms , what must ml and ms be if mj = j?
b) Show that the quadrupole moment, when mj = j, is given by

Q=2>(2j-1/2j+2)dΩ= (5/4π)1/2 l(/2l+3)
To do this start with the quadrupole moment given by Q ∫Ψ*j,j (3z2-r2) Ψj,j dv. prepare the quadrupole moment operator in terms of Y20 and use the integral,

∫Y*l,lY2,0Yl,l
(c) Apply this result to the ground state of  4121Sc , which has jπ=7/2‾. prepare the configuration for this ground state and confirm that the condition of j = l + ½ holds. Estimate 2>using 1.2A1/3 . Compare your result to the measured quadrupole moment of-0.156 ±0.003 b.
d) Apply this result to the ground state of 179F , which has jπ=5/2+ Compare your result to the measured quadrupole moment of 5.8 ±0.4 fm2 (note that this measurement does not determine the sign of the quadrupole moment, only the magnitude).
problem3) The deuteron wave function may be written |ΨD> a|3S1> b|3D1>where as states are all normalized i.e. <ΨDD> <3S1|3S1> =1 and |3D1|3D1>=1
Find b2 such that |ΨD> reproduces the known magnetic moment of the deuteron,μ=.857μN. Use the result that for J = 1,
2s'+1L'j|Û|2s+1Lj {1/2(Σ+1/2)+1/4(Σ-1/2)[S(S+1)-L(L+1)]}δs's L'LμN where (μp +μn)/μN.
problem4) A “simple” model of the deuteron. Consider a 3-dim square well of radius r0 and depth V0. i.e. V(r) = –V0 for r < r0, V(r) = 0 for r > r0. The two particles interact via this potential and have a binding energy EB, so the total energy is E = –EB. Converting to a centre of mass system we find that the radial equation for S-states (l = 0) is

d2u/dr2 + k2u=0 where k2 =2μ/?2(E-V(r))

and μ=mpmn/mp+mn is the reduced mass

and Ψ(r)=(u(r)/r) Y00 (Θ,φ) (u(r)/r)(1/√4π)

a) Show that u(r) Asin(k1,r) with k1 =√2μ(V0-EB)/?

u(r)=Be-k2r with k2 =√2μEB for r > r0
where A and B are constants.

(b) Apply boundary conditions to u(r) and obtain a relation between k1, k2, and r0 that does not involve A and B.

(c) If r0 = 2.4 fm (the diameter of the deuteron), how deep is the potential well (V0) to give the experimental binding energy of 2.225 MeV. (Note: you will have to solve an equation of the form tan(ak) =bk for k. You can do this
graphically, by using successive approximations, or by using a program
such as maple, whatever works for you.)

(d) If the wavefunction Ψ(r ) is normalized i.e. ∫ Ψ(r )2 dv=1 it can be shown that
A= [2k2 /(1+r0k2)]1/2 and B Aek2 r0 [(V0-EB)/v0]1/2 .
Find the probability that the nucleons will be found outside the range of the potential i.e. r > r0. Does the answer surprise you?

Physics, Academics

  • Category:- Physics
  • Reference No.:- M91280

Have any Question? 


Related Questions in Physics

A piece of ice of mass 10g is added to water of mass 50g in

A piece of ice of mass 10g is added to water of mass 50g in a copper calorimeter of mass 60g. The temp of water falls from 10c to 5c after addition of ice. Find the specific latent heat of fusion

The technique of interleaving which allows bursts of errors

The technique of interleaving, which allows bursts of errors to be treated as independent, is widely used, but is theoretically a poor way to protect data against burst errors, in terms of the amount of redundancy requir ...

A truck travels due east for a distance of 14 km turns

A truck travels due east for a distance of 1.4 km, turns around and goes due west for 6.9 km, and finally turns around again and travels 2.5 km due east. (a) What is the total distance that the truck travels? (b) What ar ...

The blood flow speed through an aorta with a radius of 1 cm

The blood flow speed through an aorta with a radius of 1 cm is 0.28 m/s. if hardening of the arteries causes the aorta to be constricted to a radius of 0.8 cm, what is the new blood flow speed?

A solar cell panel is attached to the exterior of an

A solar cell panel is attached to the exterior of an orbiting satellite which can be considered a vacuum. The panel is initially in the shadows. It is suddenly exposed to the sun-light. Describe the transient events that ...

In this chapter we constrained all our hyperplanes to go

In this chapter we constrained all our hyperplanes to go through the origin. In this exercise, we remove this constraint. How many regions in a plane are created by N lines in general position?

In no less than 100 words- are leaders born or made is

In no less than 100 words- Are leaders born or made? Is leadership more a matter of personal characteristics or a collection of specific behaviors anyone can learn?

A find the tangent line approximation to cos x at x pi4b

(a) Find the tangent line approximation to cos x at x = π/4. (b) Use a graph to explain how you know whether the tangent line approximation is an under- or overestimate for 0 ≤ x ≤ π/2. (c) To one decimal place, estimate ...

1 using the expression for the gradient in polar

1. Using the expression for the gradient in polar coordinates (Appendix A), find the gradient of ψ(r,θ) when Where is the gradient maximum? The terms A and a are constant. 2. Given the following expression for the pressu ...

With the ability to measure the motion of land masses

With the ability to measure the motion of land masses, continental drift has become an established fact. The North American and European continents are drifting apart at a rate of about 3 cm per year. At this rate how lo ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

WalMart Identification of theory and critical discussion

Drawing on the prescribed text and/or relevant academic literature, produce a paper which discusses the nature of group

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro