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

If adult children help pay for household expenses take over

If adult children help pay for household expenses, take over physically demanding chores, and care for their aging parents who get sick or need assistance, child-parent relationships generally

A mad doctor believes that baldness can be cured by warming

A mad doctor believes that baldness can be cured by warming the scalp with sound waves. His patients sit underneath the Bald-o-Matic loudspeakers, where their heads are bathed with 91dB of soothing 800Hz sound waves. Sup ...

A small statue is recovered in an archaeological dig its

A small statue is recovered in an archaeological dig. Its weight is measured to be 63.7lb and its volume 0.09ft3. (a) What is the statue's weight density? (b) What substance is it, most likely?

Two circular discs both with radius a are parallel with

Two circular discs, both with radius a, are parallel with mutual distance d, such that their centers are situated on a line orthogonal to the discs. The volume between the discs is filled with oil with viscosity η. One d ...

Since the 1950s the carbon dioxide concentration in the air

Since the 1950s, the carbon dioxide concentration in the air has been recorded at the Mauna Loa Observatory in Hawaii.4 A graph of this data is called the Keeling Curve, after Charles Keeling, who started recording the d ...

In no less than 100 words what are some of the differences

In no less than 100 words What are some of the differences between "attitudes" and "beliefs," as described in Ch. 4 of the text?

An electron with electric charge ofnbsp16nbspnbsp10-19nbspc

An electron with electric charge of 1.6  10 -19  C falls through a potential difference of 29 kV in the vacuum of an X-ray tube. What is the kinetic energy of the electron, assuming it started from rest and that there is ...

What is the fraction of the electron states occupied by

What is the fraction of the electron states occupied by electrons at an energy of E-E F +0.0455eV at T=300K? Use the very accurate value of the Boltzmann constant. What is the fraction of these states occupied by holes ( ...

A flat steel plate is 20 m length and 20 m width initially

A flat steel plate is 2.0 m length and 2.0 m width initially contains a very thin coating of lubricating oil used in a manufacturing process. An engineer is considering the feasibility of using hot forced air convection ...

Consider the steady-state diffusion of a solute through a

Consider the steady-state diffusion of a solute through a membranous sphere as shown in Figure6.35 (not given). Such a situation occurs when drugs are released from liposomes. The membrane is defined by the region betwee ...

  • 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

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

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen