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

Fatty deposits in blood vessels pose a health risk chemical

Fatty deposits in blood vessels pose a health risk. Chemical agents added to the blood can increase the solubility of the fatty deposits in blood, thereby providing a means to dissolve the fatty deposits in situ. To expl ...

The wetted-well column shown in figure 304 is used to

The wetted-well column shown in Figure 30.4 is used to humidify a pressurized air stream. Bone-dry air (containing no water vapor) at 2.0 atm and 27°C is introduced to the bottom of the column at a volumetric flow rate o ...

In 2011 the greenland ice sheet was melting at a rate

In 2011, the Greenland Ice Sheet was melting at a rate between 82 and 224 cubic km per year. (a) What derivative does this tell us about? Define the function and give units for each variable. (b) What numerical statement ...

The bay of fundy in canada has the largest tides in the

The Bay of Fundy in Canada has the largest tides in the world. The difference between low and high water levels is 15 meters (nearly 50 feet). At a particular point the depth of the water, y meters, is given as a functio ...

Find the most probable code word in the case where the

Find the most probable code word in the case where the normalized likelihood is (0.2, 0.2, 0.9, 0.2, 0.2, 0.2, 0.2). Also find or estimate the marginal posterior probability for each of the seven bits, and give the bit-b ...

Name some recent educational innovations and evaluate their

Name some recent educational innovations and evaluate their effectiveness. Do you think that schools would be more effective if they did not have comply with bureaucratic redtape? For example, if schools did not need app ...

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 ...

The area of the earths surface is approximately 516 x 106

The area of the Earth's surface is approximately 516 X 106 km2. What is the weight of the entire atmosphere in tonnes? Express your answer using scientific notation, in units of 1012 tonnes

One of the important advantages in using spice to solve

One of the important advantages in using SPICE to solve transmission-line problems is that it will readily give the solution for problems that would be difficult to solve by hand. For example, consider the case of two CM ...

A 349 rads 33rpm record has a 503-khz tone cut in the

A 3.49 rad/s (33rpm) record has a 5.03-kHz tone cut in the groove. If the groove is located 0.100 m from the center of the record (see drawing), what is the "wavelength" in the groove?

  • 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