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

Suppose you are using a cool mist vaporizer in a room where

Suppose you are using a cool mist vaporizer in a room where the relative humidity is 20% at 20 degrees Celsius. The room is 3 m x 3m x 2.7 m. Determine the amount of water vapor in grams and liters that must be added to ...

A plane polarized electrodynamics wave travelling in a

A plane polarized electrodynamics wave travelling in a dielectric medium of refractive index 'n' is reflected at normal incidence from the surface of a conductor. Find the phase change undergone by its electric vector if ...

Three spiders are resting on the vertices of a triangular

Three spiders are resting on the vertices of a triangular web. The sides of the triangular web have a length of a = 0.58 m, as depicted in the figure. Two of the spiders (S1 and S3) have +4.6 µC charge, while the other ( ...

The trivial file transfer protocol rfc 1350 is an

The Trivial File Transfer Protocol (RFC 1350) is an application layer protocol that uses the Stop-and-Wait protocol. To transfer a file from a server to a client, the server breaks the file into blocks of 512 bytes and s ...

1 consider r one-period model for the price of a stock s

1. Consider R one-period model for the price of a stock s: suppose Its time-0 value S0 is known, and it is known that at t i11w 7’, its value is either Su or Sd. Assume further that V is a derivative on S expiring at tim ...

Suppose that a network layer entity requests its data link

Suppose that a network layer entity requests its data link layer to set up a connection to another network layer entity. In order to setup a connection in a data link, the initiating data link entity sends a SETUP frame, ...

A child throws a penny off of the eiffel tower h 324 m

A child throws a penny off of the Eiffel tower (h = 324 m) with a downward velocity of magnitude V0 = 11 m/s.Calculate the time t, in seconds, that it takes for the penny to fall .t = ____ Find the speed at which the pen ...

Discuss the merits of the end-to-end vs hop-by-hop

Discuss the merits of the end-to-end vs. hop-by-hop approaches to providing a constant transfer delay for information transferred from a sending end system to a receiving end system.

Assume you were conducting a project on bio digester

Assume you were conducting a project on bio digester installation from pig remains and supply it to the kitchen.give a detailed procedure that you would follow using the guiding steps provided.also remember to include th ...

You plan to fly a small airplane from san jose airport to

You plan to fly a small airplane from San Jose Airport to Reno-Tahoe International Airport. Using a map you find that on the map San Jose Airport if 475 miles north and12.2 miles west of the origin, and Reno-Tahoe airpor ...

  • 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

A cola-dispensing machine is set to dispense 9 ounces of

A cola-dispensing machine is set to dispense 9 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manuf

What is marketingbullwhat is marketing think back to your

What is Marketing? • "What is marketing"? Think back to your impressions before you started this class versus how you

Question -your client david smith runs a small it

QUESTION - Your client, David Smith runs a small IT consulting business specialising in computer software and techno

Inspection of a random sample of 22 aircraft showed that 15

Inspection of a random sample of 22 aircraft showed that 15 needed repairs to fix a wiring problem that might compromise

Effective hrmquestionhow can an effective hrm system help

Effective HRM Question How can an effective HRM system help facilitate the achievement of an organization's strate