Ls coupling presentation

Russal Saunders coupling, L-s coupling, J-J coupling, Spin orbital coupling

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2. Russell-Saunders Coupling
Presentation by:
Group : Champions
Group members:
M. Usman Mustafa (Group leader)
ZeeshanAnjum
Zeeshanrauf
Imran Khalid
SadamHussain
KaleemullahMughal
ZohaibArshad
5
th
semester session 2013-17
2The IslamiaUniversity of BahawalpurDepartment of PHYSICS

3. 3
The IslamiaUniversity of BahawalpurDepartment of PHYSICS

4. Insert title text here
What is coupling?
Couplingistheactofcombiningtwothings.
Couplingsaremechanicalelementsthat‘couples’twodriveelementswhich
enablesmotiontobetransferredfromoneelementtoanother.
Inordertotransmittorquebetweentwoshaftsthateithertendtolieinthesame
lineorslightlymisaligned,acouplingisused.
Ofspecialinterestisthecouplingoftwo(ormore)vibratorysystems(e.g.
resonantcircuits)bymeansofspringsormagneticfields
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5. Russell-Saunders Coupling
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Coupling in Physics
•There are two types of coupling
•L-S coupling & J-J coupling
Inphysics,twosystemsarecouplediftheyareinteractingwitheach
other.

6. Russell-Saunders Coupling
Russell-SaundersofL-Scouplingnotationforatomicstatesisasystemof
notatingobservedstatesforatoms,baseduponaparticularconceptionof
theangularmomentumpossessedbyeachstate,andthesourcesofsuch
angularmomentaintheatom.
What is L-S coupling notation :
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7. Russell-Saunders Coupling
Total angular Momentum of an atom
Total angular momentum associated with the
atom is measured along its projection along
observation axis (z-axis)
Ifmorethanonesourceofangularmomentum(spinororbital
motioncontributestoA.M),wewillonlyobservethetotalangular
momentumfromthissourceincluded
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8. Russell-Saunders Coupling
Different sources = Spin angular momentum &
Orbital angular momentum
Thetotalangularmomentumofanatom(a
vectorJ)canbeshowntobeconsistentwith
thevectoradditionofallthevarioussourcesof
angularmomentumintheatom.
Total angular Momentum of an atom
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9. Russell-Saunders Coupling
Total angular Momentum of an atom
Contributions come from various sources that “couple” or combine
together to give the resulting total.
Herewe’lldiscusstheangularmomentumformanyelectron
system.
Whenmorethanoneelectroncontributesorbitalandspinangular
momentatothetotalangularmomentumJofanatomJisstillthe
vectorsumoftheseindividualmomenta.
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10. Quantum numbers:
oPrincipal Quantum number (n).
oOrbital angular momentum quantum number (l).
oMagnetic Quantum number (m).
oSpin Quantum number(m).
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11. Quantum numbers:
Theprincipalquantumnumber(n)describesthesizeoftheorbital.
Theangularquantumnumber(l)describestheshapeoftheorbital.
Themagneticquantumnumber(m)describetheorientationinspace
ofaparticularorbital.
TheSpinquantumnumber(m)describethespin.
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12. Russell-Saunders Coupling
Inthisscheme,theusualpatternforallatomsisthattheorbitalangular
momentaLofthevariouselectronsarecoupledtogetherintoasingle
resultantL(combinevectorially).
The spin angular momenta s
iare also coupled together into another single
resultant s.
??????=??????
1+??????
2+??????
3+⋯………
??????=??????
1+??????
2+??????
3+⋯………
Finding total Angular momentum:
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13. Russell-Saunders Coupling
ThemomentaLandStheninteractviathespin-orbiteffecttoformthe
totalangularmomentumJ.ThisschemeiscalledLScoupling.
•ThemomentaLandScombinetoformthetotalangularmomentumJas
??????=??????+??????
Finding total Angular momentum:
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14. Russell-Saunders Coupling
ForagivenvalueofL,theallowedvaluesofJare
??????=??????+??????,??????+??????−1,….,|??????−??????|
Whentwoorbitalangularmomentahavingquantumnumbersl
1andl
2
combine,theallowedvaluesofLare
??????=??????
1+??????
2,??????
1+??????
2−1,…..,|??????
1−??????
2|
Similarly the allowed values are calculated for S and J.
For L>S, there are 2S+1 values of J.
For L<S, the number of possible values of J are 2L+1.
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15. Russell-Saunders Coupling
The value of 2S+1 is called the multiplicity of the state.
Multiplicity of state:
Foratwoelectronsystem(s
1=s
2=1/2),thetotalspinangularmomentum
quantumnumberS=0(spinantiparallel)or1(spinparallel).WhenS=0,wehave
2S+1=1andsuchstatesarereferredtoassingletstates.
Singlet state:
Triplet state:
when S=1 and 2S+1=3, these are referred to as triplet state.
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16. Russell-Saunders Coupling
Term symbol of the state:
Todescribestatesconveniently,onerequiresanotation.ThesymbolnL
jused
forasingleelectronischangedasfollows.
State symbol or Term symbol = n
2S+1
L
j
Where,
Thesuperscript2S+1representsthemultiplicityofthestate,
SubscriptJisthetotalangularmomentumquantumnumber,and
LstandforS,P,D,…….
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17. J-J Coupling
Difference in J-J coupling, compared with L-S:
InJ-JcouplinglandsforeachelectroncombinetoformaseparateJandall
theJ-vectorsarethenvectoriallyaddedtoformJ.Thusforeachactive
electronJ
1=l
1+s
1;J
2=l
2+s
2;J
3=l
3+s
3,……etc.andJ=J
1+J
2+J
3+…=∑J
i.This
couplingschemeisknownasJ-Jcouplingwhichisdistinctlydifferentfrom
L-Scouplingscheme.
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18. Russell-Saunders Coupling
ifS=1/2,L=1,J=3/2,1/2.Thecorrespondingstateswillbe
2
P
3/2and
2
P
1/2,readas
doubletPthreehalvesanddoubletPhalf.
How to read L-S coupling notation ?
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19. Russell-Saunders Coupling
Modern Physics by G. Aruldhas(university of kerala) & P. Rajagopal
(Mahatma Gandhi University).
Principles of Modern Physics by Ajay K Saxena.
Modern Physics by S. L. Kakani& ShubhraKakani.
Physics of atoms and molecules by B. H. Bransdenand C. J. Joachain.
Wikipedia
Reference:
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22. Russell-Saunders Coupling
Any Question
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23. Russell-Saunders Coupling
Can anyone define…….
What would you understand by the term Doublet state?
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24. Russell-Saunders Coupling
Can any one solve it down?
A state is denoted as
4
D
5/2. Find,
(i) what are the values of L, S and J?
(ii) What is the minimum number of electrons which could give rise to this?
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25. Russell-Saunders Coupling
Presentation by:
Group :Champions
Group members:
M. Usman Mustafa (Group leader)
ZeeshanAnjum
Zeeshanrauf
Imran Khalid
SadamHussain
KaleemullahMughal
ZohaibArshad
5
th
semester session 2013-17
25The IslamiaUniversity of BahawalpurDepartment of PHYSICS

26. Thankyou
Good Bye for now
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