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)
 Zeeshan Anjum
 Zeeshan rauf
 Imran Khalid
 Sadam Hussain
 Kaleem ullah Mughal
 Zohaib Arshad
5th semester session 2013-17
2The Islamia University of Bahawalpur Department of PHYSICS

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The Islamia University of Bahawalpur Department of PHYSICS

4. Insert title text here
 What is coupling?
 Coupling is the act of combining two things.
 Couplings are mechanical elements that ‘couples’ two drive elements which
enables motion to be transferred from one element to another.
 In order to transmit torque between two shafts that either tend to lie in the same
line or slightly misaligned, a coupling is used.
 Of special interest is the coupling of two (or more) vibratory systems (e.g.
resonant circuits) by means of springs or magnetic fields
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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
In physics, two systems are coupled if they are interacting with each
other.

6. Russell-Saunders Coupling
 Russell-Saunders of L-S coupling notation for atomic states is a system of
notating observed states for atoms, based upon a particular conception of
the angular momentum possessed by each state, and the sources of such
angular momenta in the atom.
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)
 If more than one source of angular momentum (spin or orbital
motion contributes to A.M), we will only observe the total angular
momentum from this source included
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8. Russell-Saunders Coupling
 Different sources = Spin angular momentum &
Orbital angular momentum
 The total angular momentum of an atom (a
vector J) can be shown to be consistent with
the vector addition of all the various sources of
angular momentum in the atom.
 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.
 Here we’ll discuss the angular momentum for many electron
system.
 When more than one electron contributes orbital and spin angular
momenta to the total angular momentum J of an atom J is still the
vector sum of these individual momenta.
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10. Quantum numbers:
o Principal Quantum number (n).
o Orbital angular momentum quantum number (l).
o Magnetic Quantum number (m).
o Spin Quantum number(m).
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11. Quantum numbers:
 The principal quantum number (n) describes the size of the orbital.
 The angular quantum number (l) describes the shape of the orbital.
 The magnetic quantum number (m) describe the orientation in space
of a particular orbital.
 The Spin quantum number (m) describe the spin.
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12. Russell-Saunders Coupling
 In this scheme, the usual pattern for all atoms is that the orbital angular
momenta L of the various electrons are coupled together into a single
resultant L(combine vectorially).
 The spin angular momenta si are also coupled together into another single
resultant s.
𝐿 = 𝐿1 + 𝐿2 + 𝐿3 + ⋯ … … …
𝑆 = 𝑆1 + 𝑆2 + 𝑆3 + ⋯ … … …
Finding total Angular momentum:
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13. Russell-Saunders Coupling
 The momenta L and S then interact via the spin-orbit effect to form the
total angular momentum J. This scheme is called LS coupling.
• The momenta L and S combine to form the total angular momentum J as
𝐽 = 𝐿 + 𝑆
Finding total Angular momentum:
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14. Russell-Saunders Coupling
 For a given value of L, the allowed values of J are
𝐽 = 𝐿 + 𝑆 , 𝐿 + 𝑆 − 1 , … . , |𝐿 − 𝑆|
 When two orbital angular momenta having quantum numbers l1 and l2
combine, the allowed values of L are
𝐿 = 𝑙1 + 𝑙2 , 𝑙1 + 𝑙2 − 1 , … . . , |𝑙1 − 𝑙2|
 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:
 For a two electron system (s1=s2=1/2), the total spin angular momentum
quantum number S=0 (spin antiparallel) or 1 (spin parallel). When S=0, we have
2S+1=1 and such states are referred to as singlet states.
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:
 To describe states conveniently, one requires a notation. The symbol n Lj used
for a single electron is changed as follows.
 State symbol or Term symbol = n 2S+1Lj
Where,
The superscript 2S+1 represents the multiplicity of the state,
Subscript J is the total angular momentum quantum number, and
L stand for S,P,D,…….
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17. J-J Coupling
Difference in J-J coupling, compared with L-S:
 In J-J coupling l and s for each electron combine to form a separate J and all
the J-vectors are then vectorially added to form J. Thus for each active
electron J1=l1 + s1; J2=l2 +s2; J3=l3 + s3,……etc. and J=J1 + J2 + J3 + … = ∑Ji. This
coupling scheme is known as J-J coupling which is distinctly different from
L-S coupling scheme.
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18. Russell-Saunders Coupling
 if S=1/2, L=1, J=3/2, 1/2. The corresponding states will be 2P3/2 and 2P1/2, read as
doublet P three halves and doublet P half.
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 & Shubhra Kakani.
 Physics of atoms and molecules by B. H. Bransden and 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 4D5/2. 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)
 Zeeshan Anjum
 Zeeshan rauf
 Imran Khalid
 Sadam Hussain
 Kaleem ullah Mughal
 Zohaib Arshad
5th semester session 2013-17
25The Islamia University of Bahawalpur Department of PHYSICS

26. Thankyou
Good Bye for now
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