Nuclear Forces

  Nuclear Forces

[ 1 ] Nuclear Forces :

 

- The First Glimpse Of The Extince And Nature Of Nuclear Force

  Came From The Rutherfrd Scettering Of Alpha Particles.

- At Small Impact Parameter Values When The Alpha Particales

  Get's Very Close To The Target Nuclei And The Cross Section

  Begin To Deviate Significantly From The Coulomb Scettering.

- Exstence Of A New And Strong Attractive Force Becmes

  Apparent From The Following Properties Of Nuclear Force On

  The Basis Of Various Observations And Emprirical Facts.

 

(1) Nuclear Forces Is Always Attractive :

- Between Two Neutrons ,Between Two Protons And Between

  Neutron And Proton.

- Existence Of Neuteons And Protons In A Bound Stae Is It'sself

  An Evidence Of This.

 

(2) Nuclear Force Is Short Ranged :

- If It Were Not So ,Alll The Nucleons In Different Nuclei Will

  Coalesce Into One Big Nucleus And Everything Will Probably

  Tarn Into A Huge Nucleus Like A Super-Neutron Star And There

  Will Be No More A Variety Of Element In Nature.

 

(3) Nuclear Force Is Very Strong :

- This Is Evident From The Large Binding Energy Of Nuclei About

  8 Mev Per Nucleon

- The Average Binding Energy Of Electron In Atoms Is In The

   Range Of Ev To Kev Only.

 

(4) Nuuclear Force Saturates :

- This Is Actully An Outcome Of The Short Range Nature Of The

  Nuclear Force.

- Each Nucleon In A Nucleus Interacts With Its Neighbors Only As

  A Results The Binding Energy Per Nucleon Rises Rapidly For

  Light Mass Nuclei And Quickly Saturates The Plot Of Binding

  Energy Vs Nucleon Number A. Also The Binding Energy Of

  Deutron Is Just 1.1 Mev Per Nucleon Which Quickly Rises To

  6mev In The 4he And Further Beyond.

 

(5) Nuclear Force Is Charge Symmetric :

- It Is Same For a p-p And n-n Pair As An Example Consider The

  Followings Evidence For Charge Symmetry.

 

- 2 p-p Pairs 1 n-n Pairs 2 p-n Pairs,p-p Pairs Binding Energy =

  8.48 Mev Binding Energy = 7.71 Mev

- The Difference In The Be Between The Two Is 0.77 Mev.

  Assuming He To Be A Uniformly Charged Sphere Of Radius 2.24

  Fermi

- The Differance Is Almost Entirly Accounted For By The Coulomb

  Energy Implying that p-p And n-n Interaction Is Same.

 

(6) Nuclear Force Is Charge Independant :

- The Force Is Same For n-p As It Is For n-n And p-p Pairs

  Provided The n-p Paire Is In The Same Isospin State.

- A p-p And n-n Pairs Can Occupay Isospin t = 1 State Only.

- If The n-p Pair Also Occupies t=1 State Thean The Force Is The

  Same.

- Experimantel Data On Isobars Conferm The Isospin Invariance

  And, Therefor Charge Independant.

 

(7) nuclear force is spin dependant :

- As An Example Deuteron In Its Ground Sate (And The Only

  Bound Sate) Exists Only In Spin Triplet State. The Spin Singlet

  State Is Unbund.

 

(8) Nuclear Force Has A Tensor Nature :

- The Arrangment Of Nucleon Spins In A Nucleus Whether Two

  Nucleons Are Placed Side By Side Or One On To Of The Other

  Althought Total Spin Is 1 In Both The Case Makes A Difference

  In Thire Binding Howsoever Small.

- The Tensor Dependence Is Generally Expressed By The Term

 

  If Vector σ1 And Vector σ2 Are Parallel To Vector r And If The

  Two Are Perpendiculer To Vector R The Value Of (Vector σ1 Dot

  Vector σ2) Is Deffernt In The Two Cases Even For The Same

  Value Of Total Spin I.E. Vector Σ The Magnetic Moment Of

  Deutron Can Not Be Explained With Out The Tensor Nature Of

  Nucler Force.

 

(9) Nucler Force Also Has Velocity :

- Dependence Or A Dependence On The Spin Orbital Term It Is

  Given Be A Term Like

 

- It Is Attrective When Vector L & Vector S = 1/2 (Vector σ1 +

  Vector σ2) Are Parallel And Repulsive When They Are Anti

  Parallel.

 

(10) Nucler Force Has An Exchange Charecter :

- This Is A Purely Quantum Featue And May Be Understood By

   Knowledge The Way Nucler Force Is Mediated.

- Two Nucleons When Interacting With Each Other Can Exchange

  Thier Spin,Iso Spin Or A Combination Of Both.

- These Are Repesented By Bartlett (B) Hisenberg (H) And

  Majoran (M) Terms Which Contribute To The Force According 

  To The Signs Given Below

 

- The Sign Dependans On The Nature Os State Repesents The

   Wigner Term Which Is No Exchange At All.

- Bartlett Force Lead To Spin Exchange Majorana Force To

  Isospin Exchange And Heiisenberg Force T A Combination Of

  Spin And Isospin Typically Spin Exchange Is Proportional To

  Vector σ1 Dot Vector σ2 And Isospin Exchange Is Proportional

  To Vector τ1 Dot Vector τ2 .

- The Exchange Force Can Explin The Saturation As It Has

   Repulsive Terms Also

- As Nucleon  Num,Ber Increses The Repulsive Force Balance The

  Attractive Force Which Prevents A Collapse Of The Nucleus.

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