Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

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Nuclear Force

• Spin dependent difference in neutron scattering cross sections of ortho- and para-hydrogen. • Compare n-p to n-n and p-p Charge independence of nuclear force.

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

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Nuclear Force

Mirror Nuclei

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

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If two charges, q and q' exchange photons, the Coulomb force occurs between them.

If pions are exchanged between two nucleons, the strong nuclear force occurs. Remember the weak nuclear force…

Just

for comparis

on.

_

epn

What about What about forces between forces between

quarks?quarks?Color?Color?

Krane 4.5Krane 4.5

Boson?

Nuclear Force

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

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Nuclear Force

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

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• Only Hadrons.• Typical time: 10-24 s. (c, 10-15 m).• Exchange of light 140 MeV pions.• t = ħ/E = 4.7 x 10-24 s. (Why E?). • Range t c = ħ/mc = 1.4 x 10-15 m.• Range and time complicated by possibilities of heavier hadron exchange.• Isospin. Conservation of Isospin. Only relevant to hadrons.• Hadron multiplets: Doublet of nucleons and triplet of pions and …• The members of a multiplet have the same strangeness, hypercharge, spin, etc… , but differ in charge and differ slightly in mass.• Relationship between particle and nuclear physics.• Accelerators and large accelerators.

Nuclear Force

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

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Isospin

• IsospinIsospin Magnitude • T3 can take T, T-1, T-2, ….., -T. • 1,2,3 not x,y,z (Isospin space).• Singlets (T = 0), Doublets (T = ½), Triplet (T = 1), Quartet (??).• -T3 for antiparticles.• Isospin addition: for a collection of hadrons (e.g. in interaction)

• Example: +-p scattering, Tmax = 3/2, T3 = 3/2 T can only be 3/2.

)1( TT

i

iTT )(max i

iTT )(33 3TT

Read Krane 11.3.Read Krane 11.3.

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

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The Deuteron

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

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The Deuteron• Deuterium (atom).•The only bound state of two nucleons simplest bound state.• Neither di-proton nor di-neutron are stable. Why?

• Experimentally 2.224 MeV (Recoil..!).• Also inverse (,n) reaction using Bremsstrahlung (Recoil…!).• Mass spectroscopy mass of D (or deuterium atom).• mc2 = 2.224…??…MeV Very weakly bound.• Mass doublet method all results are in agreement.• Compare 2.224 MeV to 8 MeV (average B/A for nuclei).• Only ground state. (There is an additional virtual state).

HHn 21

HW 18HW 18 Problems 4.1 - 4.5 in Krane.

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

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The DeuteronV(r) = -V0 r < R = 0 r > R• Oversimplified.HW 19HW 19 Assuming Assuming ll = 0 = 0, show , show that Vthat V00 35 MeV. 35 MeV.

(Follow Krane Ch.4 and (Follow Krane Ch.4 and Problem 4.6), or similarly Problem 4.6), or similarly any other reference.any other reference.• Really weakly bound.• What if the force were a bit weaker…?

Yukawa?Yukawa?

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

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The Deuteron

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

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The Deuteron• Experiment deuteron is in triplet state = 1.• Experiment even parity.

• = l + sn + sp parity = (-1)l

• Adding spins of proton and neutron gives: s = 0 (antiparallel) or s = 1 (parallel).• For = 1

parallel s-state evenparallel p-state oddantiparallel p-state oddparallel d-state even

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

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• Experiment = 0.8574376 N spins are aligned…..But.?• Direct addition 0.8798038 N.

• Direct addition of spin components assumes s-state (no orbital component).• Discrepancy d-state admixture.

= a00 + a22

= a020 + a2

22

HW 20 In solving HW 19 you assumed an s-state. How good was that assumption?

The Deuteron

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

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The Deuteron

• S-state No quadrupole moment.• Experiment +0.00288 b.HW 21HW 21Discuss this discrepancy.

• From and Q, is it really admixture?• What about other effects?• Important to know the d-state wavefunction.

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

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Nuclear Force

Read Secs. 4.4 and 4.5 in Krane.