Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 1 Nuclear Binding...

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

Nuclear Binding Energy

Btot(A,Z) = [ ZmH + Nmn - m(A,Z) ] c2 Bm

Bave(A,Z) = Btot(A,Z) / A HW 9HW 9 Krane 3.9Atomic masses from: HW 10HW 10 Krane 3.12http://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl?ele=&all=all&ascii=ascii&isotype=all

Separation Energy Neutron separation energy: (BE of last neutron)Sn = [ m(A-1,Z) + mn – m(A,Z) ] c2

= Btot(A,Z) - Btot(A-1,Z) HW 11HW 11 Show that

HW 12HW 12 Similarly, find Sp and S.

HW 13HW 13 Krane 3.13 HW 14HW 14 Krane 3.14

Magicnumbers

Nuclear Binding EnergyMagic

numbers

In generalX Y + aSa(X) = (ma + mY –mX) c2

= BX –BY –Ba The energy needed to remove a nucleon from a nucleus ~ 8 MeV average binding energy per nucleon (Exceptions???).

Mass spectroscopy B.Nuclear reactions S.Nuclear reactions Q-value

~200 MeV

Fission

Coulomb effectSurface effect

HWc 4HWc 4Think of a computer program to

reproduce this graph.

HW 15HW 15A typical research reactor has power on the

order of 10 MW.

a) Estimate the number of 235U fission events that occur in the reactor per second.

b) Estimate the fuel-burning rate in g/s.

Is the nucleon bounded equally to everyother nucleon?C ≡ this presumed binding energy.Btot = C(A-1) A ½Bave = ½ C(A-1) Linear ??!!! Directly proportional ??!!! Clearly wrong … ! wrong assumption finite range of strong force, and force saturation.

Lead isotopes Z = 82

For constant ZSn (even N) > Sn (odd N)For constant NSp (even Z) > Sp (odd Z)

Remember HW 14 (Krane 3.14).

208Pb (doubly magic) can then easily remove the “extra” neutron in 209Pb.

Neutron Number N

Extra Binding between pairs of “identical” nucleons in the same state (Pauli … !) Stability (e.g. -particle, N=2, Z=2).

Sn (A, Z, even N) – Sn (A-1, Z, N-1)This is the neutron pairing energy.

even-even more stable than even-odd or odd-even and these are more tightly bound than odd-odd nuclei.

Abundance SystematicsOdd N Even N Total

Even Z

Compare:• even Z to odd Z.• even N to odd N.• even A to odd A.• even-even to even-odd to odd-even to odd-odd.

HWc 1HWc 1\\

Neutron ExcessZ Vs N (For Stable Isotopes)

0 20 40 60 80 100 120 140N

Even A

Z = NAsymmetry

AsymmetryRemember HWc 1.

Neutron Excess

Remember HWc 1.

Asymmetry

Abundance Systematics

NEUTRON NUMBER

MASS NUMBER

r s r s

Formation process

Abundance

The Semi-empirical Mass Formula

• von Weizsäcker in 1935.• Liquid drop. Shell structure.• Main assumptions:

1. Incompressible matter of the nucleus R A⅓.

2.Nuclear force saturates.• Binding energy is the sum of terms:1. Volume term. 4. Asymmetry term.2. Surface term. 5. Pairing term.3. Coulomb term. 6. Closed shell term.…..

Volume Term Bv = + av ABv volume R3 A Bv / A is a constant i.e. number of neighbors of each nucleon is independent of the overall size of the nucleus.

The other terms are “corrections” to this term.

BV constant

Surface Term Bs = - as A⅔

• Binding energy of inner nucleons is higher than that at the surface.

• Light nuclei contain larger number (per total) at the surface.• At the surface there are:

Nucleons.

Remember t/R A-1/3

Coulomb Term BC = - aC Z(Z-1) / A⅓

• Charge density Z / R3.• W 2 R5. Why ???• W Z2 / R. • Actually: W Z(Z-1) / R. • BC / A = - aC Z(Z-1) / A4/3

Remember HW 8 … ?!

Quiz 1Quiz 1

...)1()(),( 31

AZZaAaAaMMZAMZAM CSVHnn

From our information so farso far we can write:

For A = 125, what value of Z makes M(A,Z) a minimum?

Is this reasonable…???

So …..!!!!

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh). 1 Nuclear Binding...

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