Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

1

Nuclear Size

Alpha particle (+2e)

Gold nucleus (+79e)d

Quite old!!!Not exactly for A

u!!!

Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

2

Nuclear Size

• Closest approach “d”.• E = ECoulomb d = 2kZe2/E

• What about the recoil nucleus?• HW 7HW 7 Show that

where mN : mass of the nucleus m : mass of alpha

What are the values of d for 10, 20, 30 and 40 MeV on Au?How does this explain … ?

)(

2 2

mmE

mkZed

N

N

Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

3

Nuclear Shape

• Crude Nucleons in the nucleus are confined to an approximately spherically symmetric structure Nuclear radius.• Deformations…! Consequences….!!• Is there a sharp spherical wall…???!!!

• HW 8HW 8if it is assumed that the charge is uniformly spherically distributed in a nucleus, show that the electric potential energy of a proton is given by:

R

eZZKE

2)1(

5

3

Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

4

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 Prove that

HW 12HW 12 Similarly, find Sp and S.

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

Magicnumbers

Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

5

Nuclear Binding EnergyMagic

numbers

Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

6

Nuclear Binding Energy

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

Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

7

Nuclear Binding Energy

~200 MeV

Fission

Fusi

on

Coulomb effectSurface effect

HWc 4HWc 4Think of a computer program to

reproduce this graph.

Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

8

Nuclear Binding Energy

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.

Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

9

Nuclear Binding Energy

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.

Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

10

Nuclear Binding Energy

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

Ne

utr

on

Se

pa

ratio

n E

nerg

y S

n (

Me

V)

208 P

b

Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

11

Nuclear Binding Energy

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.

Symmetry?

Symmetry?

Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

12

Abundance SystematicsOdd N Even N Total

Odd Z

Even Z

Total

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\\

Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

13

Neutron ExcessZ Vs N (For Stable Isotopes)

0

10

20

30

40

50

60

70

80

90

0 20 40 60 80 100 120 140N

Z

Odd A

Even A

Z = NAsymmetry

AsymmetryRemember HWc 1.

Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

14

Neutron Excess

Remember HWc 1.

Asymmetry

Asymmetry