Download - Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh). 1 Neutron Excess Remember HWc 1. Asymmetry.

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

1

Neutron Excess

Remember HWc 1.

Asymmetry

Asymmetry


2

Abundance Systematics


3

Abundance Systematics

NEUTRON NUMBER

MASS NUMBER

AB

UN

DA

NC

EN

EU

TR

ON

CA

PT

UR

E

CR

OS

S S

EC

TIO

N

r s r s

Formation process

Abundance


4


5

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.…..


6


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.

A

BV constant


7


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:

32

2

322

0 44

Ar

Ar

o

Nucleons.

31

1

AA

Bs

Remember t/R A-1/3


8


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 … ?!

3

3

4r

drr24


9



10


Quiz 1Quiz 1

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

32

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 …..!!!!


11


• Light nuclei: N = Z = A/2 (preferable).• Deviation from this “symmetry” less BE and stability.• Neutron excess (N-Z) is necessary for heavier nuclei.• Ba / A = - aa (N-Z)2 / A2.• Back to this when we talk about the shell model.

Asymmetry Term Ba = - aa (A-2Z)2 / A


12


Pairing Term Bp = Extra Binding between pairs of identical nucleons in the same state (Pauli !) Stability (e.g. -particle, N=2, Z=2).even-even more stable than even-odd or odd-even and these are more tightly bound than odd-odd nuclei.Remember HWc 1HWc 1\\ ….?!Bp expected to decrease with A; effect of unpaired nucleon decrease with total number of nucleons. But empirical evidence show that:

A-¾ .

oddZoddNAa

oddA

evenZevenNAa

p

p

43

43

0

Effect on:• Fission.• Magnetic moment.Effect of high angular momentum.


13


Closed Shell Term Bshell =

• Extra binding energy for magic numbers of N and Z.• Shell model.• 1 – 2 MeV more binding.


14


• Fitting to experimental data. • More than one set of constants av, as …..

• In what constants does r0 appear?• Accuracy to ~ 1% of experimental values (BE).• Atomic masses 1 part in 104.• Uncertainties at magic numbers.• Additional term for deformation.


15

])2()1([

)(),(

1231

32

AZAaAZZaAaAa

MMZAMZAM

aCSV

Hnn


Variations…….Variations…….Additional physics….Additional physics….Fitting……(Global vs. local)…..Fitting……(Global vs. local)…..


16

Work it out …

?

?

?

),( 2

ZZZAM

?0 min

ZZ

M

A

])2()1([

)(),(

1231

32

AZAaAZZaAaAa

MMZAMZAM

aCSV

Hnn


17

Mass Parabolas and Stability

311

31

32

2

4

4)(

),(

AaAa

aAaMM

AaAaAaAM

ZZZAM

Ca

aCHn

aSVn

2

0 min

ZZ

M

A

HW 16HW 16


18



19


Double decay! Both Sides!


20



21


Odd-Odd

Even-Even

Vertical spacing between both parabolas ?

• Determine constants from atomic masses.


22



23

Nuclear Spin• Neutrons and protons have s = ½ (ms = ± ½) so they are fermions and obey the Pauli-Exclusion Principle.•The Pauli-Exclusion Principle applies to neutrons and protons separately (distinguishable from each other) (IsospinIsospin).• Nucleus seen as single entity with intrinsic angular momentum .• Associated with each nuclear spin is a nuclear magnetic moment which produces magnetic interactions with its environment. •The suggestion that the angular momenta of nucleons tend to form pairs is supported by the fact that all nuclei with even Z and even N have nuclear spin =0. • Iron isotopes (even-Z), for even-N (even-A) nuclei =0. • Odd-A contribution of odd neutron half-integer spin.• Cobalt (odd-Z), for even-N contribution of odd proton half-integer spin.• Odd-N two unpaired nucleons large integer spin.


24

Nuclear Spin

Z A SpinNatural

AbundanceHalf-life Decay

26 54 0 0.059 stable ...

26 55 3/2 ... 2.7y EC

26 56 0 0.9172 stable ...

26 57 1/2 0.021 stable ...

26 58 0 0.0028 stable ...

26 60 0 ... 1.5My -


25

Nuclear Spin

Z A SpinNatural

AbundanceHalf-life Decay

27 56 4 ... 77.7d +

27 57 7/2 ... 271d EC

27 59 7/2 1.00 stable ...

27 60 5 ... 5.272y -