what have we learned last time? q value binding energy semiempirical binding energy formula...

What have we learned last time?What have we learned last time?

• Q value

• Binding energy

• Semiempirical binding energy formula

• Stability

Nuclear ReactionsNuclear Reactions

Scattering ReactionsScattering Reactions

• Elastic scattering

A(a,a)A

• Inelastic scattering

A(a,a’)A*

Other reactionsOther reactions

FedCo

FeHedCo

NindCo

CopdCo

NidCo

CoddCo

CoddCo

5726

5927

5826

32

5927

6028

5927

6027

5927

6128

5927

5927

5927

5927

5927

),(

),(

),(

),(

),(

*'),(

),(

Energetics of nuclear reactionsEnergetics of nuclear reactions

• Energy, mass number, momentum conservation

• Q-value : positive exoergic; negative endoergic

• Example of endoergic14N + 4He 1H + 17O + Q

Q = -1.19 MeV

Is it enough to start the reaction?

Momentum correctionMomentum correction

Coulomb barrier correctionCoulomb barrier correction

14N + 4He 1H + 17O + Q

yx

yx

yx

yx

RR

ZZ

RR

eZZV

44.12

MeV6.3)14()4(4.1

7244.144.13/13/1

yx

yx

RR

ZZV

Threshold energy in SL: 3.6 MeV [(4+14)/14] = 4.6 MeV

Cross sectionCross section

• Symbol σ

• Geometrical cross section

σ = π (Rtarget)2

10-24 cm2

Barn, 1 b = 10-24 cm2 = 100 fm2

1 mb = 10-27 cm2

1 μm = 10-30 cm2

Measurements of cross Measurements of cross sectionssections

• Thin targets

• Thick targets

Compound Nucleus ReactionsCompound Nucleus Reactions

yrast line – lowest energy for a given angular momentum

3-4 MeV/A

Discovery of FissionDiscovery of Fission

• 1938

• average number of 2.4 neutrons.

• statistical phenomenon, Gaussian distribution, independent of

the fissioning nucleus.

QnKrBaUUn 38936

14456

*23692

23592

10

Otto Hahn and Lise Meitner, 1913, at the KWI for Chemistry in Berlin

1944 Nobel Prize in Chemistry for Otto Hahn "for his discovery of the fission of heavy atomic nuclei”

Until 1938 all scientists believed that the elements with Z > 92 (transuranium elements) arise when uranium atoms are bombarded with neutrons.

Radioactive Decay ProcessesRadioactive Decay Processes

Pr141331414141min1814125141

9310931093min793693 6

dhs

yhs

CeLaBaCs

NbZrYSrRb

QnRbCsUUn 29337

14155

*23692

23592

10

These radioactive products are the waste products of nuclear reactors.

The fragments in the vicinity of A = 95 and A = 140 share 92 protons.Prompt neutrons are emitted in 10-16 s.Delayed neutrons intensity 1 in 100 fissions or 0.02 neutrons per fission(from neutron emission). Delayed neutrons are essential for controlling the reactors.

Mass Distribution of FissionMass Distribution of Fission

95 140

symmetric

Source: University of Waterloo

Neutron Cross Sections for Neutron Cross Sections for fission of U and Pufission of U and Pu

1 b = 10-28 m2; 1 MeV = 1.6 x 10-13 J

1/v -dependence

Source: World Nuclear Association

Binding energy per nucleonBinding energy per nucleon

http://hyperphysics.phy-astr.gsu.edu/

Q-valueQ-valueEnergy released in a nuclear reaction (> 0 if energy is released, < 0 if energy is used)

Example: The sun is powered by the fusion of hydrogen into helium:

4p 4He + 2 e+ + 2e

Mass difference dMreleased as energydE = dM x c2

mmmmcQ eHenucpnuc 224/ 42

Fusion ReactionFusion Reaction

QnHeHH

QnHeHH

QHepH

432

322

32

How Do We Produce Exotic Nuclei?How Do We Produce Exotic Nuclei?

5858Zn and the Zn and the rprp-process-process

Astrophysicsrp-process:• hot and explosive hydrogen burning environments (X-ray burst) • stops at 56Ni?• beyond 56Ni: 56Ni(p,γ)57Cu(p,γ)58Zn• rates 56Ni(p,γ)57Cu; spectroscopy of 57Cu• rates 56Ni(d,p); spectroscopy of 57Cu• 57Cu(p,γ)58Zn – no information• calculations based on 58Ni-58Zn mirror symmetry

Spectroscopic Information58Zn (Z=30, N=28)• no excited states, spin and parity• predicted from 58Ni

29

30

5958

60

60

5856 57

61

59

Cu

Ni

Zn

28

59

30

58

57

29 3128

N=Z

?

• no excited states in Z > N

• mirror symmetry

– 59Zn-59Cu

– 58Zn-58Cu

• rp-process

5858ZnZn2828

36Ar + 24Mg → 60Zn*→ 58Zn + 2nnμb (20 x 10-34 m2)

Spokespersons: C. Andreoiu and P.E. Garrett, University of Guelph @ Argonne National Laboratory, Chicago, 2006

Gammasphere + Ancillary DetectorsGammasphere + Ancillary Detectors

• Gammasphere (100 Ge detectors)• MICROBALL (95 CsI) • 20 neutron detectors

Particle Detectors - MICROBALLParticle Detectors - MICROBALL

• 95 CsI detectors• average efficiency

80% alphas70% protons

D.G. Sarantites et al. Nucl. Instrum. Meth. A 400, 87 (1997)