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Nuclear Reactions

Reactions

A + a → B + bA (a,b) BElastic scattering: 12C (p,p)12C Inelastic scattering: 12C (p,p´)12C*

Rearrangement reaction: 54Fe (32S,28Si)58NiCapture reaction: 12C (p,γ)13NOthers: 2H(n,2n)1H

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Terminology

Channels (Entrance and Exit) p – proton d – deuteron (deuterium): 2H t – triton (tritium): 3H α – alpha (Helium-4): 4He Photodisintegration – reaction with γ in entrance

channel Capture – nucleon absorbed and γ in exit channel

Q-value in Reactions

The Q-value in reactions is the difference betweenthe mass energies of the entrance channel particlesand the exit channel particles.

The Q-value is the energy release in the reaction. For elastic collisions Q = 0 in inelastic collisions

Q < 0.

( ) ( ) 2]ExitEntrance[ cMMQ !=

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Q-value and Kinetic energy

The Q-value can also be expressed in terms of theincoming and outgoing kinetic energies.

For fixed target experiments KA = 0. For exothermic reactions Q > 0 some of the mass

energy is converted to kinetic energy. For endothermic reactions Q < 0 some of the

incoming particle’s kinetic energy is converted tomass.

aABb KKKKQ !!+=

Threshold Kinetic Energy

In endothermic reactions the kinetic energy of theincoming particle must be sufficient to supply the neededmass and conserve momentum.

The minimum kinetic energy of the incoming particleneeded to initiate the reaction is called the thresholdenergy.

!!"

#$$%

& +'=

A

Aath

M

MMQK

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A Typical Experiment

Incoming particle beam

Detector

Faraday Cup

Target

What do we measure?

Detector might measure the outgoingparticle’s: Type of particle Energy Momentum (direction and magnitude) Number of particles (of each type)

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Number of particles

The number of particles detected dependson a variety of factors: Beam flux Number of “targets” – target thickness Detector placement, size and efficiency Physical properties of the reaction

Cross-section

The cross-section is related to the probability thata certain reaction will take place.

Independent of other factors such as beam flux ortarget size.

σ has units of area: barn (b) = 10-28 cm

spot) beam within nuclei target ofer area)(numbnit incident/u particles of(number

emitted particles outgoing ofnumber =!

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Cross-section as Effective Area

One way tovisualize cross-section is to thinkof it as theeffective area ofthe target(assuming theincident particleis point-like.)

Cross-section of a Reaction

Cross-section is a measure of the reactionprobability.

R1

R2

b b R1 + R2

Collision of two classical spheres.

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Calculating Cross-section fromExperimental Parameters Y = yield = number of reactions/unit time n = particle density

= number of target particles/unit volume t = thickness of target A = area of beam spot Φi = incident flux

= beam particles/[(unit time)(unit area)]

Experimental Cross-section

The yield is Y = ΦinAtσso the total cross-section is

nAt

Y

i!

="

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Differential Cross-section

An actual experiment does not measure thetotal yield but the yield of particles thatscatter into the detector.

The detector is placed at a position (r,θ,φ)and has an active area facing the target.

In general the cross-section is not isotropic– it depends on (θ,φ) .

Nuclear Reactions

Mechanisms

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Direct reactions

Reaction energy ~ 20 MeV or greaterDominated by strong interactionExamples:

Knockout Pickup Stripping

Compound Nucleus Mechanism

Low energy (< 20 MeV)A composite nucleus is formed.Time scale on order of 10-15 s.

16O

p + 15Nd + 14N

3He + 13C4He + 12C6Li + 10B

p + 15Nd + 14N

3He + 13C4He + 12C6Li + 10B

n + 15Ot + 13Nγ + 16O

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Energy Level of CompoundNucleusResonances

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h!"#

Fission and Fusion

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Fission

Nucleus splits into two roughly equal sizedfission fragments ( and a few stray nucleonsin some cases.)

Moves lower on the binding energy curve.Spontaneous fission: Z2/A >48, A > 220Spontaneous fission has low rates compared

to alpha decay.

Induced fission

Neutron is absorbed producing acompound nucleus that quicklyfissions.

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Prompt and Delayed Neutrons Neutrons released with the

fragments are called promptneutrons. These have high kineticenergies and a low cross sectionfor absorption.

The neutron-rich fission fragmentsmay also emit neutrons during thetheir beta decay back to the line ofstability. These have low kineticenergies and high absorption crosssections. Fission fragments usually

have unequal masses.

Chain Reactions

Emitted neutrons can be used to create secondaryfission reactions and so on.

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Controlled Chain Reactions

Moderating material is used to slow fastneutrons. (water, graphite)

Control rods absorb neutrons (cadmium).

Nuclear Reactors

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Fusion

Two light nucleicombine to form aheavier nucleus.

Fusion vs. Fission

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Stellar Fusion

The p-p chain

Stellar Nucleosynthesis

All elements with the exception of H, He and Liwere made in stars.

Nuclear processes that provide the energy of a starmake heavier nuclei out of the H and He.

Some nuclei are made during the normal lifetimeof a star.

The nuclei above 56Fe on the binding energy curveare made only during supernovae explosions.

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The r-process100

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Known massKnown half-lifer process waiting point (ETFSI-Q)

Solar

r-ab

unda

nces

Fusion Power –Magnetic confinement

http://ippex.pppl.gov/

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Fusion Power –Magnetic Confinement

National Spherical Torus Experiment

Fusion Power –Inertial Confinement

NOVA Laser test chamber

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Fusion Power –Inertial Confinement

National Ignition Facility