Forest NucPhys I Nuclear Reactions

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Nuclear Reactions

Types of Reactions

[math]a + X \rightarrow Y + b[/math]
elastic scattering
X & Y and a & b are the same particles, momentum and energy are conserved, typically all are in their ground state
In-elastic scattering
If Y or b are in an excited state, energy is not conserved it is used to excite one of the exiting particles.

Elastic collisions are usually referred to as collisions and not nuclear reactions.

Direct Reactions

knockout reaction
a & b are the same but there are 3 total particles in the final state.
[math]n + X \rightarrow Y + 3n = X(n,3n)Y[/math]

KnockOut Reaction Forest NucPhys I.png

Transfer Reaction
a nuclear from projectile a is transfered to target X

Transfer Reaction Forest NucPhys I.png

Nuclear PhotoEffect
projectile a ejects a nucleon from target X
[math]e - + Mo-100 \rightarrow Mo-99 + n + e- = X(e,e'n)Y[/math]

NuclearPhotoEffect Forest NucPhys I.png


Capture Reaction Forest NucPhys I.png

Compound reactions

Compound reaction
projectiel a is captured by target X forming an intermediate state which then decays, possibly through multiple excited nuclear states/species, to Y and b

This is typically a low energy reaction in which particle Y doesn't leave the target material but the intermediate state may be surmised at through the detection of particle b.

CompoundReaction Forest Nucl I.pngCompoundReaction nf Forest Nucl I.png


14 nucleon system

Consider three different nuclear isobars all containing 14 nucleons ( isotopes are same Z, isotones are same N, so isobars are same A)

[math]{14 \atop 6} C_8[/math], [math]{14 \atop 7} N_7[/math], [math]{14 \atop 8} O_6[/math]

Experimentally it is observed that

[math]{14 \atop 6} C_8[/math] has a half life of about 5000 years and a [math]J^{\pi} = 0^+[/math].

When it does decay it goes to [math]{14 \atop 7} N_7[/math] by emitting a \beta^- particle with a Q value of 156.473 keV.

The [math]{14 \atop 7} N_7[/math] state it goes to has [math]J^{\pi} = 1^+[/math]

[math]{14 \atop 7} N_7[/math] is stable.

The ground state of [math]{14 \atop 8} O_6[/math] has a half life of about 70.61 seconds and a [math]J^{\pi} = 0^+[/math].

When it does decay it goes to [math]{14 \atop 7} N_7[/math] by emitting a \beta^+ particle with a Q value of 5.143 MeV.