Lesson 7

Alpha Decay

Alpha decay (α)

• Decay by the emission of doublycharged helium nuclei 4He2+.

• 238U→234Th + 4He• ΔZ = -2, ΔN=-2, ΔA=-4• All nuclei with Z≥83 decay by α-decay

as do some rare earth nuclei.Alphadecay is also known in the 100Sn region.

Alpha Decay• The emitted α-particles are

monoenergetic,ranging in energy from 1.8-11.6MeV (typically 4-9 MeV).

• They can be stopped by a piece of paper andare thus an internal radiation hazard ratherthan an external hazard.

• The naturally occurring α-emitters form longseries of nuclei that decay to one another.Some of these naturally occurring decaysseries involve isotopes of Rn, a gas.

Important Features ofAlpha Decay

• Generally energy of decay increaseswith increasing Z, but in any case theenergy of the emitted α-particle is lessthan the Coulomb barrier for the α-nucleus interaction.

• For e-e nuclei, decay leads to gs ofdaughter. For odd A nuclei, decay isnot to the gs but a low-lying excitedstate.

Energetics of Alpha Decay

• Qalpha

Energetics of Alpha Decay(cont.)

• Qalpha --Generally increases with increasing Z, but issubject to shell effects.

N=152-154Z=82, N=126

Qα, Tα

!

Q" = (Mparent #Mdaughter #Malpha )c2

T" =Q"

Mdaughter

Mparent

Trecoil =Q"

Malpha

Mparent

Difference between detecting emitted alpha particle and detecting alpha from implanted atom.

Closed decay cycles

Used to measure unknown masses or Q values forbeta decay

Understanding naturalalpha-decay chains

• In the U natural decay series, see pattern ofmixed alpha and beta decays. Why?

Understanding Alpha Decay

• The problem:

Understanding AlphaDecay (cont.)

• The Geiger Nuttall Law

!

log(t1/ 2) = A +B

Q"

Theory of Alpha Decay

• One of the first successes ofquantum mechanics

!

" = fT

f =v

2R=

2(V0

+Q) /µ

2R~ 10

21/s

T # e$2G

2G =2

h2m(V (x) $ E[ ]

1/ 2dx

x1

x2

%

2G =2

h2µ(

Z&ZDe2

r$Q& )

'

( )

*

+ ,

1/ 2

drR

b

%

b =Z&ZDe

2

Q&

After some algebra and simplifying for the nuclear case

!

2G = 22µ

h2Q"

Z"ZDe2( )#

2

$

% &

'

( ) ~ 60 *120

T ~ 10*55 *10*27

Then

!

t1/ 2

=ln2

"=ln2

fT=

ln2

2 V0

+Q#( ) /µ[ ]1/ 2

2Re$2G

This is called the “one-body” theory of alpha decay

How well does one-bodytheory work?

Role of “pre-formation factor”

Effect of angularmomentum

Selection Rules

Which states of daughter arepopulated in alpha decay?

• Dominant effect is Qα

• Angular momentum effectAngular momentum =

!

l

Parity = (-1)

!

l

Hindrance FactorsHindrance Factor=t1/2(meas)/t1/2(one-body)

Proton Decay• Same theory as alpha decay, except no pre-

formation factor for protons• Where do you expect to see proton decay?

(Sp=0)

proton dripline

Proton Decay(cont.)

• Proton energies are low andtransmission factors are small.

Proton Decay(cont.)• Alpha decay complicates measurements

Heavy Particle Decay• What about emitting particles other than

alphas or protons?

Q12C