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The Decay of Unstable Nuclei. Decay. Heavy Particle Decay. electrometer. Discovery of a Radioactivity. Heavy nuclides ( Gd , U, Pu ,..) spontaneously emit a particles. Mass systematics  energetically allowed.

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discovery of a radioactivity


Discovery of a Radioactivity

Heavy nuclides (Gd, U, Pu,..) spontaneously emit a particles.Mass systematics  energetically allowed

Marie & Pierre Curie (1897-1904) studied “pitchblende”Ra: powerfulaemitter

Alpha Decay

a particles energetically preferred (light particles)

energy release in a decay
Energy Release in a Decay

“Q-Value” for a Decay:



Shell effect at N=126, Z=82

Odd-even staggering

Alpha Decay

Geiger-Nuttall Rule:Inverse relation between a-decay half life and decay energy for even-even nuclei

examples alpha decay schemes spectra
Examples: Alpha Decay Schemes/Spectra

Short-range a particles

Long-range a particles

Alpha Decay

Many a emitters: Ea ~6 MeV (short range)Heavy emitters also: Ea~ 8 MeV (long range)

solution to a puzzle tunneling the coulomb barrier
Solution to a Puzzle: Tunneling the Coulomb Barrier

Answered Puzzle:

If nucleus stable : t1/2 ∞

If nucleus unstable : t1/2 0

Not found in macroscopic nature

George Gamov

Low stability  high a energy

a-Nucleus Coulomb Potential

Resolution of Puzzle Quantum meta-stability(if nucleus has intrinsic a structure, Pa=1):

Gamov: Intrinsic a wave function “leaks” out

Superposition of

repulsive Coulomb potential + attractive nuclear potential creates “barrier” which is penetrable for a particle

Alpha Decay

UaTh= 28 MeV


Ea= 4MeV

RaTh=9 fm

Nuclear Potential

quantal barrier penetration
Quantal Barrier Penetration

General solution of Schrödinger Equ.: Lin. Comb. of exponentials

E, U







0 d


Alpha Decay

Particle escape probability l(system decay) depends on barrier height & thickness the number of states

barriers of arbitrary shape
Barriers of Arbitrary Shape

Approximate by step function





Alpha Decay

Application: Z1=2, Z2=Z-2

the geiger nuttal rule
The Geiger-Nuttal Rule

a half life vs. a energy


Alpha Decay

What are the Z dependent scaling factors A?

decay dynamics
Decay Dynamics

Classical considerations/order of magnitude:

Pre-existence of a particle in nuclear medium, Pa (Nuclear cluster structure  “Spectroscopic Factor S”)

Finite probability for barrier encounters, frequency, fa(velocity, effective mass)

Barrier penetration, Ta(geometry of Coulomb barrier)

Angle of incidence on barrier, angular momentum, a

Great uncertainties in absolute decay rates

a-Nucleus Potential

Alpha Decay

UaTh= 28 MeV




RaTh=9 fm

Nuclear Potential


angular momentum and parity in a decay
Angular Momentum and Parity in a Decay

a-Nucleus effective Potential

Solve 1-D Schrödinger Equ. For a-daughter system with effective radial potential (Coulomb + centrifugal)  conserved angular momentum

Alpha Decay

Nuclear Potential

Spin/parity selection rule for a transitions:

 = 0 most probable a decay

Higher  values hindered significantly because of small T

Estimate range of -values from Ea and nuclear radii !

dependent a transmission coefficients
-Dependent a Transmission Coefficients

 ≠ 0 but not very large: a-daughter effective radial potential (Coulomb + centrifugal)  Linearization at barrier


R R r

Alpha Decay

Absolute values not very good, by orders of magnitude

Can decrease T by factors 5-10 for D=+1

Pocket formula Loveland et al., Modern Nuclear Chemistry, Wiley Interscience, 2006

a decay patterns
a Decay Patterns

Guess some final nuclear spins Ip

a Decay of 251Fm


479 keV

Alpha Decay


0 keV

From Krane, Introductory Nuclear Physics

spontaneous nucleon decay
Spontaneous Nucleon Decay

New: The “Drip” lines:

More limits to nuclear stability



Alpha Decay


Near drip lines: nucleons can be emitted from excited states.Need secondary beams to explore regions far off stability


Adapted from NSCL ISF White Paper, 2006

proton decay
Proton Decay

Near proton drip line, nuclei become p-unstable at E* ~ 1 MeV.

Coulomb+centrifugal barrier  long lifetime (isomeric state)

0.39 s



Si singles

Alpha Decay

I. Mukha et al., PRL 95, 22501 (2005)

di proton decay
Di-Proton Decay

Alpha Decay

spontaneous cluster decay
Spontaneous Cluster Decay

Observed for 221Fr – 242Cm: Cluster radioactivity (14C-34Si)

Solenoid Magnet Spectrometer

Telescope ID(Z, E )




energetically possible.

Magnetic spectrometer:

adjustable acceptance, remove unwanted particles, here: strong a lines

Can use very strong sources,


Alpha Decay

Spectrometer Transmission(acceptance)

Gales et al., PRL 53 (1984)

results 223 ra decay products
Results: 223Ra Decay Products

Measured Branching (Telescope in focus):

Expected from Gamov factor:

Very different preformation factors ?

Alpha Decay


E (MeV)

Gales et al., PRL 53 (1984)

structure effects in cluster decay half lives
Structure Effects in Cluster Decay Half Lives

Ra Isotopes




Alpha Decay


Due to barrier penetrabilities T

Unpaired neutron suppresses cluster emission from g.s., not from excited states

Hussonnois et al., PRC 42 R495 (1990)

theoretical ambiguity
Theoretical Ambiguity

Alpha Decay

Fission and a approach need different barriers  map barrier shape by inverse (fusion) process at different energies.

Barrier for

cluster decay

A.A. Ogloblin et al., NPA 738, 313(2004)