PART1
Survey of General properties of Beta decay
PART2
Beta decay and nuclear astrophysics
PART3
Beta decay in n-rich nuclei
-  in-flight fragmentation facilities
-  ISOL facilities
-  TAS experiments
PART1
Survey of General properties of Beta decay
Beta decay: survey of general properties
Beta Decay: universal term for all weak-­‐‑interaction transitions between two neighboring isobars
Takes place is 3 different forms
β-, β+ & EC (capture of an atomic electron)
β+: p à n + e+ + ν EC: p + e-­‐‑ à n + ν ∼ β-: n à p + e-­‐‑ + ν a nucleon inside the nucleus is transformed into another
3
Beta decay: survey of general properties (1)
•  β- decay
−
n
→
pe
νe
–  β decay
+
+
p
→
ne
νe
–  β decay
−
pe
→ nν e
–  Electron capture (EC)
•  β- decay is the most common type of radioactive decay
–  All nuclides not lying in the valley of stability can βdecay
4
Beta decay: survey of general properties (2)
β- decay is a weak interaction
“semileptonic” decay
The quark level Feynman diagram for
β- decay is shown on left
Because beta decay is a
three body decay, the
electron energy spectrum
is a continuum
5
Beta decay: survey of general properties (3)
•  The Q value in beta decay is
effectively shared between the
electron and antineutrino
–  The electron endpoint energy is Q
Q value for β − decay is
Qβ − = M ( A, Z ) − M ( A, Z + 1)
Note these are
atomic masses
(
Qβ − = TM ( A, Z +1)+ + Te + Tν ≈ Te + Tν since TM ( A, Z +1)+ < keV
)
Qβ − = (Te )max = (Tν )max
note!!: Qβ + = M ( A, Z ) − M ( A, Z − 1) − 2me c 2
6
Classification of β decay transition
Iiπi
Εβ
I i= I f + L β + S β
π iπ f = (−1)
Lβ
Ifπf
L β =l β −( β + ) +lν~ (ν )
{
S β = s β −( β + ) + sν~ (ν ) =
0
↑↓
1 ↓↓or ↑↑
Lβ = n defines the degree of forbiddenness (n)
allowed
when Lβ=n=0 and πiπf=+1
ΔI = I i− I f ≡ 0,1
forbidden
when the angular momentum conservation requires that Lβ=n >0 and/or πiπf=-­‐‑1
7
Classification of allowed decay
(π iπ f = +1)
Fermi
Gamow-­‐‑Teller
0+
0+
0+
Εβ
1+
ΔI = I i−I f ≡ 1
L β = 0 S β =1 ↑↑or ↓↓
ΔI = I i− I f ≡ 0
L β = 0 S β = 0 ↓↑
2+
2+
Εβ
mixed Fermi & Gamow-­‐‑Teller
Εβ
ΔI = I i− I f ≡ 0
I i≠ 0
8
Classification of β decay transitions
Type of transition
Order of forbiddenness
Allowed
ΔI
πiπf
0,+1
+1
Forbidden unique
1
2
3
4
.
2
3
4
5
.
-­‐‑1
+1
-­‐‑1
+1
.
Forbidden
1
2
3
4
.
0, 1
2
3
4
.
-­‐‑1
+1
-­‐‑1
+1
.
9
Useful empirical rules
The fifth power beta decay rule:
the speed of a β transition increases approximately in proportion to the fifth power of the total transition energy (if other things are being equal, of course)
Ii
If
Εβ
1
τ
∝ [(M ( Z ) − M ( Z ± 1) )c 2 ]5
q  depends on spin and parity changes between the initial and final state
q  additional hindrance due to nuclear structure effects :
isospin, “l-­‐‑forbidden”, “K-­‐‑forbidden”, etc. 10
β decay lifetime
t ≡ T1β/ 2i
T1exp
= / 2 partial half-­‐‑life of a given β- (β+,EC) decay branch (i)
Pβ i
ln 2
g2
=
n
T1/ 2 2π 3
W
∫
1
peWe (W0 − We ) 2 F ( Z ,We )Cn dWe
g – week interaction coupling constant
pe – momentum of the β particle
We – total energy of the β particle
W0 – maximum energy of the β particle
F(Z,We) – Fermi function – distortion of the β particle wave function by the nuclear charge
Cn – shape factor
Z – atomic number
11
Fermi Golden Rule
•  Treat beta decay as a transition that depends upon the
strength of coupling between the initial and final states
•  Decay constant is given by Fermi's Golden Rule
2π
2
λβ =
M ρ ( Eo ); M = ∫ψ f Vψ i dv

–  matrix element which couples the initial and final states
–  a phase space factor which describes the volume of
phase space available for the outgoing leptons
–  Small system perturbation
•  Contained within M
•  E is Q value
•  Rate proportional to the strength of the coupling between
the initial and final states factored by the density of final
states available to the system
Comparative Half Lives
•  Based on probability of electron energy emission coupled with
spectrum and the Coulomb correction fot1/2 is called the
comparative half life of a transition
ln 2
λ=
= K M if
Wo
t1/ 2
f o = ∫ F ( Z ,W )W (W 2 − 1)1/ 2 (Wo − W ) 2 dW
K = 64π 4 mo5c 4 g 2 / h 7
2
fo
1
•  Assumes matrix element is independent of energy (true for allowed
transitions)
•  Yields ft (or fot1/2), comparative half-life
–  may be thought of as the half life corrected for differences in
Z and Wo
•  fo can be determine when Fermi function is 1 (low Z)
•  Rapid estimation connecting ft and energy
Comparative Half Lives
log f β − = 4.0 log Eo + 0.78 + 0.02 Z − 0.005( Z − 1) log Eo
log f β +
log f EC
E ⎞
⎛
= 4.0 log Eo + 0.79 + 0.007 Z − 0.009( Z + 1)⎜ log o ⎟
3 ⎠
⎝
= 2.0 log Eo − 5.6 + 3.5 log( Z + 1)
•  Z is daughter and Eo is maximum energy in MeV (Q value)
•  Log ft = log f + log t1/2
–  t1/2 in seconds
2
Logft calculations
•
14 O
to
14N
–  positron decay
–  Q=1.81 MeV
–  T1/2 =70.6 s
2
log f β +
E ⎞
⎛
= 4.0 log Eo + 0.79 + 0.007Z − 0.009( Z + 1)⎜ log o ⎟
3 ⎠
⎝
log f β +
1.81 ⎞
⎛
= 4.0 log 1.81 + 0.79 + 0.007(7) − 0.009(7 + 1)⎜ log
⎟
3 ⎠
⎝
•  Log fβ+ = 1.83, log t =
1.84
•  Log ft=3.67
2
Log ft values
log ft = log f + log t
coming from experiment
coming from calculations
Type ΔI (πiπ
f)
β-
EC + β+
allowed
0, +1 (+)
log f 0−
log( f 0EC + f 0+ )
β-
EC + β+
1st-­‐‑forb unique
"
2 (-­‐‑)
log f 0− + log( f1− / f 0− )
Decay Mode
log f
log[( f1EC + f1+ ) /( f 0EC + f 0+ )]
N.B. Gove and M. Martin, Nuclear Data Tables 10 (1971) 205
16
Log ft calculation
•  212Bi beta decay
•  Q = 2.254 MeV
•  T1/2 = 3600 seconds
–  64 % beta branch
–  λβ =1.22E-4 s-1
–  T1/2Beta =5625 seconds
log f β − = 4.0 log Eo + 0.78 + 0.02 Z − 0.005( Z − 1) log Eo
log f β − = 4.0 log 2.254 + 0.78 + 0.02(84) − 0.005(84 − 1) log 2.254
•  Log f=3.73; log t=3.75
•  Log ft=7.48
Log ft data
•  What drives the changes in the log ft values for 205Hg?
Log f
q  ENSDF analysis program LOGFT – both Windows & Linux distribution
hRp://www.nndc.bnl.gov/nndcscr/ensdf_pgm/analysis/logft/
q  LOGFT Web interface at NNDC hRp://www.nndc.bnl.gov/logft/
19
Log t
t ≡ T1/ 2
βi
T1exp
= /2
Pβ i
Pβi = η[ I tot (out) − I tot (in)]
I tot (out / in) = ∑ Iγ i (1 + αT i )
i
αT ( M 1) + δ 2αT ( E 2)
αT ( M 1 + E 2) =
1+ δ 2
q  What we want to know accurately
ü T1/2, Iγ, αT & δ
In
I tot (521 + 721) = 0.086(16)
I tot (416 + 619) = 0.78(10)
= 0.69(10)
(net)
Out
η = 0.0022 → t = 2.056 ×106 [s] → log t = 6.31 → log f = 2.386 → log ft = 8.7
2
0
Rules for spin/parity assignments
q  There are only a few cases where unambiguous assignment can be made
q  “pandemonium effect” – neutron rich nuclei – log ft is a just lower limit!
q  needs to know the decay scheme and its properties accurately!
21
~1000 cases
Log ft values –latest review
~3900 cases -­‐‑> gives centroids and widths
22
B. Singh, J.L. Rodriguez, S.S.M. Wong & J.K. Tuli
PART2
Beta decay and nuclear astrophysics
Creation of the elements
Nucleosynthesis is a gradual, still ongoing process:
Dense clouds
Big Bang
M~104..6 Mo
108 y
Condensation
Interstellar
medium
H, He
Star formation
continuous
enrichment,
increasing
metallicity
M > 0.7Mo
Life of a star
Nucleosynthesis:
Stable burning
106..10 y
Dust mixing
Remnants
(White dwarf,
neutron star, black hole)
Nucleosynthesis
Nucleosynthesis:
Explosive burning
Death of a star
(Supernova, planetary nebula)
Nucleosynthesis
Most of the heavy elements (Z>30) are
formed in neutron capture processes,
either the slow (s) or rapid (r) process
r process
rp process
np process
s process
protons
Cosmic Rays
neutrons
Mass known
Half-life known
nothing known
Light element primary process
LEPP
stellar burning
Big Bang
p process
Contribution of different processes
Contribution of the diff. processes to the solar abundances
Ba: s-process
Eu: r-process
s-process:
Astrophysical model
Ba
Eu
p-process:
Astrophysical model
r-process:
Abundance of
enriched-r-process
star
LEPP = solar-s-p-r
R-process basics
Element formation beyond iron involving rapid
neutron capture and radioactive decay
High neutron density
β-decay
Seed
Waiting point
(n,γ)-(γ-n) equilibrium
Y(Z,A+1)
G(Z,A+1) Sn(Z,A+1)/kT
~ nnT-3/2
e
G(Z,A)
Y(Z,A)
Waiting point approximation
Nuclear physics in the r-process
β-delayed n-emission
branchings
(final abundances)
Fission rates and distributions:
•  n-induced
•  spontaneous
•  β-delayed
β-decay half-lives
(progenitor abundances,
process speed)
n-capture rates
Smoothing progenitor
abundances during freezeout
ν-physics ?
Seed production
rates
Masses:
•  Sn location of the path
•  Qβ, Sn theoretical β-decay properties,
n-capture rates
Beta-delayed neutron emission
The knowledge we have
on nuclear structure and
dynamics is based on
about 3000 nuclei,
whereas still more than
5000 new nuclei must
exist.
β-delayed neutron
emission probability
Almost all these new
nuclei are expected to be
neutron emitters, and
hence, an understanding
of this property and the
involved technique
becomes of pivotal
impotance for NS and
future studies.
Pn
Known Pn-Values
stability
Pn: Moeller et al PRC67(2003)
•  Practically all NEW nuclei, are expected to be neutron emitters!
* Sn < Qβ * decay to states above Sn
Conditions for delayed neutron emission
148Cs
Pn= 20%
β-
n
147Ba
T1/2= 146 ms
β148Ba
T1/2= 612 ms
β148La T1/2=
è neutron emission competes and can dominate over γ-ray de-excitation
The process will dominate far from stability on the n-rich side.
Pn è gives info on decay above Sn è stringent test on β-strength function
1.26 s
Impact on r-process abundances
During „Freeze-­‐out“: detour of β-­‐decay chains ð r-­‐abundance changes During „Freeze-­‐out“: enhancement of neutron flux ð r-­‐abundance changes Pn x 0.4
Pn / 10
Pn xPn
10x 10
In 134 138 ms βn, β2n N=126
PART3
Beta decay in n-rich nuclei
-  in-flight fragmentation facilities
-  ISOL facilities
-  TAS experiments
N-rich nuclei: short half-lives regime
Nuclei produced by means of relativistic frangmentation/fission of
heavy nuclei on thin targets
•  GSI, Riken, MSU, (Ganil)
•  > 50 MeV/u è producton of cocktail beams of many nuclei
•  Use of spectrometers to transport and eparate nuclei of interest
è Relatively long decay paths Δt > 150-300 ns
•  Nuclei are then brought to rest in final focal plane and let decay
pros
Cons
•  Possibility of studying a set of
•  Low production rates
nuclei AT THE SAME TIME
è Diminishing at increasing N/Z
•  Van be used to study both shortratio
living (ms ) and long living (100s )
•  Need to run at low rate to
nuclei
distinguish contributions from
•  Study mother and daughter decay
each nucleus
at same time (if mother nculeus
has isomeric states > 1µs)
•  Get informations already with few
particles
Experimental technique
* Active, position sensitive, pixelated stopper to correlate implanted ions
(mother) with β-decay (daughter).
è stack of several DSSSD to ensure implantation and detect electrons
* Measure γ rays (internal structure) from decays of ns-ms isomeric states
in original implanted ion, and/or excited states in daughter nucleus
N-rich nuclei: short half-lives regime
GSI
beam
RIKEN
Beta-delayed gammas
β-delayed gamma spectroscopy of daughter
Ion-beta correlation techniques:
distinguish implantation and decay within same detector
Implantation-decay correlations
with large background
(half lifes similar to the
implantation rate):
ü  implant-decay
time correlation:
active catcher
ü  implant-decay position
correlation: granularity
ü  implant of several ions:
thickness and area
ü  energy of the implanted ion and
the emitted β
GSI
RIKEN
* Dual gain pre-amps on DSSSD to get
* Low gain branch for implanted ions
energies of implanted ion and β-particle * High-gain branch for β and α decays
* All events time stamped with MHz
clock.
Ion-beta correlation techniques:
conditions
Typical Trigger conditions
Implantation:
Signal coming from separator
(egs. Last scintillator before stoppers)
Decay:
OR signal coming from Si detectors
β  and α
correlations
Prompt-time
γ correlations
γ rays are usully acquired as SLAVE in
both trigger conditions
Additional conditions to be added off-line during data reduction/analysis:
-  Time correlation btw. Identified implantation and subsequent decay
requiring also position correlation (neighbour pixels) and maximum
“surviving” time (egs. 3xT1/2)
-  γ correlation to ensure correct correlation (no bg): delayed γ within
~100-200 ns window
-  Time spectrum using TIMESTAMPS and with γ gate
Beta Counting System (BCS) [MSU/SIMBA@GSI]
• Implantation DSSD:
x-y position (pixel), time
• Decay DSSD:
x-y position (pixel), time
4 x Si PIN DSSD (40⋅40)
Silicon PIN Stack
6 x SSSD
(16)
Veto light particles
Ge
Beta calorimetry
Full reconstruction of all quantities: time/gamma/Qvalue
Implantation station:The Neutron Emission Ratio Observer (NERO)
3He
Proportional BF3 Proportional
Counters
Counters
Nuclei with β-decay
Polyethylene
Moderator
Nuclei with β-decay AND
neutron(s)
Boron Carbide
Shielding
G. Lorusso, J.Pereira et al.,
PoS NIC-IX (2007)
Pn-values
Measurement of neutron in “delayed”
coincidence with β-decay
100Sn
region
Nature 486, 341 (2012)
~260 100Sn nuclei produced (0.75/h)
~ 126 fully reconstructed decay chains
2.62
Measuring long half-lives
produced
implanted
Fragmentation of 238U beam @ 1GeV/u
Ibeam ~ 3*109 pps
Beam extraction 1s, beam cycle 3s
forward
backward
213Pb->213Tl
211Tl
211Pb
WARNING: long lifetimes and high rates
imply a careful study of bg contributions
è ion-β correlations : out of beam + ionβ position correlations + ion-β time
correlations
è uncorrelated decays determined from
backward-time ion-β correlations
212Tl
212Pb
New spectroscopic
information in 219Po
211-212-213Tl
Ad-hoc numerical procedure
•  Long half-lives è cover many beam repetition cycles
•  High rate è possible double implantations
Standard techniques are not available
è numerical fit based on Monte Carlo simulations of the
implantation-decay process including experimental
implantation rates and having as free parameters the β decay
half life and the β detection efficiency
218Bi:
Benchmark of
Analysis
χ2 fits to two independent time correlations:
• Experimental ion-β time-correlated spectra
• Calculated time distribution obtained from Monte-Carlo
simulations
Fitting function: ratio of forward/backward time-distribution
functions
H. de Witte et al., PRC (2004)
43
Important results in heavy mass region
The description of
first-forbidden (ff) transitions
using macroscopic statistical models
seems a good approach for these nuclei
at variance from N<126 nuclei
FRDM+QRPA and DF3 + QRPA
models in agreement with our
measurements
G.Benzoni et al., PLB 715 (2012) 293
ISOL: Isotope Separation On Line
Nuclei produced by ISOL method, spallation/fission/fragmentation on
thick targets, followed by chemical/physical processes to extract desired
nuclei
•  High intensity proton beams and beams produced at very low energies
(60 keV) [possibility for post-acceleration]
•  Monoisotopical beams sometimes achieved. Impurities due to few
contaminant species
ISOL: Isotope Separation On Line
•  ISOLDE, Ganil, ALTO,
Jyvaskyla, SPES….
Laser
1
1
H
2
He
2
3
Li
4
Be
3
11
Na
12
Mg
4
19
K
20
Ca
21
Sc
22
Ti
23
V
24
Cr
25
Mn
26
Fe
27
Co
28
Ni
29
Cu
5
37
Rb
38
Sr
39
Y
40
Zr
41
Nb
42
Mo
43
Tc
44
Ru
45
Rh
46
Pd
6
55
Cs
56
Ba
*
71
Lu
72
Hf
73
Ta
74
W
75
Re
76
Os
77
Ir
7
87
Fr
88
Ra
**
103
Lr
104
Rf
105
Db
106
Sg
107
Bh
108
Hs
* Lanthanides
*
57
La
58
Ce
59
Pr
60
Nd
61
Pm
** Actinides
**
89
Ac
90
Th
91
Pa
92
U
93
Np
5
B
6
C
7
N
8
O
9
F
10
Ne
13
Al
14
Si
15
P
16
S
17
Cl
18
Ar
30
Zn
31
Ga
32
Ge
33
As
34
Se
35
Br
36
Kr
47
Ag
48
Cd
49
In
50
Sn
51
Sb
52
Te
53
I
54
Xe
78
Pt
79
Au
80
Hg
81
Tl
82
Pb
83
Bi
84
Po
85
At
86
Rn
109
Mt
110
Ds
111
Rg
62
Sm
63
Eu
64
Gd
65
Tb
66
Dy
67
Ho
68
Er
69
Tm
70
Yb
94
Pu
95
Am
96
Cm
97
Bk
98
Cf
99
Es
100
Fm
101
Md
102
No
pros
•
•
•
•
Cons
Usually high cross sections
•  Short-living nuclei cannot be
No need to re-accelarated beams
accessed since they decay inUsually can accept high rates
flight
Study mother and daughter decay •  Not all nuclei can be successfully
at same time (if mother nucleus
extracted
has isomeric states > 1ms)
•  Relatively Long-living nuclei
(> 100ms) owing to intermediate
processes of effusion and
diffusion
TAPE Station systems
Principle of operation
RI beam
0.5 inch Al-coated mylar tape.
Implantation
point
Decay
point
Each “point” is a measuring point and can be equipped with egs. Ge
detectors and Plastic or Si detectors for β particles
Trigger given by implantation signal and β signal
Long-living activity is removed by moving away the tape
In-beam vs TAPE Station systems: figures
In-beam
Tape station
•  Low production rates
•  Require little statistics
•  can be used to study both shortliving ( ms ) and long living (100s )
nuclei
•  Get informations already with few
particles
•  Can focus on single case
è Clean signal
•  Usually higher cross-sections
•  Only nuclei T1/2> 100 ms
•  Naturally eliminating bg activity
•  εimplant ~ 70 %
•  εβ < 50%
•  εγ ~ 15 % (in best case) (**)
•  Εimplantjj, ~ 100%(*)
•  εβ ~ 50-60%
•  εγ ~ 10 % (**)
(*) provided T1/2 is large otherwise we have losses due to decays “on the way”
(**) of course it depends on many parameters: number of detectors, distance
from implantation point, other reactions (prompt-flash in case of in-beam)
Example:
60Co
decay from http://www.nndc.bnl.gov/
Feeding:=Iβ = Pf*100
Comparative half-life: ft
pmax
f (Zʹ′,Q) = const ⋅
2
2
∫ F(Zʹ′, p)p (Q − E ) dp
e
0
€
ft f = constʹ′
1
M if
2
= constʹ′
1
Bi→ f
Pβ (E)
1
Sβ (E) =
=
f (Zʹ′,Qβ − E)T1/2 ft(E)
Bi→ f
1
=
Ψf τ ± or στ ± Ψi
2J i + 1
T1/2
tf =
Pf
T1/2 =
ln(2)
λ
2
= τ ln(2)
The problem of measuring the β-feeding
β
ZAN
Real
situation
f2 = I γ 2
f1 = 0
(Iγ 2 = Iγ 1 )
2
γ2
1
γ1
Z+1AN-1
Eγ 1 Eγ 2
•  Ge €
detectors
are conventionally used to
€
construct the level scheme populated in
the decay
• From the γ intensity balance we deduce
the β-feeding
The problem of measuring the β-feeding
β
ZAN
Apparent
situation
f2 = 0
f1 = Iγ 1
2
γ2
1
γ1
Z+1AN-1
Eγ 1 Eγ 2
€ happens if we miss some
• €What
intensity
Single γ ~ ε
Coinc γ 1γ 2 ~ ε1ε 2
Pandemonium effect
f (t) = ∑i E i λi Ni (t)
ZAN
ZAN
β- decays
β- decays
€
Z+1AN-1
Z+1AN-1
Eβ = ∑ I β (Ei ) Eβ ,i
Eβoverestimation.
Eγ = ∑ I β (Ei )Ei
Eγunderestimation
i
i
TAGS measurements
Since the gamma detection is the only
reasonable way to solve the problem, we need
a highly efficient device:
A TOTAL ABSORTION SPECTROMETER
But there is a change in philosophy. Instead of
detecting the individual gamma rays we sum
the energy deposited by the gamma cascades
in the detector.
A TAS is like a calorimeter!
Big crystal, 4π (BaF2/NaI/HPGe)
d
=
R
(
B
)
⋅f
TAGS analysys
β-decay
di = ∑ Rij f j
or d = R ⋅ f
j
R is the response function of the spectrometer, Rij
means the probability that feeding at a level j gives
counts in data channel i of the spectrum
The response matrix R can be constructed by recursive convolution:
j −1
R j = ∑ b jk g jk ⊗ R k
k =0
gjk: γ-response for j è k transition
Rk: response for level k
bjk: branching ratio for j è k transition
Mathematical formalization by Tain, Cano, et al.
3
2
1
0
TAS experimental setup
Si det.
TAS det (NaI(tl))
Rad. beam .
Ge det.
(Det 1 & det 2).
Det 1: 20 cm diam., 20 cm
length, 5 cm hole
Tape station
Det2: 20 cm diam, 10 cm length
LNPI design (St. Petersburg)
Lucrecia: the TAS at ISOLDE (CERN)
(Madrid-Strasbourg-Surrey-Valencia)
•  A large NaI cylindrical
crystal 38 cm Ø, 38cm
length
•  An X-ray detector (Ge)
•  A β detector
•  Possibility of collection
point inside the crystal
Results of the analysis for 104Tc
d and R(b)*ffinal
D. Jordan, PhD Thesis, Valencia, 2010
D. Jordan, PRC 87, 044318 (2013)
T1/2 = 1098(18) s; Qβ= 5516(6) keV
Eβ(TAGS) = 931 (10) keV
ΔEβ = -664 keV
Eβ(JEFF-3.1) = 1595 (75) keV
Eγ(TAGS) = 3229 (24) keV
Eγ(JEFF-3.1) = 1890 (31) keV
ΔEγ = 1339 keV
Conclusions
reasons to study beta decay:
Ø  Access to gross informations on the decay, Half-life, Pn etc.
Ø  First information on excited states far from stability
Ø  Spin assignments owing to selection rules
Ø  Access to non-yrast states
Ø  Definition of shapes of daughter nuclei
Ø  Connection to mass measurements
Ø  Input for astrophysics and reactor heat calculation….
……many more…