• Paul Mantica
• Lecture 1
• Euroschool for Exotic Beams
• Leuven, Belgium - 2009
Mantica-Euroschool, September 2009 Slide 1

Beta decay properties of unstable nuclei far from stability can provide valuable insight into nuclear shell structure and nuclear deformation changes toward the drip lines.
Precise beta-decay half-lives, end point energies, and branching ratios to unbound states are crucial nuclear physics input parameters for network calculations of the astrophysical rapid neutron capture process.
The selective method of beta decay, in combination with spectroscopic measurements of gamma-rays and neutrons, will open new opportunities to study, for example:
• Gamow-Teller strength in N~Z nuclei to 100 Sn
• Persistence of shell gaps in extreme neutron-rich nuclei ( 60 Ca, 128 Pd)
• r-process waiting point nuclei along N=82 ( 124 Mo, 123 Nb, …) and N=126
( 195 Tm, 194 Er …)
• E(4 + )/E(2 + ) and phase transitions away from stability ( 122 Pd, 90 Ge, 148 Xe, …)
• and others …
Mantica-Euroschool, September 2009 Slide 2

Significant progress has been made in the measurement of beta-decay properties of exotic nuclei, attributed directly to particle-detection techniques employed with fast beams.
Advantage of fast beams:
• Can correlate implantations and decays event-by-event
– ID of decay parent
• suitable for cocktail beams
– crucial for systematic investigations
• reduction in background and increased sensitivity
– half-life: few per day
– beta-neutron: few per hour
– beta-gamma: few per minute
Mantica-Euroschool, September 2009 Slide 3

Beta decay half-lives
All waiting points along N=82 and many along N=126 will be established
First 2 + energies
Major advance in characterizing the systematic variation of E(2 + ) and
E(4 + )/E(2 + ) with increasing neutron number
Mantica-Euroschool, September 2009 Slide 4

BCS
SeGA
Needs:
• Fast beams via fragmentation or fission
• Highly-segmented implantation detector
• Overall implantation rate < 500 s -1
– high resolution separator
• Digital readout (dedicated electronics)
• Ancillary detectors
– electrons, neutrons, photons, etc.
• Floor space: 3 m x 3 m x 3 m
Observables:
• Half-lives
NERO
• Q values (masses)
• Absolute branching ratios
• Excited states in daughter nuclei
• Microsecond isomers
–excited states in parent
Mantica-Euroschool, September 2009 Slide 5

204 Bi
EC/ b + decay
204 Pb b decay b decay
204
81
123
 204
82

122

 
EC decay
204
83
Bi
121
 e   204
82
Pb -
122
 ν
204 Tl b + decay
204
83
Bi
121
 204
82
Pb -
122
 β   ν
Neutron number
Mantica-Euroschool, September 2009 Slide 6

isomer half-lives
T
1/2
T
1/2 beta half-lives
A p
X n
Beta endpoint energy g
Q b absolute beta branching b –
A p isomeric gamma rays
n
 p
A

1
n

1 delayed neutron branching b –

 n
P n g b – S n
A p
1
 1
Y n2 g g g

p
A
 1
Y n1 delayed gamma rays
Mantica-Euroschool, September 2009 Slide 7

12
10
8
6
A=204 Mass Chain
4
2
204 Tl
204 Bi
0 Mass = f
1
(A)Z 2 + f
2
(A)Z+ f
3
(A)d
-2
204 Pb
78 79 80 81 82 83 84 85 86 87 88
Proton Number (Z)
Mantica-Euroschool, September 2009 Slide 8

b decay
204
81
123
 204
82

122

 
EC decay
204
83
Bi
121
 e   204
82
Pb -
122
 ν
Q
β -
 [M( 204 Tl)  M( 204 Pb)]c 2
Q
β -
 Δ( 204 Tl)  Δ( 204 Pb)
Q
EC
Q
EC
 [M( 204 Bi)  M( 204 Pb)]c 2
 Δ( 204 Bi)  Δ( 204 Pb) b + decay
204
83
Bi
121
 204
82
Pb -
122
 β   ν Q
β 
 [M( 204 Tl)  M( 204 Pb) 2m e
]c 2
Q
β 
 Δ( 204 Tl)  Δ( 204 Pb) 2m e c 2
Mantica-Euroschool, September 2009 Slide 9

64
29
35
 64
28
34

 
Decay energy is shared between the electron and the neutrino
~1/3 E b
(max)
Energy spectrum is for the positron is continuous up to the endpoint energy
Mantica-Euroschool, September 2009 Slide 10

Radioactive decay and growth as the form of a first order rate law
N t
=N o e l t
N o is the initial number of nuclei
N t is the number of nuclei at time t e is a mathematical constant 2.7182818284
l is the decay constant
The characteristic rate of a radioactive decay is conveniently given in terms of the half life
1/2
l 
l
The half life is the average time required to reduce the initial number of nuclei by a factor of 2
Mantica-Euroschool, September 2009 Slide 11

120
100
80
60
40
20
0
0 1 2 3 4 5 6 7 8 9 10
Time (arbitrary units)
Mantica-Euroschool, September 2009 Slide 12

There are a wide range of beta decay half lifes:
Isotope
40 K
21
Decay Energy (E
0
)
0.044 MeV
Half life
4.00 x 10 16 s
50 K
31
14.2 MeV 4.27 x 10 -1 s
In general, large decay energies are associated with very short beta-decay half-lives
λ  t ln2
1/2
 K M if
2 f
0 logf
0
 4.0logE
0 for β  decay
 0.78
 0.02Z
 0.005(Z  1)logE
0
Rate is proportional to Decay Energy (E
0
) and Proton Number (Z)
Mantica-Euroschool, September 2009 Slide 13

However, beta-decay half-lives also depend strongly on the properties of the initial and final states involved in the decay
Isotope
32 Si
18
66 Ni
38
Decay Energy (E
0
)
0.221 MeV
0.20 MeV
Half life
4.73 x 10 9 s
1.96 x 10 5 s
Beta transition strength is expressed as a product of the energy factor times the half-life (log f
0 t values).
Mantica-Euroschool, September 2009 Slide 14

• Allowed transitions come in two types:
• Fermi
(
D  =0) and Gamow-Teller
(
D  = 1).
– Relative orientation of angular momentum vectors for the emitted neutrino and fast electron
• Log f o t is an expression of the transition strength that considers the energy of decay (f o value) and the time for decay (t), where t is the partial half-life for the decay.
log f o t = log f o
+ log t log t is the logarithm of the partial half-life of the beta decay t = [t
1/2
]/branch (in seconds)
Superallowed Fermi Decay
D
J=0
Dp
=no log ft ~ 3.5
Allowed Decay
D
J=0,1
Dp
=no log ft ~ 4-7 parity p
=(-1) 
Mantica-Euroschool, September 2009 Slide 15

1
T
1/2

0


E i

Q
S
β
β
  i
 f

Z, R, Q
β

E i

S b
(E) is the beta-strength function f is the Fermi function
R is the nuclear radius
Q
E i b is the endpoint energy is the energy of the final state
T
1/2
 a

(Q b
- C) -b a = 2740 s b = 4.5
Q b
= b endpoint energy
C = cutoff energy (pairing gap in daughter)
Gross b decay results overestimate the half-lives of the most neutron-rich isotopes
• b
-decay rate to low-energy states in daughter underestimated
Tachibana et al.
, Prog. Theor. Phys. 84, 641 (1990)
Pfeiffer, Kratz and Möller, Prog. Nucl. Energy 41, 39 (2002)
Mantica-Euroschool, September 2009 Slide 16

Note that:
1. Fermi function is dominated by the phase space factor (Q b
-E i
) 5
2. The average error increases as
T
1/2 increases
3. Inclusion of first forbidden decay (ff) improves average error for longer T
1/2 values
4. Uncertainty in masses far from stability does not dramatically impact T large)
1/2
, since relative error does not increase rapidly (Q b is
Möller et al ., PRC 67, 055802 (2003)
Mantica-Euroschool, September 2009 Slide 17

• Paul Mantica
• Lecture 2
• Euroschool for Exotic Beams
• Leuven, Belgium - 2009
Mantica-Euroschool, September 2009 Slide 18

• 30 Faculty
– 19 Experimental
– 7 Theory
– 4 Accelerator Physics
• 60 Graduate Students
• 50 Undergraduate
Students
• 700 member Users
Group
• Selected to design and establish Facility for
Rare Isotope Beams
(FRIB)
… a world leader in rare isotope research and education
Biochemistry
NSCL
Law school
Chemistry
Mantica-Euroschool, September 2009 Slide 19

Mantica-Euroschool, September 2009 Slide 20

78 Kr Fragmentation @ 70 MeV/A
D
E

• Fast-moving projectile is abraded, resulting projectile-like fragment travels with a velocity similar to initial projectile
• Produce many isotopes below the initial projectile A radioactive and Z , both stable and
• Separation does not depend on the chemical properties of the isotopes
 TOF
Each fragment can be uniquely identified using time-of-flight, energy-loss, and magnetic rigidity
Mantica-Euroschool, September 2009 Slide 21

K500
A1900
Primary stable atoms are ionized in an ECR source and injected into the accelerating system composed of the coupled K500 and
K1200 superconducting cyclotrons
K1200
The fast, stable beam is then impinged on a target at the object of the A1900 separator
Mantica-Euroschool, September 2009 Slide 22

• D p/p = 5% max
• B r
= 6.0 Tm max
• 8 msr solid angle
• 35 m in length
ECR ion sources
K500
The A1900 Fragment Separator is used to select the rare isotope of interest from unwanted fragmentation products
A1900 focal plane target
K1200 wedge
Production of 78 Ni from 140 MeV/A 86 Kr
Morrissey et al ., NIM B 204, 90 (2003)
Mantica-Euroschool, September 2009 Slide 23

PINS
Planer Ge
Backplate
Implantation detector:
1 each MSL type BB1-1000
4 cm x 4 cm active area
1 mm thick
40 1-mm strips in x and y
Calorimeter:
6 each MSL type W
5 cm active area
1 mm thick
16 strips in one dimension
Prisciandaro et al ., NIM A 505, 140 (2003)
Mantica-Euroschool, September 2009 Slide 24

Primary interaction is via the electromagnetic interaction between the positive charge of the heavy ion and the negative charge of the orbital electrons within the detection medium.
The maximum energy that can be transferred is
4Em e
/m
Where m and E are the particle mass and energy, respectively, and m the electron mass. Since m e mass, the energy transfer is small.
e is is much smaller than the incoming particle primary particle loses its energy over MANY interactions produce many excited atoms or ion pairs in the detector material
Mantica-Euroschool, September 2009 Slide 25

The linear stopping power for charged particles is given as
S
 dE dx
Bethe

Bloch

0.3071
MeV
 cm
2 g
ρ
Zq
Aβ
2
2

 ln


W max
I


 β 2 
δ
2

C
Z


Through the Bethe formula, the linear stopping power is a function of the atomic number of the stopping material (Z) and the ion charge (q) and velocity ( b =v/c) of the incident particle
Range can be obtained by integrating the energy loss rate along the path of the ion:
R(T)
 
0
T  dE dx

1 dE
-dE dx
Distance of penetration
Mantica-Euroschool, September 2009 Slide 26

10000
1000
100
10
1
0
Alpha particles in silicon
200 400 600 800
Alpha particle energy (MeV)
15
1000
0
10
5
30
25
20
50
45
40
35
Stopping power scales with ion mass, charge and energy:
 dE dx

Aq
2
E
Scaling can be extended to range calculations:
R
2
 
2

M
2
M
1 q
1
2 q
2
2
R
1

 T
2
M
M
2
1

 http://www.physics.nist.gov/PhysRefData/Star/Text/ASTAR.html
Mantica-Euroschool, September 2009 Slide 27

78
The range of 100 MeV/A 78 Ni in Si can be scaled from the range of 100
MeV/A alpha particles.
R
2
 
2

M
2
M
1 q
1
2 q
2
2
R
1

 T
2
M
1
M
2


R
Ni 78

7800 MeV


78
4
2
2
28
2
R
α

400 MeV

R
Ni 78

7800 MeV
 
1 9 .
5

0.0051


10 g cm
2
R
Ni 78

7800 MeV

 0.994
g cm 2
 2.33
g cm 3
 0.426
cm
Mantica-Euroschool, September 2009 Slide 28

Fast electrons lose energy at a lower rate and follow a more torturous path through absorbing materials. This can be attributed to the low ion charge (z = 1) and low mass of the electron.
Fast electrons can also lose energy through radiative processes
S  (1/v) 2 NZ (electronic)
S  NEZ 2 (radiative)
Therefore the radiative loses are most important for high energy electrons where the absorbing material has a large atomic number.
S radiative
S electronic

ZE
800 MeV
Mantica-Euroschool, September 2009 Slide 29

100
10
1
0
Electrons in silicon
12
10
8
The range of a 10 MeV beta particle in Si is 5.8 g/cm 2
6 r (Si) = 2.33 g/cm 3
4
2
Therefore, the amount of Si required to fully stop a 10
MeV beta particle is ~ 2.5 cm!
5 10
Electron energy (MeV)
15 20
0 http://physics.nist.gov/PhysRefData/Star/Text/ESTAR.html
Mantica-Euroschool, September 2009 Slide 30

Challenge: beta
D E ~ 100’s of keV beam E ~ 1’s of GeV
CPA16 dual gain preamp from MultiChannel
Systems: 16 channels, 50
W input impedance,
2V output, ~350 ns rise time.
Low gain:
0.03 V/pC output to ADCs
High gain:
2.0 V/pC output to Pico
Systems 16 ch shaper
Mantica-Euroschool, September 2009 Slide 31

PID
Conventional BCS Electronics: Block Diagram
PID
NIM Trigger
Digitization
VME Readout
CAMAC Shapers
Digitized waveform: shortlived proton decay of 145 Tm
Grzywacz NIMB 204, 649 (2003)
XIA PIXE-16
660 channels commissioned and in use with SeGA
Mantica-Euroschool, September 2009 Slide 32

Implant activity into a stopper material for time t implant
.
Cease implantation and observe decay for time t decay
.
If necessary, introduce a “clean” stopper material and repeat.
For deposit of a single isotope:
A
0
A  A
0 e  λt
A=N l
For example shown: t implant
=4  t
1/2
= t decay
A  A
0
(1  e  λt )
Time
Mantica-Euroschool, September 2009 Slide 33

• Correlations between an implantation event and subsequent b decay events are done based on position and time
• Information regarding the particle ID is carried over to a correlated decay event, therefore, b decays are unambiguously identified
• Both prompt and delayed g rays can also be unambiguously assigned
• Decay curves are generated from the difference in absolute times between and implantation and correlated decay event b
The high pixel
A z q+ density of the DSSD and low implantation
Implantation Decay rates (less than 200 ions/second) are essential to reduce probabilities for incorrect correlations
Absolute time
Position (x,y)
Absolute time
Position (x,y)
Energy loss and time of flight
Fragment total kinetic energy
Gate the g
-array ADCs for 20 m s
Energy of outgoing particle
Gate the g
-array ADCs for 20 m s
Mantica-Euroschool, September 2009 Slide 34

The Bateman equations provide a means for analyzing a chain of many successive radioactive decays.
1 (parent)

2 (daughter)

3 (grand
 daughter)
 n
Special assumption: At t=0, only parent is present.
N n

C
1 e
 λ
1 t 
C
2 e
 λ
2 t   C n e
 λ n t
C
1


λ
2
 λ
1

λ
1
λ
λ
3

2

λ
1
λ n 1
 
λ n
 λ
1
 N
1
0
C
2


λ
1
 λ
2

λ
1
λ
3
λ

2

λ
2
λ n 1
 
λ n
 λ
2
 N
1
0
C n


λ
1
 λ n

λ
λ
1
λ
2

2
λ
 λ n 1
 
λ n n 1
 λ n
 N
1
0
Mantica-Euroschool, September 2009 Slide 35

For nuclei far from stability, the typical condition is that
T
1/2
(parent)

T
1/2
(daughter)

T
1/2
(grand
 daughter) 
1
0,9 parent
This condition is the nonequilibrium case for radioactive decay, and, for a three-generation decay, the number of granddaughter nuclei will eventually equal the initial number of parent nuclei (assuming the daughter and grand-daughter are not produced directly)
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1 daughter grand-daughter
0
0 500
Time (arb. units)
1000
Mantica-Euroschool, September 2009 Slide 36

L
123
(λ
1
)

N
123 i


1

δ(n i

1)
 p
1
(λ
1
)
 δ(n i

2)
 p
2
(λ
1
)
 δ(n i

3)
 p
3
(λ
1
)

1 decay observed: p
1
(λ
1
)

P
101
(λ
1
)

P
102
(λ
1
)

P
103
(λ
1
)

P
104
(λ
1
)
B r
Background

(bt c
) r e
 bt c r!
P
101

D
1
ε
1

( D
2

D
2
ε
2
D
3

D
2
ε
2
D
3
ε
3
)

B
0
P
102

D
1
ε
1
D
2
ε
2

( D
3

D
3
ε
3
)

B
0
P
103

D
1
ε
1
D
2
ε
2
D
3
ε
3

B
0
P
104

( D
1

D
1
ε
1
D
2

D
1
ε
1
D
2
ε
2
D
3

D
1
ε
1
D
2
ε
1
D
3
ε
3
)

B
1
Decay Functions
D i

F i
(λ i
, t)
D i

1

F i
(λ i
, t)
Efficiency
(
ε 
1

ε
ε)
2 decays observed: 10 scenarios → p
2
(λ
1
)
3 decays observed: 20 scenarios → p
3
(λ
1
)
ε, λ
2
, λ
3
 constant
Pereira et al ., PRC 79, 035806 (2009)
Mantica-Euroschool, September 2009 Slide 37

Background rate was determined uniquely for each 100 Sn decay by considering the entire time-lapsed history of implantations into the
DSSD
The simulation below shows the close matching between simulated and observed decay rate.
Determination of the 100 Sn half-life came from maximizing the likelihood function, considering also those implantation events that were not correlated with a decay
N
0

1
P
0

(λ
P
0
1
(λ
)
1
)
N
123
Since N
0 depends on l
1 itself, an iterative process is used to maximize the function
(j

1)
1

123
1
0
1
N
0
(λ
1 f
)

L
(j

1)
(λ
1
)
 λ
1 λ
1
 λ
1
(f

1 )

0
Mantica-Euroschool, September 2009 Slide 38

• Paul Mantica
• Lecture 3
• Euroschool for Exotic Beams
• Leuven, Belgium - 2009
Mantica-Euroschool, September 2009 Slide 39

Demonstrated burst conditions [1]
• T=1.5-2 GK
• r ~
10 6 g/cm 3
• l b
• l p
~ 0.6 s -1
~ 10,000 s -1
Termination point
Reactions of rp-process
Feeding from
( a
,p)-process
Parameters:
• b
-decay rates
• ( a
, g
),(p, g
) rates
• Masses
Schatz et al., NPA 688, 150c (2001)
Mantica-Euroschool, September 2009 Slide 40

Not only is the production of 84 Mo overwhelmed by peak production of lighter isotones, but the low-momentum tails of the more prolifically produced, near stable isotopes also dominate the total yield, even with use of a wedge degrader.
Selected Fragment: Mo-84
Projectile: 124 Xe 48+ at 140 MeV/A
Target: 9 Be, 305 mg/cm 2
Acceptance: 1%
Wedge: 27 Al, 180 mg/cm 2
N=
42
Mo
41
Nb
40
Zr
39
Y
38
Sr
37
Rb
40
82
81
80
79
78
77
83
82
81
3
80
42
84 85
0.08
0.4
83
4
84
3
82
7
81
60 400
83
3
82
79 80
500 1000
78 79
2000 1000
81
80
44
86
85
84
83
82
81
87
86
85
84
83
82
Rate in pps/pnA from LISE++
Mantica-Euroschool, September 2009 Slide 41

The RF Fragment Separator was commissioned at NSCL in April 2007. The first beta-decay campaign to study neutrondeficient nuclei was initiated October 2007.
Operating principle:
Beam species that have similar B r differ in TOF.
Beam Packets
Mantica-Euroschool, September 2009 Slide 42

84
V = 0 kV
Y slits = 50 mm
I beam
= 0.8 pnA
83 s -1 over DSSD
V = 47 kV
Y slits = 10 mm
I beam
= 10 pnA
0.5 s -1 over DSSD
78 Rb
77 Kr
76 Br
74 Se
73 As
All beam
84 Mo
83 Nb
82 Zr
81 Zr
80 Y
79 Sr
V=0 kV V=47 kV Rejection
1* 1
15
80
16
40
1
2
20
130
4000
10
200
85
2
0.6
47
18700
13500
1150
1980
0.4
0.3
15
5
700
83**
630
0.5**
0.8 pnA 10 pnA
46700
45000
77
400
1.1
180
* Rates relative to 84 Mo, 5 × 10 -4 pps/pnA
** particles/s-pnA
PID are normalized to same number of 80 Y implantations
Mantica-Euroschool, September 2009 Slide 43

84
84 Mo is a waiting point along the rp-process. The re-measured half-life was found to be more than 1s shorter than the previous value, accelerating mass processing along the rp-process pathway.
Previous T
1/2
= 3.7 (+1.0, -0.8) s
Decay curve for 84 Mo
T
1/2
= 2.2
±
0.2 s
Half-lives of even-even N=Z nuclei compared with theory
Stoker et al., PRC 79, 015803 (2009)
Mantica-Euroschool, September 2009 Slide 44

84
Maximum likelihood analysis requires extraction of correlated beta decays.
Correlations were defined for 84 Mo by limiting the time window for correlations to less than 20 s after an implantation.
In addition, beta decays that occurred in the same pixel as the implantation, or any of the four nearest-neighbor pixels, were considered.
Three generations of decays were taken into account to generate the likelihood function. The log t between a given
84 Mo implantation and the subsequent one, two, and three beta correlations are shown to the right.
The half-life value from the maximum likelihood analysis was consistent with that extracted from the decay curve fit.
Mantica-Euroschool, September 2009 Slide 45

84
The order of magnitude uncertainty in the final 84 Sr abundance has been reduced to less than a factor of 2 with the new half-life.
A=84 abundances
Previous uncertainty bounded by divergent theoretical T
1/2 predictions
(0.8 s lower bound; 6.0 s upper bound)
83
Nb(p,
α) 80
Zr(β

)
80
Y(p,
γ) 81
Zr


(β
 (p,

)
γ)
81
82
Y(p,
Nb(β
γ)

)



82
Zr(p,
γ) 83
Nb
Schatz et al., Phys. Rep. 294, 167 (1998)
Mantica-Euroschool, September 2009 Slide 46

For nuclei with Z > N, the proton drip line is located where the proton separation energy equals zero
S p


M(A

1, Z

1)

M(p)

M(A, Z)
 c
2

B tot
(A, Z)

B tot
(A

1, Z

1)
Neutron-deficient nuclei near the proton drip line typically have large
Q
EC values, and beta decay can directly populate proton unbound states.
The “delayed” protons will be emitted with the apparent half-life of the beta decay.
Sp
Mantica-Euroschool, September 2009 Slide 47

When the level density of the proton unbound states in the daughter is smaller than the resolution of the particle detector, the individual protons cannot be distinguished. A statistical treatment of the proton spectrum can then be applied.
I p
 
  if
I i
β
E p


Γ i p
Γ
 if p
Γ i
γ


E p
I i
β
Γ if p
Γ i
γ
E1




2.5
 10  4
2π r
J i
 U
0
E 3
γ f
E1

 1 ft


J i
I 
 1

J i
 1
σ
ρ
T
2

 
I

ρ
E
J i x
 E
 
γ
 dE
γ
Need GT matrix element
< s >, level densities r , and transmission coefficient for proton decay T ℓ
Huang et al., PRC 59, 2402 (1999)
Mantica-Euroschool, September 2009 Slide 48

81
Delayed gamma rays
Delayed protons
Mantica-Euroschool, September 2009 Slide 49

Known ground state alpha emitters among the neutron-deficient Te isotopes result in the theoretical termination of the rp process with the Sn-Sb-Te cycle.
Decay data in the vicinity of the doublymagic nucleus 100 Sn is critical to the characterization of the nuclear structure effects in this region of the nuclear chart.
Sn-Sb-Te cycle. The solid lines indicate reaction flows of more than 10%.
Schatz et al., PRL 86 3471 (2001)
Mantica-Euroschool, September 2009 Slide 50

100
Simple shell model calculation would predict GT decay to a single p g
9/2
-1 n g
7/2
+1 state in 100 In with B(GT) = 17.8
2p-2h admixtures in both the 100 Sn initial and the 100 In final states will fragment the B(GT), but most of the strength is still expected to reside within the Q b window
The calculation to the right considers such mutliparticle-multihole admixtures.
The lowest 1 + state in 100 In is predominantly 1p1h, but the B(GT) is reduced by a factor of 4.
Extraction of B(GT) for 100 Sn requires accurate determination of T
1/2 and branching ratios to final states in 100 In
100 Sn → 100 In
Brown and Rykaczewski, PRC 50, R2270 (1994)
Mantica-Euroschool, September 2009 Slide 51

102
2800 102 Sn nuclei
T
1/2
= 3.8(2) s; Q
EC
= 5.76(14) MeV
Both high resolution and calorimetric g
-ray detection
Faestermann et al ., EPJ A 15, 185 (2002) Karny et al ., EPJ A 25, s01, 135 (2005)
Mantica-Euroschool, September 2009 Slide 52

102 Sn: B(GT) = 4.2(9)
Hindrance Factor h h

B ( GT ) theory
B ( GT ) experiment
B ( GT ) theory
  f
 f s  i
2
B ( GT ) experiment
  f



 g
6147
A
/ g
V s

2
 f ( Q
EC
I b

E

)

T
1 / 2


 h ( 102 Sn) = 3.7
Karny et al ., EPJ A 25, s01, 135 (2005)
Mantica-Euroschool, September 2009 Slide 53

100
Production
• GANIL [Lewitowicz et al.
, PLB 322, 20 (1994)]
– 112 Sn at 63 MeV∙A onto a 144 mg/cm 2 Ni target
– 11 events attributed to 100 Sn 48+ in 44 hours
– cross section for 100 Sn
≥ 120 pb
• GSI [Schneider et al.
, ZPA 348, 241 (1994)]
– 124 Xe at 1095 GeV∙A onto a 6 g/cm 2 Be target
– 9 events attributed to 100 Sn 50+ in 277 hours
– cross section for 100 Sn ~11 pb
GANIL
100 Sn
GSI
100 Sn Decay
• GSI [Summerer et al.
, NPA 616, 341c (1997)]
– 6 events followed by subsequent b decay
– T
1/2
= 0.94 (+0.54, -0.27) s
– Q b
= 7.2 (+0.8, -0.5) MeV
– B(GT) = 11.3 (+6.5, -8.3) assuming all decay to a single 1 + state in 100 In
Mantica-Euroschool, September 2009 Slide 54

• Radio Frequency Fragment
Separator (RFFS)
Purification of neutron-deficient beams by time-of-flight
 1.5-m long RF cavity, V max
=100 kV
 First campaign in Fall 2008
 Beam rejection factor of >200 for 100 Sn
NSF MRI PHY-05-20930
Mantica-Euroschool, September 2009 Slide 55

100
• Only the third time 100 Sn was ever produced and studied.
Primary beam dose of 6.7 x 10 16 112 Sn ions over 11.5 days
Counts s expt
(pb) s
EPAX
(pb)
97 Cd 1.14(1) x 10 5 3900(700) 6500
99 In 3.02(9) x 10 4 900(200) 1000
101 Sn 3.6(3) x 10 3 100(30) 100
96 Cd
98 In
274(24)
216(21)
5.5(14)
3.8(12)
170
41
100 Sn 14(5) 0.25(15) 6.6
Ratio
1.7(3)
1.1(3)
1.0(4)
31(+10, -6)
11(+5, -3)
26(+40, -10)
• Production rate of 100 Sn and other
N=Z nuclei was below EPAX predictions
Bazin et al.
, PRL 101, 252501 (2008)
Mantica-Euroschool, September 2009 Slide 56

Log(time) curves
100
98
96
The half-lives of the ground states of heavy
N=Z nuclei were deduced by event-by-event decay correlation measurements and analyzed based on a maximum likelihood probability function. The new values are:
• 96 Cd: 1.3 (+0.24, -0.21) s
• 98 In: 0.047 (13) s
• 100 Sn: 0.55 (+0.70, -0.31) s
Comparison with theory
Bazin et al.
, PRL 101, 252501 (2008)
Mantica-Euroschool, September 2009 Slide 57

101
Ground state spin and parity of 101 Sn up for debate
• 7/2 + from Darby et al.
[next presentation]
• a decay fine structure
• 5/2 + from Seweryniak et al.
, PRL 99, 022504 (2007).
• g
-ray correlated with protons from 101 Sn decay
Z=50 isotopes
N=51 isotones
Mantica-Euroschool, September 2009 Slide 58

101
The b
-delayed proton spectrum from
101 Sn is strongly influenced by the angular momentum of the ground state
Factor of 4 improvement in statistics over previous measurement. Shape of spectrum more consistent with the model-dependent statistical treatment assuming 5/2 + ground state spin and parity
Lorusso et al ., PoS (NiC-X) 172 (2008)
Kavatsyuk et al ., EPJ A 31, 319 (2007)
Mantica-Euroschool, September 2009 Slide 59

b
Delayed proton emission observed for first time in
98,99 In and 96 Cd
Approved experiments to study b p and other decay modes in much lighter, neutrondeficient nuclei
Mantica-Euroschool, September 2009 Slide 60

All N=Z odd, odd nuclei above A=75 have very short (< 100 ms) b -decay half-lives
Several of these nuclides have two b decaying states
Short half-lives indicative of superallowed
Fermi 0 +  0 + b decays
Rate pnA·s
Total in
96 h
Open questions:
• Do the states with short b halflives correspond to the ground states of the parents?
82 Nb 0.26
86 Tc 0.06
45,000
10,000
E(2 + ) in daughter
(keV)
407
566 e g
(%) Counts in 2 + 
0 + peak*
11 1,000
9 180
• Are there
82 b -decaying isomers in
Nb and 86 Tc?
* Assumes 0.5% branching to non-analog states.
Isomer and b -delayed g -ray spectroscopy on odd-odd,
N=Z nuclides with A > 80.
• What is the ground-state to ground-state branching ratio for the short-lived b decays?
Faestermann et al.
, EPJ A 15 185 (2002)
Mantica-Euroschool, September 2009 Slide 61

• Paul Mantica
• Lecture 4
• Euroschool for Exotic Beams
• Leuven, Belgium - 2009
Mantica-Euroschool, September 2009 Slide 62

For nuclei with N > Z, the neutron drip line is located where the neutron separation energy equals zero
S n


M(A

1, Z)

M(n)

M(A, Z)
 c
2 
B tot
(A, Z)

B tot
(A

1, Z)
Neutron-rich nuclei near the proton drip line typically have large Q b values, and beta decay can directly populate neutron unbound states.
The “delayed” neutrons will be emitted with the apparent half-life of the beta decay.
Parallels delayed proton emission…
Mantica-Euroschool, September 2009 Slide 63

p f
7/2 fills j
>
=  + 1/2 j
<
=  – 1/2 p g
9/2 fills
34
56 p g
9/2
– n g
7/2
32 p f
7/2
– n f
5/2
Attractive:
Repulsive:

 j
 j
 and and j

 j


 and
 j

 and
 j
 and and j

 j




In general:
• Radial wavefunctions must be similar
• Large  and 
´ enhance tensor monopole effect
Otsuka et al.
, PRL 95, 232502 (2005)
Mantica-Euroschool, September 2009 Slide 64

Z

Sn
Sb
N=50
d
3/2 h
11/2 s
1/2 g
7/2 d
5/2 protons
N=82
Z=50
N
 neutrons d
3/2 h
11/2 s
1/2 g
7/2 d
5/2
82
78
66
64
56
Mantica-Euroschool, September 2009 Slide 65

51
proton g
7/2 d
5/2 orbital “moves” relative to proton when neutron h
11/2 orbital is occupied
Mantica-Euroschool, September 2009 Slide 66

Proton-neutron interaction is strongest when the orbitals they occupy strongly overlap. This overlap is maximum when  n
~  p
. The attractive nature of the monopole interaction may lead to a re-arrangement of the single-particle orbitals.
e ~ j p h
11/2 d
3/2 s
1/2 g
7/2 d
5/2
50 g
9/2
40 p
1/2 f
5/2 p
3/2 protons
 e j p
  j n
50 j n j p V
M neutrons d
3/2 h
11/2 s
1/2 g
7/2 d
5/2 g
9/2 j n j p v
2 j n
In
51
Sb, a change in the proton single-particle states is observed upon filling of the h orbital.
11/2 neutron
Mantica-Euroschool, September 2009 Slide 67

Ca (Z=20)
Ti (Z=22) f
Removal of protons from
7/2 orbital produces significant energy gap between n f
5/2 and n p
1/2 orbitals at Ti (Z=22) and
Ca (Z=20)
Two questions to be addressed:
1. Is there evidence for an
N=34 subshell closure in Ca?
2. How are the neutron spe’s evolving with changing proton number?
Honma et al.
, PRC 65, 061301(R) (2002)
Mantica-Euroschool, September 2009 Slide 68

20
28
+
50
82
The excitation energy of the first excited 2 + state in eveneven nuclei can provide initial insight into the degree of nuclear collectivity
126
E
2


1225 MeV b
2
A
7
3
Mantica-Euroschool, September 2009 Slide 69

66
Dy
deformed single-particle vibrational

66
+
+
3000
3.5
3.3 for rigid rotor
3 2500
2.5
2000
66
Dy
2
1500
1.5
1000
1
500 4 +
0.5
2 +
0
66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104
0
Neutron Number
Mantica-Euroschool, September 2009 Slide 71

+
p f
7/2 fills p f
7/2 fills
Excited states in 54 Ca
34 have remained elusive!
Mantica-Euroschool, September 2009 Slide 72

Primary beam: 76 Ge 130 MeV/nucleon
Momentum Acceptance: 5%
300 mg/cm 2 Al wedge at I2 position
B r
1,2
B r
3,4
= 4.3867 Tm
= 4.1339 Tm
Target 352 mg/cm 2 Be
16 hours
B r
1,2
B r
3,4
= 4.4030 Tm
= 4.1339 Tm
Target 352 mg/cm 2 Be
167 hours
Mantica-Euroschool, September 2009 Slide 73

212
53-56
314
148
690
Mantica et al.
, PRC 77, 014313 (2008)
Mantica-Euroschool, September 2009 Slide 74

53-56
1/2
Gross Theory
(No N=32,34 gaps)
Shell Model
(N=32,34 gaps)
N=32
No discrimination between theoretical treatments at N=34
Honma et al.
, PRC 69, 034335 (2004)
Mantica-Euroschool, September 2009 Slide 75

16-detector SeGA arrangement – 24 cm i.d.
Warm FETs
Resolution < 3.5 keV at 1.3 MeV
Stopped beam experiments
Mueller et al ., NIM A 466, 492(2003)
Mantica-Euroschool, September 2009 Slide 76

54
Delayed gamma rays
0+
54 Ca
( n p
1/2
) 2
T
Q
1/2 b
= 86
±
7 ms
= 10.33
±
0.79 MeV (sys.)
1+
(3)+
54 Sc
( p f
7/2
) 1 ( n f
5/2
) 1
4+
2+
0+
54 Ti
Decay curve gated on delayed gamma rays
Mantica-Euroschool, September 2009 Slide 77

Absolute intensities for gamma-ray transitions are obtained from the following:
• Number of parent nuclei correlated with beta decay
• Number of detected gamma rays
• Gamma array peak efficiency curve
Direct feeding to the ground state determined from missing absolute gamma-ray intensity.
In the case of the decay of 54 Ca, the state at 247 keV.
apparent beta feeding all proceeds through the excited
N o
= 136
N g e g
= 23
= 14%
For the 247keV transition in 54 Ca
I g
(abs) ~ 100% log f o t = log f o
+ log t partial
E b
(max) = Q b
– E x
= 10.33 MeV -0.28 MeV
= 10.05 MeV t partial
= t
1/2
/branch
= 0.086 s/1.0
= 0.086 s log f o t = 4.25
± 0.18
http://www.nndc.bnl.gov/logft/
Mantica-Euroschool, September 2009 Slide 78

509 discrete g rays
Q
EC
= 8.91 MeV
Hardy et al.
, PLB 71, 307 (1977)
4.2 MeV
The word “apparent” was purposefully used in the description of the beta feeding following the decay of 54 Ca. Note that the
Q b value is more than 10 MeV. There is the likelihood of the presence of higherenergy with intensities below detection threshold. These unobserved transitions will impact the calculated branching ratios.
Only I g
> 1% shown
Gierlik et al.
, NPA 724, 313 (2003)
Mantica-Euroschool, September 2009 Slide 79

Neutron-rich nuclei will have Q b values that fall above S n in the daugher nucleus. Therefore, detection of neutrons with high efficiency can offset the impact of unobserved gamma rays on calculated beta branches.
T
1/2
Q b
= 86
±
7 ms
= 10.33
±
0.79 MeV (sys.)
0+
54 Ca neutrons
S n
= 4.6
± 0.5 MeV discrete gamma rays
Simultaneous neutron and gamma measurements are not straightforward, as both demand high solid angle coverage, but require different active media for efficient detection.
1+
(3)+
54 Sc
Mantica-Euroschool, September 2009 Slide 80

• Nuclear properties (e.g. mass) determine r-process yields
• Predicted r-process yields do not match observations
• Need masses, half-lives, and neutron branchings
N=82
N=126
Nucleosynthetic process in Type II supernovae(?) or neutron star mergers(?)
Rapid neutron captures on seed nuclei followed by b
decays
Path on neutron-rich side of stability
K.-L. Kratz ISOLDE Workshop, CERN, Geneva, Dec. 15 - 17, 2003
Mantica-Euroschool, September 2009 Slide 81

Time between arrival and decays: r-process nuclei
78 Ni 77 Ni time (ms)
MLH
75 Co
Result for half-life: 110 +100
-60 ms
Compare to theoretical estimate used:470 ms
74 Co 73 Co
Time of flight (m/q)
MSU – Mainz – LANL – Maryland – Notre Dame
Mantica-Euroschool, September 2009 Slide 82

NERO consists of 44 BF
3 and
16 3 He proportional counters.
3 He Proportional
Counters
BCS
BF
3
Proportional
Counters
Polyethylene
Moderator
Cadmium
Shielding
NERO efficiency
~45% to 1 MeV
0.5
0.4
0.3
0.2
0.1
Inner
Middle
Outer
Total
0
0.001
0.01
0.1
Energy (MeV)
1 10
Lorusso et al ., PoS (NIC-IX), 243 (2006)
Mantica-Euroschool, September 2009 Slide 83

1/2
QRPA Moeller et al. 1997
QRPA Moeller et al. 2003
CQRPA Borzov 2005
OXBASH Lisetzky et al.
This work
Previous work
Mantica-Euroschool, September 2009 Slide 84

120
75
Can use combination of
T
1/2 and P n to isolate ground state deformation
P n

5.4%
Small neutron branching observed for 120 Rh decay not consistent with macroscopic models that include an adhoc quenching of the N=82 shell closure
Montes et al.
, PRC 73, 035801 (2006)
Mantica-Euroschool, September 2009 Slide 85

n
The delayed gamma-ray spectra from
55 Sc and 56 Sc have “identical” transitions with energies 592 and 1204 keV:
Provides evidence for delayed neutron emission following decay of 56 Sc.
The absolute gamma ray intensities can be used to deduce P n
; however, this will be a lower limit, since the calculation only considers neutron transitions that populate daughter.
excited states in the A-1
Mantica-Euroschool, September 2009 Slide 86

56
56 Sc has two β-decaying states: a short-lived, low-spin state and a longer-lived high spin states. 56 Sc also has a microsecond isomer that decays by several prompt gamma rays.
Mantica-Euroschool, September 2009 Slide 87

• Paul Mantica
• Lecture 4
• Euroschool for Exotic Beams
• Leuven, Belgium - 2009
Mantica-Euroschool, September 2009 Slide 88

MSU selected to design and establish
FRIB at the present NSCL site
Mantica-Euroschool, September 2009 Slide 89

Mantica-Euroschool, September 2009 Slide 90

• FRIB with 400 kW for all beams and minimum energy of 200 MeV/u will have beam rates for some isotopes up to 100 times higher than other facilities
• For example: FRIB intensity will allow the key benchmark nuclei 54 Ca
(reaccelerated beams) and 60 Ca (fast beams) to be studied
Mantica-Euroschool, September 2009 Slide 91

• A full suite of experimental equipment will be available for fast, stopped and reaccelerated beams
• New equipment
– Stopped beam area (LASERS)
– ISLA Recoil Separator
– Solenoid spectrometer
– Active Target TPC
Mantica-Euroschool, September 2009 Slide 92