University of Surrey-23/11/2010
•Symmetries and Conservation Laws
•Introduction of Isospin
• Charge Exchange Reactions
• Beta Decay
• Combined Analysis
• Recent experiments at Osaka, GSI and GANIL
University of Surrey-23/11/2010
Symmetries in Physics
• A symmetry of a system is a property or feature of the system
that remains the same under a transformation (or change).
• For us the most important aspect of symmetry is the invariance of
Physical Laws under an arbitrary differentiable transformation.
• Noether’s Theorem (1918) – symmetry properties of a physical
system are closely related to Conservation Laws for the system
Noether E (1918). "Invariante Variationsprobleme". Nachr. D. König. Gesellsch.
D. Wiss. Zu Göttingen, Math-phys. Klasse 1918: 235–257.
http://arxiv.org/abs/physics/0503066v1.
Examples
Invariance
Conserved Quantity
Translation in time
Translation in Space
Rotation in Space
Energy
linear Momentum
Angular momentum
Inversion of co-ordinates
Charge Conjugation
Time reversal
CPT
Parity
Charge parity
Time parity
Product of C,P and T
Broken Symmetries
• Broken symmetries are almost as important as exact symmetries because many
of Nature’s symmetries are not exact.
• An example of an exact symmetry is Lorenz invariance. [No preferred reference
system or orientation in the Universe]
•Two ways a symmetry is broken
- spontaneous or “hidden” symmetry breaking
e.g Mass of photon = 0 in free space but it acquires an effective mass
when in a superconductor because of the condensation of Cooper
electron pairs
- Underlying equations are not symmetric
e.g. Isospin is a “truly” broken symmetry because of the EM interaction
Isospin
• First suggestion of Isospin (T) came from Heisenberg(1932)
- neutron and proton should be treated as different states of same particle
the nucleon
• The beginning
- mass of proton = 938.2723 MeV/c2
- mass of neutron = 939.5656 MeV/c2
• n
p + e- + e
neutron half life = 613.9(8) s
d quark
lighter u quark plus W boson
• neutron dipole moment < 2.9 x 10-26 e.cm
}
Δmc2 = 1.29 MeV
Mirror Nuclei - A = 7
•Comparison of levels in A = 7
nuclei 7Li and 7Be
•They are clearly very similar
apart from the difference in
the Coulomb energy
Mirror Nuclei - A = 7
•Here we see the same
two level schemes with
the Coulomb energy of
~ 1.5 MeV removed.
•This clearly shows that nuclear
Forces are charge symmetric
i.e n-n = p-p
Charge Independence of Nuclear Forces.
• A = 14 triplet
• The three nuclei can be seen as
12C
{
+n-n = 14C
+n-p = 14N
+p-p = 14O
• 14C and 14O are mirror nuclei. Their level structures are consistent with
charge symmetry. The g.s. of 14N does not fit.
•Beta decay from 14O to 0+ state in 14N at 2.3MeV is very fast (super allowed)
which tells us that the configurations are the same. This compares with the
very slow beta decay from 14C to the 14N ground state.
•This supports all pairs of interactions being equal [n-n = n-p = p-p]
•Near equality of the scattering length and potential in p-p and n-p scattering
in the singlet spin state also supports Charge Independence
Isospin
• This leads us to formal idea of isospin. If n and p are two states of the same particle,
just like spin up and spin down then we can introduce isospin T with substates
TZ = +1/2 for the neutron and -1/2 for the proton.
• Formally description of Isospin operator wave functions is same as for spin
• Isospin space. Conservation of isospin means invariance of | T | under rotation
• Electric charge is given by
Q
B
- TZ
=
e
2
• In Strong interactions we cannot distinguish between n and p. Since Q and B
are conserved so is TZ
• For a nucleus
TZ = (N - Z)
2
Spin System
Isospin System
SZ
TZ
-2
12O
-2
-1
12N
-1
12C
0
+1
12B
+1
+2
12Be
+2
0
S=2
T=2
Nuclear Reactions and Isospin.
• If Isospin is conserved in the
A = 14
Strong Interaction then in
16O
+d
14N
+ 4He
T=1
we cannot populate the
T=1
state at 2.3 MeV in 14N
T=1
T=0
TZ = +1
• 16O + d
14N
TZ = 0
TZ = -1
+ 4He
The 2.3MeV state is not populated
0
0
0,1
0
T
in this reaction
0
0
0
0
TZ
Charge Exchange Reactions
• In Charge Exchange reactions both energy and charge are transferred between
target and projectile nucleus.
• Most frequently studied – (p,n) and (3He,t) but also (n,p) and (d,2He)
- experiments usually carried out at 100-500 MeV/nucleon and Oo (small
momentum transfer q)
• Energy resolution in (p,n) is much poorer than in (3He,t)
but cross-section is typically 10 times
larger.
• (p,n) takes place throughout the
nuclear volume whereas (3He,t)
takes place at surface.
Charge Exchange Reactions
• Charge Exchange reactions show importance of Isospin
in reactions.
T0 + 1
T0
T0 - 1
(p,n)
T0
If target nucleus in (p,n) type reaction has Isospin T then
residual nuclear states have T = T0 – 1 at low energy and
T = T at high excitation energy.
• If T is not a good quantum number then at high energy
where the states form a continuum then states with T = T
and T = T0-1 would merge completely.
•In experiment when we measure the neutrons from
a (p,n) reaction we find a sharp peak superimposed
on a continuum.
Charge Exchange Reactions
Incident proton is captured into a state which is
the isobaric analogue of the state of the valence
neutron in the target ground state whilst the
neutron is kicked out into the continuum.
This proton has the same wavefunction as the
initial valence neutron.
Hence the high probability of exciting this state.
If T is the isospin of the target g.s. and its IAS
Then the IAS is embedded in a continuum of states
of lower isospin.
The fact that it does not merge with them means that
The IAS is pure and T is a good quantum number
[Fujiwara et al.(1995) Tours Symposium II shows
this IAS excited in (3He,t) at Oo at Osaka.]
Spin-Isospin Excitations in Nuclei
• They can be studied in Strong, Weak and Electromagnetic interactions.
• Thus they can be studied in Charge Exchange, Beta Decay and in EM excitations.
• The relevant operator is στ so these are isovector transitions.
• Remember Beta Decay :- Allowed transitions
Fermi transitions - L = 0, S = 0, T = 0, TZ = +/- 1
- connect Isobaric Analogue States
- Strong in Charge Exchange and Beta Decay
- Operator τ (tau)
- Isoscalar transitions
Gamow-Teller transitions - L = 0, S = 1, T = 1, TZ = +/- 1
- Most common type of transition in CE and beta decay
- Operator στ
- Isovector transitions
One consequence – Corresponding T = 1 transitions in conjugate nuclei
are identical in all properties.
T = 1 transitions in conjugate nuclei
Isobaric triplets marked by dashed lines
Note that (p,p/) and (p,n) can excite the
T = 1, 0+ IAS via the στ isovector interaction.
•T = 0, 1+ states only excited via isoscalar
transitions in (p,p/)
•So comparison of spectra from (p,p/)
and (3He,t) allows us to determine T
The Gamow-Teller Resonance
Light Nuclei
[D.R.Tilley et al.,
NPA708(2002)3]
Heavy Nuclei
[J.Janecke et al.,NPA552(193)323]
fp-shell should be a good place to
study the transition
Adventages of studying fp Shell
Nuclei with T=1
58 Zn
30
28
We have large Q-values 54
Ni
Tz=-1
58Ni
50Fe
54Fe
46Cr
42Ti
50Cr
ß+
(3He,t)
Tz=(N-Z)/2
46Ti
42 Ca
20
22
We have the stable targets
Tz=+1
The (3He,t) reaction in the fp-shell
• Residual interaction between two particles.
particle-particle is attractive
particle-hole is repulsive
hole-hole is attractive.
•(3He,t) deposits a proton and kicks out a neutron.
•42Sc – p-p and everything ends in 1st excited state
•46V - now we have p-h as well and strength moves up.
•50Mn – trend continues
•54Co – end of shell many more p-h possibilities than h-h so strength is
at higher energy.
2000
1000
0
0
0.960.
12N
g.s.
12N
0.424
0.193
16F
46Ti(3He,t)46V
5.728 (1+)
3.870 (1+)
3.654
(1+)
4.332 (1+)
2.978 (1+)
3.392 (1+)
3.689 (1+)
2
Y. Fujita et. al.,
PRL 95 212501 (2005)
T. Adachi et. al.,
PRC 73, 024311 (2006)
50Cr(3He,t)50Mn
Y. Fujita et. al.,
PRL 95 212501 (2005)
5.921 (1+)
3000
3.377 (1+)
2000
42Ca(3He,t)42Sc
3.895
(1+)
4.550 (1+)
4.828
(1+)
2.461 (1+)
2.699 (1+)
1.433 (1+)
2.411 (1+)
2.694 (1+)
4000
0.937 (1+)
6000
g.s(IAS
)
0.652 (1+)
1000
g.s.(IAS)
Counts
2000
0.994 (1+)
3000
g.S
(IAS)
500
g.s.(IAS
)
1000
0.611 (1+)
1500
g.s.
Charge Exchange Reactions Results (RCNP-Osaka)
4
6
54Fe(3He,t)54Co
T. Adachi et al., NPA 788, 70c (2007).
8
10
12
Ex in daughter nuclei (MeV)
The reduced transition strength – B(GT)
The reduced transition strength B(GT) from the initial state with spin Ji, isospin Ti
and Tzi to the final state with Jf,Tf and Tzf is
Where CGT is the Clebsch-Gordan coefficient (TiTzi1 +-1| TfTzf) and
the MGT(στ) is the isovector spin-type matrix element.
Note:- This involves the square of the matrix element and spin and isospin
geometrical factors
Combined Analysis (CE – β Decay)
 decay
Charge Exchange Reactions at 0º
T.N.Taddeucci et al. Nucl.Phys. A469 125-172 (1987)
Scientific Motivation
Tz=+1
Tz=0
Tz=-1
(in isospin symmetry space*)
1+
 + -decay
CE reactions
1+
1+
(p,n)-type
Vst
0+
If isospin symmetry exists, mirror
nuclei should populate the same
states with the same probability, in
the daughter nuclei, in the
two mirror processes: CE reactions
and Beta Decay
Advantages :
st
1+
, IAS
Vt 0+
t
0+
Tz=0
CE reactions: No restriction in
excitation energy of Gamow-Teller
states
Beta Decay: Absolute
Normalisation of B(GT)
st
Vst
Tz=+1
1+
1+
B(GT) measures transition
probabilities
Tz=-1
Main idea: if isospin symmetry holds then
we can combine β-decay and Charge Exchange
reactions to study Gamow Teller transitions B(GT)
0+
Tz=-1
T=1
58Zn
30
0+
Tz=+1
T=1
58Fe
28
28
30
β+-decay
Big advantage:
Absolute normalisation
of the B(GT)
Disadvantages:
energy window restriction
and suppression of the β-feeding
due to the Fermi factor
T=1 case is particularly
simple because the final
state is identical
Charge exchange ((p,n) or 3He,t))
(under special circumstances)
0+
Tz=0
T=1
Big advantage:
No restriction in
excitation energy
of GT states, no excitation
energy dependence (or very weak)
Big disadvantage:
No absolute B(GT) values
Fermi
Gamow Teller
Combined Analysis
• Assume Isospin symmetry
• Precisely known T1/2 and Q
• Measured transition
intensities from (3He,t)
Combining this knowledge
we can predict what we
would see in the β-decay
Combined Analysis
• Results of (3He,t) reactions at Osaka
• Measurements at 140 MeV/nucleon
•Measurements at 00
• Energy resolution ~ 30 KeV
This allows one-to-one comparison with
β – decay
• β – decay
Programme of studying the complementary
β – decays initiated at GSI and GANIL
Beta Decay Experiments @ RISING
Production of 54Ni, 50Fe, 46Cr and 42Ti
Beam 58Ni@680 MeV/u 109 pps
Target Be 400mg/cm2
production
Separation in flight with the
Fragment Separator (FRS)
selection
implantation
identificatio
n
50Fe
~2 millions counts
spectroscopy
Desired ion
35m
Event by event identification
100-700MeV/u
Active stopper
Analysis: CRACOW program by J. Grebosz (IFJ PAN-GSI)
Francisco Molina IFIC(Valencia)
RISING (Ge Array)
15 Euroball Cluster Ge Detectors (7 crystals each)
Beta(keV) and H.I.(GeV) detector
Francisco Molina IFIC(Valencia)
Santiago, December 2009
46Ti(3He,t)46V
e+e-
High-resolution CE study
at RCNP, Osaka,
T. Adachi, et al, PRC 73 (’06)
β-decay study of 46Cr
produced in a fragmentation
reaction at GSI, F. Molina et al,
 decay: 46Cr46V
preliminary
Importance of a precise T1/2 measurement
absolute B(GT) values can be obtained
via reconstruction of beta-decay spectrum
Feedings  1 / ti
1
1
1

+ 
T1/ 2 t Fermi iGT ti
-decay B(F)=N-Z Relative feeding intensity
from (3He,t)
experiment,
Absolute intensity: B(GT)
experimental
T1/2
Y. Fujita et al.
PRL 95 (‘05) 212501
(ti =partial half-life)
Immediate Time Correlations
We record Implantation signals in DSSSD detectors. The subsequent betas
are recorded in DSSSDs. Gammas coming at the same time are recorded as well.
Analysis :- Simplest analysis assumes that beta immediately after an implant is
from the corresponding beta decay. However beta efficiency is only approx 40%.
Accordingly if we try to analyse the T1/2 using immediate betas only we will get
the wrong answer.
Results – Immediate Correlations
for A = 54
Measuring the half-life
Alternative:- look for all implant – beta correlations.
Most will be wrong but we will also get all good correlations. Provided other
correlations are due to randoms we will get a picture like the one below
Correlations with all betas
Case shown is 54Ni decay
Red – correlation in same pixel Blue – correlation in different part of detector
Correlations with all betas
Case shown is 54Ni decay
Red – correlation in same pixel Blue – correlation in different part of detector
- Now normalised
T1/2 for 54Ni
Background subtracted and fit to two successive decays.
T1/2 = 114.4 (1.0) ms
Decay of 54Ni
Beta-delayed gammas from 50Fe
Decay Scheme for 50Fe
Combined Analysis
Motivation:-
1. Can we rely on proportionality in Charge Exchange
- Remember that although CE is studied at 00 there is a range of angles
- The reaction may not be purely στ
- Isospin is not a good quantum number
2. The comparison of B(GT) values from beta decay and CE will test the
proportionality
3. We can now normalise the B(GT) values derived from the Charge Exchange
4. The observed branching ratios also help confirm the values of T since they
appear to confirm Warburton and Weneser’s “quasi-rule No.6”
ΔT = 0 M1 transitions in self-conjugate nuclei are expected to be weaker by
a factor of 100 than the average M1 transition strength
Second goal, to study
Tz=±2 to Tz=±1 mirror transitions.
Proposed measurement beta decay
56Zn
of 56Zn
56Cu
(56Zn:
first observed at GANIL)
52Ni
48Fe
56Ni
52Co
56Co
52Fe
+
Mirror nuclei
48Mn
56Fe
52Mn
48Cr
52Cr
48V
48Ti
(3He,t)
56
30Zn26
56
26Ni30
Physics case for mirror transitions in Tz=±2 nuclei
Main difference, the final nucleus is not identical,
Excitation energy might be slightly different,
We compare transitions for different initial and final states.
Big advantage, in general we don’t have direct gs to gs transitions
RISING Efficiency Simulation
Rising Ge simulation
Including + Si + Box
2.26%
y = p0+p1*x + p2*x2 + p3*x3 +p4*x4+p5*x5 , y=log(eff) and x=log(E)
Z.Hu et al. : Nucl. Instr. and Meth. In Phys. Res. A 419 (1998) 121-131
Francisco Molina IFIC(Valencia)
Santiago, December 2009
56Fe(3He,t)
and Estimated -decay Spectrum
-decay branching
ratios can be estimated!
The E556 measurement at GANIL
in September 2008
64Zn 29+ 79 MeV/nucleon beam
average intensity of 500 nA
natNi production target
was 265 μm placed at the entrance of
the LISE spectrometer in achromatic
condition
ΔE1
ΔE2
Implantation, beta and proton detector
Veto
beam
300 μm
300 μm
1004 μm
3 mm
Plus 4 EXOGAM
gamma detectors
The experiment worked well,
Unfortunately the 6n and 8n
removal cross sections are
30 times lower than estimates
from advanced codes
On line analysis
112366/37*3600=0.84 part/sec
Lise estimation
29 part/sec
Scientific Motivation
Tz=+1
Tz=0
Tz=-1
(in isospin symmetry space*)
1+
 + -decay
CE reactions
1+
1+
(p,n)-type
Vst
0+
If isospin symmetry exists, mirror
nuclei should populate the same
states with the same probability, in
the daughter nuclei, in the
two mirror processes: CE reactions
and Beta Decay
Advantages :
st
1+
, IAS
Vt 0+
t
0+
Tz=0
CE reactions: No restriction in
excitation energy of Gamow-Teller
states
Beta Decay: Absolute
Normalisation of B(GT)
st
Vst
Tz=+1
1+
1+
B(GT) measures transition
probabilities
Tz=-1
Combined Analysis (CE – β Decay)
 decay
Charge Exchange Reactions at 0º
T.N.Taddeucci et al. Nucl.Phys. A469 125-172 (1987)