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 EnergyTranslation in Space linear MomentumRotation in Space Angular momentum

Inversion of co-ordinates ParityCharge Conjugation Charge parityTime reversal Time parityCPT 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

Δmc2 = 1.29 MeV }• 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

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

+n-n = 14C 12C +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 Be 2

- TZ

• 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

-2

-1

SZ

S = 2

+2

+1

0

12O

12N

-2

-1

TZ

T = 2

+2

+1

0

12Be

12B

12C

Spin System Isospin System

Nuclear Reactions and Isospin.

A = 14

T = 1

T = 1

T = 1

T = 0

TZ = +1 TZ = 0 TZ = -1

• If Isospin is conserved in the

Strong Interaction then in

16O + d 14N + 4He

we cannot populate the

state at 2.3 MeV in 14N

• 16O + d 14N + 4He

0 0 0,1 0 T

0 0 0 0 TZ

The 2.3MeV state is not populated in this reaction

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.

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.

T0T0 - 1

T0

T0 + 1(p,n)

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 IASThen the IAS is embedded in a continuum of states of lower isospin.The fact that it does not merge with them means thatThe 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

46Ti

50Cr

50Fe

54Ni

46Cr

ß+

(3He,t)

N=Z

T z=0

T z= +1

T z= -1

5830Zn28

58Ni

54Fe

42Ti

4220Ca22

We have the stable targetsTz=+1

We have large Q-valuesTz=-1

Adventages of studying fp Shell Nuclei with T=1

Tz=(N-Z)/2

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.

Ex in daughter nuclei (MeV)

Cou

nts

0 2 4 6 8 10 12

Charge Exchange Reactions Results (RCNP-Osaka)

0

1000

2000

3000

2000

4000

6000

1000

2000

3000

500

1000

150042Ca(3He,t)42Sc

46Ti(3He,t)46V

50Cr(3He,t)50Mn

54Fe(3He,t)54Co

g.S

(I

AS

)g

.s.

(IA

S)

g.s

(IA

S)

g.s

.(IA

S)

16F

g

.s.

0.1

93

0.4

24

12N

g

.s.

12N

0

.96

0.

0.6

11

(1+

)0

.99

4 (

1+)

1.4

33

(1+

)

2.4

61

(1+

)2

.69

9 (

1+)

2.9

78

(1+

)

3.8

70

(1+

)

0.6

52

(1+

)

2.4

11

(1+

)2

.69

4 (

1+)

3.3

92

(1+

)

3.6

54

(1

+)

0.9

37

(1+

)

4.5

50

(1

+)

4.8

28

(1

+)

3.8

95

(1

+)

3.3

77

(1+

)

5.9

21

(1+

)

4.3

32

(1+

)

5.7

28

(1+

)

3.6

89

(1+

)

T. Adachi et. al., PRC 73, 024311 (2006)

Y. Fujita et. al., PRL 95 212501 (2005)

T. Adachi et al., NPA 788, 70c (2007).

Y. Fujita et. al., PRL 95 212501 (2005)

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

The reduced transition strength – B(GT)

Combined Analysis (CE – β Decay)decay Charge Exchange Reactions at 0º

T.N.Taddeucci et al. Nucl.Phys. A469 125-172 (1987)

Scientific Motivation

CE reactions

CE reactions: No restriction in excitation energy of Gamow-Teller states

Beta Decay: Absolute Normalisation of B(GT)

Tz=+1 Tz=-1Tz=0

0+ 0+0+

1+1+

1+

1+

1+

1+

(p,n)-type

V

-decay

V

Tz=+1 Tz=0 Tz=-1

(in isospin symmetry space*)

V

, IAS

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

B(GT) measures transition probabilities

Advantages :

Big advantage:Absolute normalisation of the B(GT)Disadvantages:energy window restrictionand suppression of the β-feedingdue to the Fermi factor

0+Tz=-1T=1

0+Tz=0T=1

0+Tz=+1T=1

β+-decayCharge exchange ((p,n) or 3He,t))(under special circumstances)

Main idea: if isospin symmetry holds thenwe can combine β-decay and Charge Exchangereactions to study Gamow Teller transitions B(GT)

Big advantage:No restriction in excitation energy of GT states, no excitation energy dependence (or very weak)Big disadvantage: No absolute B(GT) values

58Zn 58Fe30 2828 30

Fermi

Gamow Teller

T=1 case is particularlysimple because the final state is identical

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 @ RISINGProduction of 54Ni, 50Fe, 46Cr and 42TiBeam 58Ni@680 MeV/u 109 ppsTarget Be 400mg/cm2

Separation in flight with theFragment Separator (FRS)

Francisco Molina IFIC(Valencia)

100-700MeV/u

production selectio

nidentification

implantation

spectroscopy

35m

Active stopper

Analysis: CRACOW program by J. Grebosz (IFJ PAN-GSI)

Event by event identification

Desired ion

50Fe

~2 millions counts

15 Euroball Cluster Ge Detectors (7 crystals each)

RISING (Ge Array)

Francisco Molina IFIC(Valencia)

Beta(keV) and H.I.(GeV) detector

Santiago, December 2009

decay: 46Cr46V

β-decay study of 46Cr produced in a fragmentation reaction at GSI, F. Molina et al,

preliminary

High-resolution CE studyat RCNP, Osaka,T. Adachi, et al, PRC 73 (’06)

46Ti(3He,t)46V

e+e-

Importance of a precise T1/2 measurement absolute B(GT) values can be obtained

via reconstruction of beta-decay spectrum

GTi

iFermi ttT111

2/1

-decay experiment, experimental

T1/2

itFeedings /1

Absolute intensity: B(GT)

Y. Fujita et al.PRL 95 (‘05) 212501

B(F)=N-Z Relative feeding intensity from (3He,t)

(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

Red – correlation in same pixel Blue – correlation in different part of detector

Correlations with all betasCase shown is 54Ni decay

Correlations with all betas

Red – correlation in same pixel Blue – correlation in different part of detector - Now normalised

Case shown is 54Ni decay

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

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”

Combined Analysis

ΔT = 0 M1 transitions in self-conjugate nuclei are expected to be weaker by a factor of 100 than the average M1 transition strength

48V

52Mn

56Co52Co

56Cu

48Mn+

(3He,t)

N=Z

Second goal, to studyTz=±2 to Tz=±1 mirror transitions. Proposed measurement beta decayof 56Zn

T z=0

T z=1

T z=-1

52Ni

T z=2

T z=-2

52Cr48Cr

52Fe

56Ni

56Fe

56Zn

48Ti

48Fe

(56Zn: first observed at GANIL)

5630Zn26

5626Ni30

Mirror nuclei

Physics case for mirror transitions in Tz=±2 nucleiMain 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

Francisco Molina IFIC(Valencia)

Z.Hu et al. : Nucl. Instr. and Meth. In Phys. Res. A 419 (1998) 121-131

y = p0+p1*x + p2*x2 + p3*x3 +p4*x4+p5*x5 , y=log(eff) and x=log(E)

Rising Ge simulation

Including + Si + Box

2.26%

RISING Efficiency Simulation

Santiago, December 2009

56Fe(3He,t) and Estimated -decay Spectrum

-decay branching ratios can be estimated!

64Zn 29+ 79 MeV/nucleon beamaverage intensity of 500 nAnatNi production targetwas 265 μm placed at the entrance ofthe LISE spectrometer in achromatic condition

ΔE1

Veto

Implantation, beta and proton detectorΔE2

300 μm 300 μm1004 μm

3 mm

beam

The E556 measurement at GANIL in September 2008

Plus 4 EXOGAMgamma detectors

Lise estimation29 part/sec

On line analysis112366/37*3600=0.84 part/sec

The experiment worked well,Unfortunately the 6n and 8n removal cross sections are 30 times lower than estimatesfrom advanced codes

Scientific Motivation

CE reactions

CE reactions: No restriction in excitation energy of Gamow-Teller states

Beta Decay: Absolute Normalisation of B(GT)

Tz=+1 Tz=-1Tz=0

0+ 0+0+

1+1+

1+

1+

1+

1+

(p,n)-type

V

-decay

V

Tz=+1 Tz=0 Tz=-1

(in isospin symmetry space*)

V

, IAS

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

B(GT) measures transition probabilities

Advantages :

Combined Analysis (CE – β Decay)decay Charge Exchange Reactions at 0º

T.N.Taddeucci et al. Nucl.Phys. A469 125-172 (1987)