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."Invariante Variationsprobleme" D. Wiss. Zu Göttingen, Math-phys. Klasse 1918: 235–257.

Examples Invariance Conserved Quantity Translation in time Energy Translation in Space linear Momentum Rotation in Space Angular momentum Inversion of co-ordinates Parity Charge Conjugation Charge parity Time reversal Time parity CPT 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 Δmc 2 = 1.29 MeV } The beginning - mass of proton = MeV/c 2 - mass of neutron = MeV/c 2 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 e.cm

Mirror Nuclei - A = 7 Comparison of levels in A = 7 nuclei 7 Li and 7 Be 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 = 14 C 12 C +n-p = 14 N +p-p = 14 O { 14 C and 14 O are mirror nuclei. Their level structures are consistent with charge symmetry. The g.s. of 14 N does not fit. Beta decay from 14 O to 0+ state in 14 N 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 14 C to the 14 N 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 T Z = +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 e 2 - T Z In Strong interactions we cannot distinguish between n and p. Since Q and B are conserved so is T Z For a nucleus T Z = (N - Z) 2

-2 SZSZ S = O 12 N -2 TZTZ T = Be 12 B 12 C Spin System Isospin System

Nuclear Reactions and Isospin. A = 14 T = 1 T = 0 T Z = +1T Z = 0T Z = -1 If Isospin is conserved in the Strong Interaction then in 16 O + d 14 N + 4 He we cannot populate the state at 2.3 MeV in 14 N 16 O + d 14 N + 4 He 0 0 0,1 0 T T Z 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 ( 3 He,t) but also (n,p) and (d, 2 He) - experiments usually carried out at MeV/nucleon and O o (small momentum transfer q) Energy resolution in (p,n) is much poorer than in ( 3 He,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 = T 0 – 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 = T 0 -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 T T0T0 T (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 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 ( 3 He,t) at O o 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,  T Z = +/- 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,  T Z = +/- 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 ( 3 He,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

46 Ti 50 Cr 50 Fe 54 Ni 46 Cr ß+ ( 3 He,t) N=Z T z =0 T z = +1 T z = Zn Ni 54 Fe 42 Ti Ca 22 We have the stable targets Tz=+1 We have large Q  -values Tz=-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 1 st 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.

E x in daughter nuclei (MeV) Counts Charge Exchange Reactions Results (RCNP-Osaka) Ca( 3 He,t) 42 Sc 46 Ti( 3 He,t) 46 V 50 Cr( 3 He,t) 50 Mn 54 Fe( 3 He,t) 54 Co g.S (IAS) g.s.(IAS ) g.s(IAS ) g.s.(IAS) 16 F g.s N g.s. 12 N (1+) (1+) (1+) (1+) (1+) (1+) (1+) (1+) (1+)2.694 (1+)3.392 (1+) (1+) (1+) (1+) (1+) (1+) (1+) (1+) (1+) (1+) (1+) T. Adachi et. al., PRC 73, (2006) Y. Fujita et. al., PRL (2005) T. Adachi et al., NPA 788, 70c (2007). Y. Fujita et. al., PRL (2005)

The reduced transition strength B(GT) from the initial state with spin J i, isospin T i and T zi to the final state with J f,T f and T zf is Where CGT is the Clebsch-Gordan coefficient (T i T zi 1 +-1| T f T zf ) and the M GT (σ τ) 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. A (1987)

Scientific Motivation CE reactions CE reactions: No restriction in excitation energy of Gamow-Teller states Beta Decay: Absolute Normalisation of B(GT) T z =+1T z =-1T z = (p,n)-type V    - decay   V  T z =+1 T z =0T z =-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 restriction and suppression of the β-feeding due to the Fermi factor 0+ Tz=-1 T=1 0+ Tz=0 T=1 0+ Tz=+1 T=1 β + -decay Charge exchange ((p,n) or 3He,t)) (under special circumstances) Main idea: if isospin symmetry holds then we can combine β-decay and Charge Exchange reactions 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 58 Zn 58 Fe Fermi Gamow Teller T=1 case is particularly simple because the final state is identical

Combined Analysis Assume Isospin symmetry Precisely known T 1/2 and Q Measured transition intensities from ( 3 He,t) Combining this knowledge we can predict what we would see in the β-decay

Combined Analysis Results of ( 3 He,t) reactions at Osaka Measurements at 140 MeV/nucleon Measurements at 0 0 Energy resolution ~ 30 KeV This allows one-to-one comparison with β – decay Programme of studying the complementary β – decays initiated at GSI and GANIL

Beta Decay RISING Production of 54Ni, 50Fe, 46Cr and 42Ti Beam MeV/u 10 9 pps Target Be 400mg/cm2 Separation in flight with the Fragment Separator (FRS) Francisco Molina IFIC(Valencia) MeV/u production selection identificatio n 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: 46 Cr  46 V β-decay study of 46Cr produced in a fragmentation reaction at GSI, F. Molina et al, preliminary High-resolution CE study at RCNP, Osaka, T. Adachi, et al, PRC 73 (’06) 46 Ti( 3 He,t) 46 V e+e-

Importance of a precise T1/2 measurement absolute B(GT) values can be obtained via reconstruction of beta-decay spectrum  -decay experiment, experimental T 1/2 Absolute intensity: B(GT) Y. Fujita et al. PRL 95 (‘05) B(F)=N-Z Relative feeding intensity from ( 3 He,t) (t i =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 T 1/2 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 betas Case shown is 54 Ni decay

Correlations with all betas Red – correlation in same pixel Blue – correlation in different part of detector - Now normalised Case shown is 54 Ni decay

T 1/2 for 54 Ni Background subtracted and fit to two successive decays. T 1/2 = (1.0) ms

Decay of 54Ni

Beta-delayed gammas from 50 Fe

Decay Scheme for 50 Fe

Motivation:- 1.Can we rely on proportionality in Charge Exchange - Remember that although CE is studied at 0 0 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

48V48V 52 Mn 56 Co 52 Co 56 Cu 48 Mn ++ ( 3 He,t) N=Z Second goal, to study Tz=±2 to Tz=±1 mirror transitions. Proposed measurement beta decay of 56Zn T z =0 T z =1 T z =-1 52 Ni T z =2 T z =-2 52 Cr 48 Cr 52 Fe 56 Ni 56 Fe 56 Zn 48 Ti 48 Fe (56 Zn: first observed at GANIL) Zn Ni 30 Mirror nuclei

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

Francisco Molina IFIC(Valencia) Z.Hu et al. : Nucl. Instr. and Meth. In Phys. Res. A 419 (1998) y = p0+p1*x + p2*x 2 + p3*x 3 +p4*x 4 +p5*x 5, y=log(eff) and x=log(E) Rising Ge simulation Including + Si + Box 2.26% RISING Efficiency Simulation Santiago, December 2009

56 Fe( 3 He,t) and Estimated  -decay Spectrum  -decay branching ratios can be estimated!

64Zn 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 Veto Implantation, beta and proton detector ΔE2 300 μm 1004 μm 3 mm beam The E556 measurement at GANIL in September 2008 Plus 4 EXOGAM gamma detectors

Lise estimation 29 part/sec On line analysis /37*3600=0.84 part/sec The experiment worked well, Unfortunately the 6n and 8n removal cross sections are 30 times lower than estimates from advanced codes

Scientific Motivation CE reactions CE reactions: No restriction in excitation energy of Gamow-Teller states Beta Decay: Absolute Normalisation of B(GT) T z =+1T z =-1T z = (p,n)-type V    - decay   V  T z =+1 T z =0T z =-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. A (1987)