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W.Gelletly

An Introduction: Isospin for the Experimenter. W.Gelletly. Physics Department,University of Surrey. University of Surrey-23/11/2010. Outline. •Symmetries and Conservation Laws •Introduction of Isospin • Charge Exchange Reactions • Beta Decay • Combined Analysis

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W.Gelletly

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  1. An Introduction: Isospin for the Experimenter W.Gelletly Physics Department,University of Surrey University of Surrey-23/11/2010

  2. Outline •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

  3. 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 Lawsunder 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. Klasse1918: 235–257. http://arxiv.org/abs/physics/0503066v1.

  4. Examples InvarianceConserved 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

  5. 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

  6. } 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 Isospin • First suggestion of Isospin(T) came from Heisenberg(1932) - neutron and proton should be treated as different states of same particle the nucleon

  7. 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

  8. 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

  9. Charge Independence of Nuclear Forces. • The three nuclei can be seen as +n-n = 14C 12C +n-p = 14N +p-p = 14O { • A = 14 triplet • 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

  10. Q B = - TZ e 2 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 • 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

  11. TZ SZ -2 -2 -1 -1 12O 0 0 T = 2 S = 2 12N +1 +1 12C +2 +2 12B 12Be Isospin System Spin System

  12. • 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 Nuclear Reactions and Isospin. A = 14 T = 1 T = 1 T = 1 T = 0 TZ = +1 TZ = 0 TZ = -1 • 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

  13. 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.

  14. • 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. T0 + 1 (p,n) T0 T0 T0 - 1 Charge Exchange Reactions

  15. 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.]

  16. 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 στso 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 - Operatorτ (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.

  17. 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

  18. 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

  19. Adventages of studying fp Shell Nuclei with T=1 5830Zn28 N=Z We have large Q-values Tz=-1 54Ni 58Ni 50Fe 54Fe 46Cr 50Cr 42Ti ß+ We have the stable targets Tz=+1 46Ti Tz= -1 (3He,t) Tz=0 4220Ca22 Tz= +1 Tz=(N-Z)/2

  20. 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.

  21. Charge Exchange Reactions Results (RCNP-Osaka) 1500 16F g.s. 0.193 0.424 42Ca(3He,t)42Sc 12N 0.960. 12N g.s. 1000 0.611 (1+) g.S (IAS) 3.689 (1+) Y. Fujita et. al., PRL 95 212501 (2005) 500 3000 g.s.(IAS) 0.994 (1+) 46Ti(3He,t)46V 2.699 (1+) 2.978 (1+) 2.461 (1+) 1.433 (1+) 2000 3.870 (1+) T. Adachi et. al., PRC 73, 024311 (2006) 1000 Counts 6000 g.s(IAS) 50Cr(3He,t)50Mn 3.654 (1+) 5.728 (1+) 0.652 (1+) 4000 Y. Fujita et. al., PRL 95 212501 (2005) 2.411 (1+) 3.392 (1+) 4.332 (1+) 2.694 (1+) 2000 3000 g.s.(IAS) 54Fe(3He,t)54Co 5.921 (1+) 4.550 (1+) 3.895 (1+) 0.937 (1+) 4.828 (1+) 3.377 (1+) 2000 T. Adachi et al., NPA 788, 70c (2007). 1000 0 0 2 4 6 8 10 12 Ex in daughter nuclei (MeV)

  22. 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

  23. Combined Analysis (CE – βDecay) b decay Charge Exchange Reactions at 0º T.N.Taddeucci et al. Nucl.Phys. A469 125-172 (1987)

  24. Scientific Motivation B(GT) measures transition probabilities T =+1 T =0 T =-1 z z z (in isospin symmetry space*) 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 + 1 CE reactions + b -decay 1+ 1+ 1+ 1+ Advantages : (p,n)-type CE reactions: No restriction in excitation energy of Gamow-Teller states st st V 1+ , IAS 0+ 0+ 0+ t t V Beta Decay: Absolute Normalisation of B(GT) st st V T =+1 T =0 T =-1 z z z

  25. 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 0+ Tz=-1 T=1 58Zn 58Fe 30 28 28 30 β+-decay Charge exchange ((p,n) or 3He,t)) (under special circumstances) 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=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 T=1 case is particularly simple because the final state is identical Fermi Gamow Teller

  26. 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

  27. 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

  28. 50Fe ~2 millions counts production selection implantation identification spectroscopy 35m 100-700MeV/u Event by event identification Active stopper Analysis: CRACOW program by J. Grebosz (IFJ PAN-GSI) Francisco Molina IFIC(Valencia) Beta Decay Experiments @ RISING Production of 54Ni, 50Fe, 46Cr and 42Ti Beam 58Ni@680 MeV/u 109 pps Target Be 400mg/cm2 Separation in flight with the Fragment Separator (FRS) Desired ion

  29. Beta(keV) and H.I.(GeV) detector RISING (Ge Array) 15 Euroball Cluster Ge Detectors (7 crystals each) Francisco Molina IFIC(Valencia) Santiago, December 2009

  30. 46Ti(3He,t)46V e+e- High-resolutionCE 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, bdecay: 46Cr46V preliminary

  31. Importance of a precise T1/2 measurementabsolute B(GT) values can be obtained via reconstruction of beta-decay spectrum b-decay experiment, experimental T1/2 B(F)=N-Z Relative feeding intensity from (3He,t) Absolute intensity: B(GT) Y. Fujita et al. PRL 95 (‘05) 212501 (ti =partial half-life)

  32. 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.

  33. Results – Immediate Correlations for A = 54

  34. 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

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

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

  37. T1/2 for 54Ni Background subtracted and fit to two successive decays. T1/2 = 114.4 (1.0) ms

  38. Decay of 54Ni

  39. Beta-delayed gammas from 50Fe

  40. Decay Scheme for 50Fe

  41. Combined Analysis • Motivation:- • 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 • The comparison of B(GT) values from beta decay and CE will test the • proportionality • We can now normalise the B(GT) values derived from the Charge Exchange • 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

  42. Second goal, to study Tz=±2 to Tz=±1 mirror transitions. Proposed measurement beta decay of 56Zn 56Zn N=Z 56Cu (56Zn: first observed at GANIL) 52Ni 56Ni 52Co 48Fe 56Co 52Fe 56Fe Tz=-2 48Mn 52Mn b+ Mirror nuclei 48Cr Tz=-1 52Cr 48V Tz=0 48Ti Tz=1 (3He,t) Tz=2 5630Zn26 5626Ni30

  43. 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 differentinitial andfinal states. Big advantage, in general we don’t have direct gs to gs transitions

  44. 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

  45. 56Fe(3He,t) and Estimated b-decay Spectrum b-decay branching ratios can be estimated!

  46. 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 Implantation, beta and proton detector ΔE2 Veto beam 3 mm 300 μm 300 μm 1004 μm Plus 4 EXOGAM gamma detectors

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