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Isomer Spectroscopy in Near-Spherical Nuclei

Isomer Spectroscopy in Near-Spherical Nuclei. Lecture at the ‘School cum Workshop on Yrast and Near-Yrast Spectroscopy’ IIT Roorkee, October 2009 Paddy Regan Department of Physics University of Surrey Guildford GU2 7XH. Outline. What is an isomer ? Electromagnetic transition rates.

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Isomer Spectroscopy in Near-Spherical Nuclei

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  1. Isomer Spectroscopy in Near-Spherical Nuclei Lecture at the ‘School cum Workshop on Yrast and Near-Yrast Spectroscopy’ IIT Roorkee, October 2009 Paddy Regan Department of Physics University of Surrey Guildford GU2 7XH

  2. Outline • What is an isomer ? • Electromagnetic transition rates. • Weisskopf Single-Particle Estimates • Shell Structure in near spherical nuclei. • Odd-A singly magic nuclei (e.g., 205Au126) • Why are E1s ‘naturally’ hindered ? • Seniority isomers, j2 & jn configurations ? • Near Magic nuclei. • Limited valence space? Core breaking? • Magnetic properties: g-factors in seniority isomers.

  3. What is an isomer ? Metastable (long-lived) nuclear excited state. ‘Long-lived’ could mean: ~10-19 seconds, shape isomers in a-cluster resonances or ~1015 years 180Ta 9-→1+ decay. Why/when do nuclear isomers occur ? (i) large change in spin (‘spin-trap’) (ii) small transition energy between states (seniority isomers) (iii) dramatic change in structure/shape (fission isomers) and/or underlying symmetry (K-isomers) What information do isomers gives you ? Isomers occur due to single particle structure. For example, transitions are hindered between states with different structures (note, this is not case for seniority isomers).

  4. 9- 250 T1/2 = 25 min 238 b- branch =33% a branch = 67% 0- 212Bi 2- 115 T1/2 = 61 min 1- 0 (25/2+) T1/2=25secs 1462 1428 (17/2+) 1065 (13/2+) 99.984% a-decay branch, 91% to 13/2+ isomer in 207Pb, 7% to 1/2- ground state in 207Pb, Qa ~ 9 MeV per decay 687 11/2+ 211Po T1/2=0.5 secs 0 9/2+ 212Bi, Z=83, N=129, 9- from vg9/2 x ph9/2 ‘High-spin’ a and b-decaying isomers just above 208Pb, basically as a result of ‘yrast’ (spin) traps.. Yrastness is what causes these isomers…they simply have ‘nowhere’ to go to (easily). This yrastness is itself caused by high-j intruders in the nuclear single particle spectrum….

  5. From P.M. Walker and G.D. Dracoulis, Nature 399, p35 (1999) Ex>1MeV, T1/2>1ms (red), T1/2>1hour (black)

  6. For a quantized (nuclear) system, the decay probability is determined by the MATRIX ELEMENT of the EM MULTIPOLE OPERATOR, where i..e, integrated over the nuclear volume. We can then get the general expression for the probability per unit time for gamma-ray emission, l(sL) , from: (see Introductory Nuclear Physics, K.S. Krane (1988) p330). EM Transition Rates Classically, the average power radiated by an EM multipole field is given by m(sL) is the time-varying electric or magnetic multipole moment. w is the (circular) frequency of the EM field

  7. Note: Transition rates get slower (i.e., longer lifetimes associated with) higher order multipole decays

  8. Weisskopf Single Particle Estimates: These are ‘yardstick’ estimates for the speed of electromagnetic decays for a given electromagnetic multipole. They depend on the size of the nucleus (i.e., A) and the energy of the photon (Eg2L+1) They estimates using of the transition rate for spherically symmetric proton orbitals for nuclei of radius r=r0A1/3.

  9. Weisskopf estimates tsp for 1Wu at A~100 and Eg = 200 keV i.e., lowest multipole decays are favoured….but need to conserve angular momentum so need at least l = Ii-If for decay to be allowed. Note, for low Eg and high-l, internal conversion also competes/dominates.

  10. The EM transition rate depends on Eg2l+1,, the highest energy transitions for the lowest l are (generally) favoured. This results in the preferential population of yrast and near-yrast states.

  11. The EM transition rate depends on Eg2l+1,, the highest energy transitions for the lowest l are (generally) favoured. This results in the preferential population of yrast and near-yrast states.

  12. The EM transition rate depends on Eg2l+1,, the highest energy transitions for the lowest l are (generally) favoured. This results in the preferential population of yrast and near-yrast states.

  13. The EM transition rate depends on Eg2l+1,, the highest energy transitions for the lowest l are (generally) favoured. This results in the preferential population of yrast and near-yrast states.

  14. The EM transition rate depends on Eg2l+1,, the highest energy transitions for the lowest l are (generally) favoured. This results in the preferential population of yrast and near-yrast states. = gamma-ray between yrast states

  15. = g ray between yrast states The EM transition rate depends on Eg2l+1, (for E2 decays Eg5) Thus, the highest energy transitions for the lowest l are usually favoured. Non-yrast states decay to yrast ones (unless very different f , K-isomers) = g ray from non-yrast state.

  16. = g ray between yrast states The EM transition rate depends on Eg2l+1, (for E2 decays Eg5) Thus, the highest energy transitions for the lowest l are usually favoured. Non-yrast states decay to yrast ones (unless very different f , K-isomers) = g ray from non-yrast state.

  17. = g ray between yrast states The EM transition rate depends on Eg2l+1, (for E2 decays Eg5) Thus, the highest energy transitions for the lowest l are usually favoured. Non-yrast states decay to yrast ones (unless very different f , K-isomers) = g ray from non-yrast state.

  18. Yrast Traps The yrast 8+ state lies lower in excitation energy than any 6+ state… i.e., would need a ‘negative’ gamma-ray energy to decay to any 6+ state

  19. Yrast Traps The yrast 8+ state can not decay to ANY 6+. The lowest order multipole allowed is l=4 Ip=8+→4+ i.e., an E4 decay.

  20. Clusters of levels+Pauli Principle  magic numbers, inert cores Concept of valence nucleons – key to structure. Many-body  few-body: each body counts. Addition of 2 neutrons in a nucleus with 150 can drastically alter structure

  21. Independent Particle Model • Put nucleons (protons and neutrons separately) into orbits. • Key question – how do we figure out the total angular momentum of a nucleus with more than one particle? • Put 2j + 1 identical nucleons (fermions) in an orbit with angular momentum j. Each one MUST go into a different magnetic substate. • Angular momenta add vectorially but projections (m values) add algebraically. So, total M is sum of m’s M = j + (j – 1) + (j – 2) + …+ 1/2 + (-1/2) + … + [ - (j – 2)] + [ - (j – 1)] + (-j) = 0 M = 0. So, if the only possible M is 0, then J= 0 Thus, a full shell of nucleons always has total angular momentum 0. This simplifies things.

  22. Podolyak et al., Phys. Lett. B672 (2009) 116 N=126 ; Z=79. Odd, single proton transition; h11/2→ d3/2 state (holes in Z=82 shell). Selection rule says lowest multipole decay allowed is l=11/2 - 3/2 = 4. Change of parity means lowest must transition be M4. 1Wu 907 keV M4 in 205Au has T1/2= 8secs. ‘Pure’ single particle (proton) transition from 11/2- state to 3/2+ state. (note, decay here is observed following INTERNAL CONVERSION). These competing decays (to gamma emission) are often observed in isomeric decays

  23. More complex nuclei… • Signatures of nuclear structure help show us which regions of the nuclear chart are explained by ‘single-particle’ excitations • or deformed regions (see Phil Walker’s lecture).

  24. 1i13/2 Why are E1 s isomeric? E1 single particle decays need to proceed between orbitals which have Delta L=1 and change parity, e.g., f7/2 and d5/2 or g9/2 and f7/2 or h11/2 and g9/2 or p3/2 and d5/2 What about typical 2-particle configs. e.g., Ip=5- from (h11/2)-1 x (s1/2)-1 Ip=4+ from (d3/2)-1 x (s1/2)-1 1h9/2 2f7/2 82 1h11/2 2d3/2 3s1/2 1g7/2 2d5/2 50 1g9/2 (40) 2p1/2 2p3/2 1f5/2 28 1f7/2 20 1d3/2 2s1/2 1d5/2 8 1p1/2 1p3/2 2 1s1/2 V= SHO + l2.+ l.s.

  25. R(E(4+) / E(2+)) Systematics plot from Burcu Cakirli

  26. e.g., 128Cd, isomeric 440 keV E1 decay. 1 Wu 440 keV E1 should have ~4x10-15s; Actually has ~300 ns (i..e hindered by ~108

  27. 1i13/2 ASIDE: Why are E1 s isomeric? E1s often observed with decay probabilities Of 10-5→10-9 Wu E1 single particle decays need to proceed between orbitals which have Dl =1 and change parity, e.g., f7/2 and d5/2 or g9/2 and f7/2 or h11/2 and g9/2 or i13/2 and h11/2 or p3/2 and d5/2 BUT these orbitals are along way from each other in terms of energy in the mean-field single particle spectrum. 1h9/2 2f7/2 82 1h11/2 2d3/2 3s1/2 1g7/2 2d5/2 50 1g9/2 (40) 2p1/2 2p3/2 1f5/2 28 1f7/2 20 1d3/2 2s1/2 1d5/2 8 1p1/2 1p3/2 2 1s1/2 V= SHO + l2.+ l.s.

  28. 1i13/2 Why are E1 s isomeric? E1 single particle decays need to proceed between orbitals which have Delta L=1 and change parity, e.g., What about typical 2-particle configs. e.g., Ip=5- from mostly (h11/2)-1 x (s1/2)-1 Ip=4+ from mostly (d3/2)-1 x (s1/2)-1 No E1 ‘allowed’ between such orbitals. E1 occur due to (very) small fractions of the wavefunction from orbitals in higher shells. Small overlap wavefunction in multipole Matrix element causes ‘slow’ E1s 1h9/2 2f7/2 82 1h11/2 2d3/2 3s1/2 1g7/2 2d5/2 50 1g9/2 (40) 2p1/2 2p3/2 1f5/2 28 1f7/2 20 1d3/2 2s1/2 1d5/2 8 1p1/2 1p3/2 2 1s1/2 V= SHO + l2.+ l.s.

  29. 1i13/2 Why are E1 s isomeric? E1s often observed with decay probabilities Of 10-5→10-8 Wu E1 single particle decays need to proceed between orbitals which have Delta L=1 and change parity, e.g., f7/2 and d5/2 or g9/2 and f7/2 or h11/2 and g9/2 or p3/2 and d5/2 BUT these orbitals are along way from each other in terms of energy in the mean-field single particle spectrum. 1h9/2 2f7/2 82 1h11/2 2d3/2 3s1/2 1g7/2 2d5/2 50 1g9/2 (40) 2p1/2 2p3/2 1f5/2 28 1f7/2 20 1d3/2 2s1/2 1d5/2 8 1p1/2 1p3/2 2 1s1/2 V= SHO + l2.+ l.s.

  30. 2 valence nucleon j2 configurations in magic; magic+-2 nuclei

  31. Seniority (spherical shell residual interaction) Isomers

  32. Geometric Interpretation of the d residual interaction for j2 configuration coupled to Spin J Use the cosine rule and recall that the magnitude of the spin vector of spin j = [ j (j+1) ]-1/2

  33. 8 q 6 4 2 0 d-interaction gives nice simple geometric rationale for Seniority Isomers from DE ~ -VoFr tan (q/2) for T=1, even J 8 6 4 DE(j2J) 2 0 e.g. Jp= (h9/2)2coupled to 0+, 2+, 4+, 6+ and 8+. q 90 180

  34. 8 6 4 2 0 d-interaction gives nice simple geometric rationale for Seniority Isomers from DE ~ -VoFr tan (q/2) for T=1, even J See e.g., Nuclear structure from a simple perspective, R.F. Casten Chap 4.)

  35. Study the evolution of shell structure as a function of N:Z ratio. 208Pb (Z=82, N=126) 132Sn (Z=50, N=82) 56Ni (Z=28, N=28) 126 82 50 (Proton) holes in high-j intruders (f7/2, g9/2 and h11/2) gives rise to ‘seniority isomers’ ‘below’ doubly magic shells. Expect 8+ and 10+ isomers in 130Cd and 206Hg. 28

  36. g = m / I , can use ‘Schmidt model’ to give estimates for what the g-factors should be for pure spherical orbits. Can measure g directly from ‘twisting’ effect of putting magnetic dipole moment, m, in a magnetic field, B. Nucleus precesses with the Larmor frequency, wL = gmNB

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