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Isobaric Analog Resonances

Isobaric Analog Resonances. TORUS Annual Meeting. June 25, 2012. Ian Thompson, LLNL. Isospin Dependence of the nucleon-nucleus Optical Potential. Usual formulation of the optical potential: where t z =1/2 for neutrons, -1/2 for protons

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Isobaric Analog Resonances

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  1. Isobaric Analog Resonances TORUS Annual Meeting • June 25, 2012 • Ian Thompson, LLNL

  2. Isospin Dependence of the nucleon-nucleus Optical Potential • Usual formulation of the optical potential: where tz=1/2 for neutrons, -1/2 for protons • N and Z are neutron and proton numbers in the target, A=N+Z, • V0 ≈ −52 MeV at center is negative, and V1≈ 26 MeV is positive: • (neutrons attract protons more than they do other neutrons) • Define targetisospin operator Tz = ½(N-Z), so

  3. Lane Equations for (p,n) reactions • Generalize to the full tensor product • This has off-diagonal terms: • Couples together the neutron and proton channels • Get direct (n,p) and (p,n) cross sections: eg. • Fermi transitions in which initial and final orbits are the same • eg. DeVito, Khoa, Austin, et al: arXiv:1202.2660v1. Coupled equations! where and Q = energy released in (p,n) = − Coulomb displacement energy

  4. Isobaric Analog RESONANCES Consider 208Pb(p,n)208Bi reaction at low energies • Here, Coulomb energies give Q=−18.9 MeV • Neutron has much less energy than proton • Neutron may be trapped below threshold • If near unoccupied bound state, gives resonance: The Isobaric Analog Resonance

  5. Isobaric Analog RESONANCES (2) Neutron single-particle levels around 208Pb Bn=7.347 MeV Can see resonances when the neutron energy is near a bound state. EnF = Ep + Q + Bn where Bn=7.347 MeV and Q = −18.9 MeV

  6. Measuring IARs: (p,p′γ) ← ← .. ← • The IAR ‘decay’ to the elastic channel gives resonance phase shifts • This is the trapped neutron charge-exchanging back to the elastic proton • But it is difficult to measure proton phase shifts accurately at the required energies (14−18 MeV) • Can the IAR decay by other channels? • Yes: OTHER neutrons could change to protons! • As long as they are in spatial orbital NOT occupied by protons • All of the neutrons in the orbitals 1h9/2 to 3p1/2 are thus allowed to charge-exchange back to continuum protons! • This leaves nucleus with a weakly bound neutron (eg 4s1/2) and a hole at or below the Fermi level (eg 3p1/2): a particle-hole inelastic excitation • Proton has energy reduced by the particle−hole energy difference: inelastic p’ • The ph state will eventually gamma-decay. • Experimentally: measure inelastic protons and gamma decays in coincidence

  7. Measured IAR (p,p′γ) coincidences Left: Resonance at 17 MeV Nearest to 4s1/2 IAR Decays at 5.292 MeV ≈ E(4s1/2) – E(3p1/2) Right: Resonance at 17.5 MeV Nearest to 2g7/2 or3d3/2 IAR Decays at 5.948 MeV ≈ E(2g7/2) – E(3p1/2)

  8. Other contributions to (p,p′γ) • The (p,p′γ) reaction to the (4s1/2)(3p1/2)−1 particle-hole state can also be modeled as: • 208Pb3p1/2(p,p’)208Pb4s1/2 inelastic n* excitation • 208Pb3p1/2+p → d+207Pb 1/2- → p’+208Pb4s1/2 two-step transfer reaction via a deuteron • These are easily modeled in FRESCO • Form a non-resonant background to IAR decay • Note: amplitudes interfere coherently

  9. Coupled channels treatment of charge-exchange (p,p′γ) in FRESCO • Fresco expands in two-body partitions. Here, 4: • p + 208Pbgs KEp=17 MeV n in 3p1/2 in 208Pbgs • p’ + 208Pbph KEp=12 MeV n in 4s1/2 on 207Pb • n + 208Bi KEn=−2 MeV n in 4s1/2 as projectile • d + 207Pb KEd=12 MeV n in deuteron • See the partitions 2. and 3. are NOT orthogonal! • Defined new overlap form in FRESCOfor such non-orthogonal bases

  10. Calculated (p,p′γ) to (4s1/2) (3p1/2)−1inelastic state in 208Pb* Inelastic cross section from overlap of neutron quasi-boundstate (#3) and neutron inelastic state (#2). This calculation used real proton potentials, and a complex deuteron potential

  11. Unresolved issues • This work is a ‘valence nucleon’ account of IAR. • In the longer-term, full structure-model calculations of widths would be good. • Verification of absolute magnitudes for all peaks. • Choosing the correct energy-averaging interval • IARs are too narrow for optical-model averaging! • Thus need (p,p′γ) coincidences to see IARs among the compound-nucleus decays • Effects of energy-dependent optical potentials • Eg. for transitions from 20 MeV to sub-threshold!

  12. Conclusions • IAR reactions probe neutron bound states with proton reactions • Should be useful for unstable isotopes! • But: • need (p,p′γ) coincidences to see IAR among all the compound-nucleus decays

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