Download - Isobaric Analog Resonances
LLNL-PRES-562100This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract
DE-AC52-07NA27344. Lawrence Livermore National Security, LLC
Isobaric Analog ResonancesTORUS Annual Meeting
Ian Thompson, LLNL
June 25, 2012
Lawrence Livermore National Laboratory LLNL-PRES-5621002
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 target isospin operator Tz = ½(N-Z), so
Isospin Dependence of the nucleon-nucleus Optical Potential
Lawrence Livermore National Laboratory LLNL-PRES-5621003
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.
Lane Equations for (p,n) reactions
where
and Q = energy released in (p,n) = − Coulomb displacement energy
Coupledequations!
Lawrence Livermore National Laboratory LLNL-PRES-5621004
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
Isobaric Analog RESONANCES
Lawrence Livermore National Laboratory LLNL-PRES-5621005
Isobaric Analog RESONANCES (2)
EnF = Ep + Q + Bn
where Bn=7.347 MeV and Q = −18.9 MeV
Neutron single-particle levels around 208Pb
Can see resonances when the neutron energy is near a bound state.
Bn=7.347 MeV
Lawrence Livermore National Laboratory LLNL-PRES-5621006
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)
Measuring IARs: (p,p′γ)
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
←←..←
Lawrence Livermore National Laboratory LLNL-PRES-5621007
Measured IAR (p,p′γ) coincidencesLeft: Resonance at 17 MeVNearest to 4s1/2 IAR
Decays at 5.292 MeV≈ E(4s1/2) – E(3p1/2)
Right: Resonance at 17.5 MeVNearest to 2g7/2 or 3d3/2 IAR
Decays at 5.948 MeV≈ E(2g7/2) – E(3p1/2)
Lawrence Livermore National Laboratory LLNL-PRES-5621008
The (p,p′γ) reaction to the (4s1/2) (3p1/2)−1 particle-hole state can also be modeled as:
1. 208Pb3p1/2(p,p’) 208Pb4s1/2 inelastic n* excitation
2. 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
Other contributions to (p,p′γ)
Lawrence Livermore National Laboratory LLNL-PRES-5621009
Fresco expands in two-body partitions. Here, 4:
1. p + 208Pbgs KEp=17 MeV n in 3p1/2 in 208Pbgs
2. p’ + 208Pbph KEp=12 MeV n in 4s1/2 on 207Pb
3. n + 208Bi KEn=−2 MeV n in 4s1/2 as projectile
4. d + 207Pb KEd=12 MeV n in deuteron See the partitions 2. and 3. are NOT orthogonal! Defined new overlap form in FRESCO
for such non-orthogonal bases
Coupled channels treatment of charge-exchange (p,p′γ) in FRESCO
Lawrence Livermore National Laboratory LLNL-PRES-56210010
Calculated (p,p′γ) to (4s1/2) (3p1/2)−1 inelastic state in 208Pb*
Inelastic cross section from overlap of neutron quasi-bound state (#3) and neutron inelastic state (#2).
This calculation usedreal proton potentials, and acomplex deuteron potential
Lawrence Livermore National Laboratory LLNL-PRES-56210011
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!
Unresolved issues
Lawrence Livermore National Laboratory LLNL-PRES-56210012
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
Conclusions