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

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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

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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!

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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

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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

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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

←←..←

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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)

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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)

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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

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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

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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

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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