exclusive reactions in few-body systems
DESCRIPTION
Exclusive Reactions in Few-body Systems. Nir Nevo Dinur , W. Leidemann, and N. Barnea. Hebrew University, Jerusalem, Israel . 10.10.2013 Inelastic Reactions in Light Nuclei IIAS-ISF Conference Jerusalem . Outline. Introduction Motivation Methods Results Summary. - PowerPoint PPT PresentationTRANSCRIPT
Exclusive Reactions in Few-
body Systems
10.10.2013Inelastic Reactions in Light Nuclei
IIAS-ISF ConferenceJerusalem
Nir Nevo Dinur, W. Leidemann, and N. Barnea
Hebrew University, Jerusalem, Israel
Outline
• Introduction• Motivation• Methods• Results• Summary
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Introduction:Nuclear Ab initio
Calculations• Ab initio - treat the dynamics of all D.o.F• Nuclear physics:
• A – number of nucleons• D.o.F – spatial, spin, isospin• State-of-the-art nuclear force models• limited to a small number of particles
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Introduction:Nuclear Force Models
1. SimpleMT(I-III) – Malfliet Tjon (+ Coulomb)<ISC>
2. PhenomenologicalAV18 (+ EM int.) + UIX (/TM/IL2,7)<ISB>
→ Simplified: AV8` + UIX`<ISC>
3. EFT-χPTN3LO (NNF) + N2LO (3NF)<ISB>
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Motivation:Why Exclusive Reactions?
1. A laboratory for testing the nuclear force models
2. Calculate observables needed for: Astrophysics; Supernovae; Unstable isotopes; Fusion reactions; etc.
• Why (EM) reactions?10/10/2013 5Exclusive reactions in few-body
systems
• EM probe the nuclear system• structure• dynamics• QED
• 4He• Test NN+3NF in 4-body system• Mimics heavy nuclei (nuclear matter)• Jπ = 0+
• 4He photodisintegration (and electron scattering)
EM reactions:4He photodisintegration
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Experimental status:• A lot of data, many discrepancies• 2012: ‘Active target’ @ TUNL with monoenergetic
photons from HIγS
Exclusive Two-body4He photodisintegration
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R. Raut et al., PRL 108, 042502 (2012)
W. Tornow et al., Phys. Rev. C 85, 061001(R) (2012) S. Quaglioni et al., Phys. Rev. C 69,
044002 (2004)
Exclusive Two-body4He photodisintegration
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Theoretical status:• 2004: (MT I-III + Coulomb) [LIT]• 2012: (AV8’ + 3NF) [MRM & CSM] does not coincide with the state-of-the-art inclusive CS
W. Horiuchi et al., Phys. Rev. C 85, 054002 (2012)
S. Quaglioni et al., Phys. Rev. C 69, 044002 (2004)
inclusive CS
MT I-III
MT I-III
Hints from inclusive4He photodisintegration
• (χEFT) [NCSM] agree with (AV18+UIX) [EIHH]• Theory vs. experiments: agreement ?
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PRL 96, 112301PLB 652, 370
Hints from inclusive4He photodisintegration
• MT overestimates the peak 10 − 15% and strongly underestimates tail
• 3NF leads to a 5-6% peak damping and 35% tail enhancement
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R(p/n) – The ratio of mirror channels
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n + 3He
p + 3H
W. Horiuchi et al., Phys. Rev. C 85, 054002 (2012)
Summary:• Experiments – GDR, R~1, not accurate enough. Tornow: R~<1 (n too
high?)• Theory – (MT/ AV8’+3NF) + Coulomb: R~1 [reproduce B. Wachter, et al.,
PRC38, 1139 (1988)]• ISB forces: ?• Need accurate exptl. data (ISB sensitive) to constrain ISB terms in the
force model
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Methods
Few-Body Method• Hyperspherical Harmonics
N = (A-1) Jacobi vectors Hyper-radius + (3N-1) angles
• The Hamiltonian:
• Bound state problems:
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M. Fabre de la Ripelle, Ann. Phys. (N.Y.) 147, 281 (1983)
Laguerre (PL); Jacobi (PJ)
Few-Body Method• Problems:
1. Permutational symmetry2. Slow convergence (huge basis needed)
• Solutions:1. HH ON SA: KN LN λ ΓA
2. Effective Interaction (EIHH): Lee-Suzuki similarity transformation Improved convergence
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N. Barnea and A. Novoselsky, Ann. Phys. 256, 192 (1997)N. Barnea et al., Phys. Rev. C 61, 054001 (2000)
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Calculating Reactions – Problem 1
Continuum wave function – conflicting asymptotics:
4He
• A=3 – Faddeev 3 coupled equations• A=4 – FY (/AGS/KVP) 18 coupled
equations• A>4 – No ab initio calculation above 3-body
threshold (except with the LIT method)
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3H+p 3He+n
2H+p+n p+n+p+n
2H+2
HTwo-body CS
More-body CS
Calculating Reactions – Problem 2
Asymptotic few-body wave function:
• Two fragments:Relative motion is a plane-wave or Coulomb-function
• Three fragments:• no analytic solution• numerical - very complicated!
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Calculating Reactions – Solution
The LIT method (inclusive case):
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V. Efros, W. Leidemann, and G .Orlandini, PLB 238, 130 (1994)V. Efros, W. Leidemann, G .Orlandini and N. Barnea, JPG
34, R459 (2007)
• No solution for the homogeneous equation• Local boundary
condition
The Inclusive LIT Equation1. Solve the equation
2. Invert the LIT – solve an integral equation:
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Exclusive Reactions – Born & FSI
Antisymmetrized asymptotic
wave function
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Final State Interaction
Exclusive Reactions – Born & FSI
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S. Quaglioni et al., Phys. Rev. C 69, 044002 (2004)
…... Born___ Born+FSI
Exclusive LIT Equations (FSI)
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The Exclusive LIT Equations• Inclusive:• Exclusive:• Hadron scattering:
The challenge: Calculate FSI on the asymptotic w.f.Other possible LIT applications:• Semi inclusive (spectral func. approx.)• Fast projectile (the Glauber approx.)10/10/2013 23Exclusive reactions in few-body
systems
V. D. Efros et al., PRC58, 582 (1998)<your name here>
(2014)
V. D. Efros, Phys. At. Nucl. 62, 1833 (1999)
Calculating the FSI• Construct an antisymmetric w.f. with spatial,
spin and isospin D.o.F. coupled to have A-particle quantum numbers
• Calculate explicitly:
• Use a trick:
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Calculating the FSIp vs. n:
1. Treat Coulomb correctly:• Add and subtract Coulomb interaction between
C.M. of fragments• Use appropriate asymptotic function
2. Distinguish between p & n channels in coupled w.f.
• (½ ½,½ -½;T 0) vs. (½ -½,½ ½;T 0) Add ISB to code
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Results
ISB Results (4He*)• Benchmark ISB calculation • Interesting new results (wait for publication)
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Kievsky et al., J.Phys.G35,063101(2008)
Results with MT I-III + Coulomb
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Few-body Method
Mechanism for specific
problemNuclear Model
SolutionConverged?
Stability Accuracy
Independent Tests
Compare with Experiment
Results With AV18+UIX
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Results With AV18+UIX
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Results With AV18+UIX
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Results With AV18+UIX
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Results With AV18+UIX
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Results With AV18+UIX
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Incl. CS:Add K=20
Results With AV18+UIX
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Summary• Exclusive reactions, e.g. 4He photodisintegration
• are of interest, but are hard to calculate• Require state-of-the-art forces, which complicate the
calculation• Our tool, based on exclusive LIT, enables:
• ab initio calculation of reactions (even beyond 3-body breakup)
• including state-of-the-art NN + 3N forces• isospin symmetry breaking (ISB)
• Preliminary results indicate:• Tensor and L2 terms have a large effect• 3NF effect in the FSI
• ISB effect: R(p/n) ~> 1 , opposite than latest experiment suggests
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