Indranil Mazumdar

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Halo World The story according to Faddeev,Efimov
and Fano
Indranil Mazumdar Dept. of Nuclear Atomic
Physics, Tata Institute of Fundamental
Research, Mumbai 400 005
Bose Institute, Kolkata 26th August, 2011
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Halo Nuclei Exotic Structures and exotic effects
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Plan of the talk

• Introduction to Nuclear Halos
• Three-body model of 2-n Halo nucleus
• probing the structural properties of 11Li
• Efimov effect in 2-n halo nuclei
• Fano resonances of Efimov states
• Probing few other candidates The Experimental
  Angle
• Summary and future scope

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Collaborators

• V.S. Bhasin Delhi Univ.
• V. Arora Delhi Univ.
• A.R.P. Rau Louisiana State Univ.

• Phys. Rev. Lett. 99, 269202
• Nucl. Phys. A790, 257
• Phys. Rev. Lett. 97, 062503
• Phys. Rev. C69, 061301(R)
• Phys. Rev. C61, 051303(R)
• Phys. Rev. C56, R5
• Phys. Rev. C50 , R550
• Few Body Systems, 2009
• Pramana, 2010
• Phys. Lett. B (In press)

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Known nuclei
terra incognita
R ROA1/3
Stable Nuclei
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R R0 A1/3 Shell Structure Magic Numbers
208Pb
11Li
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Advent of Radioactive Ion Beams
Interaction cross section measurements
I /IO e-srt sI pRI(P) RI(T)2
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R R0 A1/3 Shell Structure Magic Numbers
208Pb
11Li
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Pygmy Resonance PDR in 68Ni O. Wieland et. al.
PRL 102 , 2009
The neutron halo of extremely neutron rich
nuclei Europhys.Lett. 4, 409 (1987) P.G.Hansen,
B.Jonson
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Exotic Structure of 2-n Halo Nuclei
11Li Z3 N8
Radius 3.2 fm
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S2n 369.15 (0.65) keV
Accepted lifetime 8.80 (0.14) ms
Jp 3/2-
S2n 12.2 MeV for 18O
Typical experimental momentum distribution of
halo nuclei from fragmentation reaction
Kobayashi et al., PRL 60, 2599 (1988)
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RIBF, RIKEN JAEA, Tokai
HIMAC, Chiba CYRIC,
Tohoku RCNP, Osaka
HIRF,
Lanzhou CIAE, Beijing Vecc, Kolkata

• Production Mechanisms
• ISOL
• In-Flight projectile fragmentation

FRIB, MSU ATLAS, ANL HRIBF, Oak Ridge TRIUMF,
Canada GSI, Darmstadt SPIRAL, Ganil FLNR-JINR,
Dubna
Courtesy V. Oberacker, Vanderbilt Univ. H.
Sakurai, NIM-B (2008)
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Neutron skin
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Theoretical Models

• Shell Model Bertsch et al. (1990) PRC 41,42,
• 
  Kuo et al. PRL 78,2708 (1997) 2 frequency shell
  model
• 
  Brown (Prog. Part. Nucl. Physics 47 (2001)
• Ab initio no-core full configuration calculation
  of light nuclei
• 
  Navratil, Vary, Barrett
  PRL84(2000), PRL87(2001)
• Quantum Monte Carlo Calculations of Light Nuclei
  4,6,8 He, 6,7Li, 8,9,10 Be
  
  Pieper, Wiringa
• Cluster model
• Three-body model ( for 2n halo nuclei )
• RMF model
• EFT Braaten Hammer, Phys. Rep. 428 (2006)

Talmi Unna, PRL 4, 496 (1960) 11Be
Sn
820 keV
Sn 504 keV
Audi Wapstra
(2003)
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2010 The Golden Jubilee year of Faddeev
Equations.
L.D. Faddeev, Zh. Eksperim, I Teor. Fiz. 39, 1459
(1960) S. Weinberg, Phys. Rev. 133, B232
(1964) C. Lovelace Phys. Rev. 135, No. 5B
B1225 (1964) J. G. Taylor, Nuovo Cimento
(1964) L. Rosenberg, Phys. Rev 135, B715
(1964) A.N. Mitra, Nucl. Phys. 32, 529 (1962)
Ludwig Dmitrievich Faddeev
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LD Faddeev
AN Mitra
NN Interaction Nuclear Many-Body Problem Nov.
17 26, 2010, TIFR
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Dasgupta, Mazumdar, Bhasin, Phys. Rev C50,550
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• We Calculate
• 2-n separation energy
• Momentum distribution of n core
• Root mean square radius
• Inclusion of p-state in n-core interaction
• b-decay of 11Li

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Dasgupta, Mazumdar, Bhasin PRC50, R550
The rms radius rmatter calculated is 3.6 fm
ltr2gtmatter Ac/Altr2gtcore 1/Altr2gt r2 r2nn
r2nc
Fedorov et al (1993) Garrido et al (2002) (3.2
fm)
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11Li Vs 6He
2-particle correlations Hagino et al , PRC, 2009
Data Ieki et al, PRL 70 ,1993
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11Li
6He
11Li is different from 6He

• Strong influence of virtual s-state n-core
  interaction in 11Li

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Efimov effect
To Efimov Physics
From questionable to pathological to exotic to
a hot topic Nature Physics 5, 533 (2009)
Vitaly Efimov Univ. of Washington, Seattle
2010 The 40th year of a remarkable discovery
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Belyaev, Faddeev, Efimovs Nov. 2010, TIFR
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Efimov, 1990 Ferlaino Grimm 2010
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Theoretical searches in Atomic Systems T.K. Lim
et al. PRL38 (1977) Cornelius Glockle, J. Chem
Phys. 85 (1986) T. Gonzalez-Lezana et al. PRL 82
(1999),

V. Efimov Sov. J. Nucl. Phys 12, 589
(1971) Phys. Lett. 33B (1970) Nucl. Phys A 210
(1973) Comments Nucl. Part. Phys.19 (1990)
The case of He trimer
Amado Noble Phys. Lett. 33B (1971) Phys. Rev.
D5 (1972)
Diffraction experiments with transmission
gratings Carnal Mlynek, PRL 66
(1991) Hegerfeldt Kohler, PRL 84, (2000)
Fonseca et al. Nucl. PhysA320, (1979) Adhikari
Fonseca Phys. Rev D24 (1981)
Three-body recombination in ultra cold atoms
L.H. Thomas, Phys.Rev.47,903(1935)
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First Observation of Efimov States

• Letter
• Nature 440, 315-318 (16 March 2006)
• Evidence for Efimov quantum states in an
  ultracold gas of caesium atoms
• T. Kraemer, M. Mark, P. Waldburger, J. G.
  Danzl, C. Chin, B. Engeser, A. D. Lange, K.
  Pilch, A. Jaakkola, H.-C. Nägerl and R. Grimm

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• Magnetic tuning of the two-body interaction
• For Cs atoms in their energetically lowest state
  the s-wave scattering length a varies strongly
  with the magnetic field.
• Trap set-ups and preparation of the Cs gases
• All measurements were performed with trapped
  thermal samples of caesium atoms at temperatures
  T ranging from 10 to 250 nK.
• In set-up A they first produced an essentially
  pure BoseEinstein condensate with up to 250,000
  atoms in a far-detuned crossed optical dipole
  trap generated by two 1,060-nm Yb-doped fibre
  laser beams
• In set-up B they used an optical surface trap in
  which they prepared a thermal sample of 10,000
  atoms at T 250 nK via forced evaporation at a
  density of n0 1.0 1012 cm-3. The dipole trap
  was formed by a repulsive evanescent laser wave
  on top of a horizontal glass prism in combination
  with a single horizontally confining 1,060-nm
  laser beam propagating along the vertical
  direction

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T. Kraemer et al. Nature 440, 315
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Observation of an Efimov spectrum in an atomic
system.M. Zaccanti et al. Nature Physics 5, 586
(2009)

• System composed of ultra-cold potassium atoms
  (39K) with resonantly tunable two-body
  interaction.
• Atom-dimer resonance and loss mechanism
• Large values of a up to 25,000 ao reached.
• First two states of an Efimov spectrum seen

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Fedorov Jensen PRL 71 (1993) Fedorov, Jensen,
Riisager PRL 73 (1994) P. Descouvement PRC 52
(1995), Phys. Lett. B331 (1994)
Conditions for occurrence of Efimov states in
2-n halo nuclei.
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tn-1(p)F(p) f(p) and tc-1(p)G(p) c(p) Where
tn-1(p) ?mn-1 br (br vp2/2a e3)2
-1 tc-1(p) ?mc-1 2a 1 v2a(p2/4c e3)
-2 where mn p2ln/b12 and mc p2lc/2ab13
are the dimensionless strength parameters.
Variables p and q in the final integral equation
are also now dimensionless,
p/b1 ? p q/b1 ? q
and -mE/b13 e3, br b/b1 Factors
tn-1 and tc-1 appear on the left hand side of the
spectator functions F(p) and G(p) and are quite
sensitive. They blow up as p ? 0 and e3
approaches extremely small value.
The basic structure of the equations in terms of
the spectator functions F(p) and G(p) remains
same. But for the sensitive computational details
of the Efimov effect we recast the equations in
dimensionless quantities.
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First Evidence for low lying s-wave strength in
13Be Fragmentation of 18O, virtual state with
scattering length lt 10 fm Thoennessen, Yokoyama,
Hansen Phys. Rev. C 63, 014308
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Mazumdar, Arora Bhasin Phys. Rev. C 61, 051303(R)
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• The feature observed can be attributed to the
  singularity in the
• two body propagator LC-1 hc(p)-1.
• There is a subtle interplay between the two
  and three body energies.
• The effect of this singularity on the
  behaviour of the scattering
• amplitude has to be studied.

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For k ? 0, the singularity in the two body
cut Does not cause any problem. The amplitude has
only real part. The off-shell amplitude is
computed By inverting the resultant matrix ,
which in the limit ao(p)p?0 ? -a, the n-19C
scattering length. For non-zero incident
energies the singularity in the two body
propagator is tackled by the CSM. P ? p1e-if
and q ? qe-if The unitary requirement is the
Im(f-1k) -k Balslev Combes (1971) Matsui
(1980) Volkov et al.
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• n-18C Energy e3(0) e3(1) e3(2)
• (keV) (MeV) (keV) (keV)
• 3.00 79.5 66.95
• 100 3.10 116.6 101.4
• 3.18 152.0 137.5
• 3.25 186.6 -----
• 3.32 221.0 -----
• 3.35 238.1 -----
• 250 3.37 -----
  -----
• 300 3.44 ----- -----

Arora, Mazumdar,Bhasin, PRC 69, 061301
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Ugo Fano (1912 2001)
Third highest in citation impact of all papers
published in the entire Physical Review series.
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Fitting the Fano profile to the N-19C elastic
cross section for n-18C BE of 250 keV
s so(q e)2/(1e2)
Mazumdar, Rau, Bhasin Phys. Rev. Lett. 97 (2006)
an ancient pond a frog jumps in a deep resonance
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The resonance due to the second excited Efimov
state for n-18C BE 150 keV. The profile is
fitted by same value of q as for the 250 keV
curve.
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Comparison between He and 20C as three body
Systems in atoms and nuclei
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Discussion

• We emphasize the cardinal role of channel
  coupling.
• There is also a definite role of mass ratios
  as observed numerically.
• However, channel coupling is an elegant and
  physically plausible scenario.
• Difference can arrive between zero range and
  realistic finite range
• potentials in non-Borromean cases.
• Note, that for n-18C binding energy of 200
  keV, the scattering length is about 10 fm
• while the interaction range is about 1 fm.
• The extension of zero range to finer details of
  Efimov states in non-Borromean
• cases may not be valid.
• The discrepancy observed in the resonance vs
  virtual states in 20C clearly
• underlines the sensitive structure of the
  three-body scattering amplitude
• derived from the binary interactions.

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• The calculation have been extended to
• Two hypothetical cases very heavy core of mass
  A 100 ( 2n)
• 
  three equal masses m1m2m3
• 2) Two realistic cases of 38Mg 32Ne
• 38Mg S2n 2570 keV n core (37Mg)
  250 keV (bound)
• 32Ne S2n 1970 keV n core (31Ne)
  330 keV (bound)
• 38Mg (S2n) Audi Wapstra (2003)
• 37Mg 31Ne (Sn) Sakurai et al., PRC 54
  (1996), Jurado et al.
• PLB (2007), Nakamura et al. PRL (2009)
• We have reproduced the ground state energies and
  have found
• at least two Efimov states that vanish into the
  continuum with
• increasing n-core interaction. They again show
  up as asymmetric
• resonances at around 1.6 keV neutron incident
  energy in the

Mazumdar, Bhasin, Rau Phys. Lett. B (In Press)
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eo Equal Heavy Core (keV)
(keV) (keV) 250 455
4400 300 546
4470 350 637 4550
Ground states for the two cases

• Equal mass case strikingly different from
• unequal ( heavy core ) case.
• Evolution of Efimov states in heavy core
• of 100 fully consistent with 20C results.

Mazumdar Few Body Systems, 2009
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TABLE Ground and excited states for three cases
studied, namely, mass 102 (columns 2, 3, 4),
38Mg (column 5, 6, 7), and 32Ne (columns 8, 9,
10) for different two body input parameters.
32Ne
38Mg
102A
n-Core Energy ?2 keV ?3(0) keV ?3(1) keV ?3(2) keV ?3(0) keV ?3(1) keV ?3(2) keV ?3(0) keV ?3(1) keV ?3(2) keV
40 60 80 100 120 140 180 250 300 350 4020 4080 4130 4170 4220 4259 4345 4460 4530 4590 53.6 70.4 86.9 103.1 (119.3) 44.4 61.7 (78.4) 3550 3610 3670 3710 3750 3790 3860 3980 4040 4120 61.3 80.8 99.2 117 134.5 151.6 185.6 49.9 67.1 84.16 101.4 (118.9) 3420 3480 3530 3570 3620 3650 3730 3852 3910 3980 61.5 81.0 99.8 117.5 135 152.5 186.5 50 67.2 84.3 101.5 (118.9)
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Heavy Core
38Mg
32Ne
Mazumdar, Bhasin, Rau Phys. Lett. B (In Press)
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• Production of 20C secondary beam with reasonable
  flux
• Acceleration and Breakup of 20C on heavy target
• Detection of the neutrons and the core in
  coincidence
• Measurement of g-rays as well

Another experimental scenario 19C beam on
deuteron target Neutron stripping reaction

• The Arsenal
• Neutron detectors array
• Gamma array
• Charged particle array

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Summary

• A three body model with s-state interactions
  account for most of the gross
• features of 11Li in a reasonable way.
• Inclusion of p-state in the n-9Li contributes
  marginally.
• A virtual state of a few keV (2 to 4) energy
  corresponding to scattering length
• from -50 to -100 fm for the n-12Be predicts
  the ground state and excited states of
• 14Be.
• 19B, 22C and 20C are investigated and it is shown
  that Borromean type nuclei are
• much less vulnerable to respond to Efimov
  effect
• 20C is a promising candidate for Efimov states at
  energies below the n-(nc)
• breakup threshold.
• The bound Efimov states in 20C move into the
  continuum and reappear as
• Resonances with increasing strength of the
  binary interaction.
• Asymmetric resonances in elastic n19C scattering
  are attributed to Efimov states

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Present Activities

• Resonant states above the three body breakup
  threshold in 20C.
• Structure calculations for 12Be
• Fano resonances of Efimov states in 16C, 19B, 22C
  and analytical
• derivation of the Fano index q.
• Role of Efimov states in Bose-Einstein
  condensation.
• Studying the proton halo (17Ne) nucleus.
• three charged particle,
  Belyaev, Shlyk, NPA 790 (2007)
• Reanalyze profiles of GDR on ground states for
  its asymmetry.
• Planning for possible experiments with 20C beam

Epilogue the richness of undestanding reveals
even greater richness of ignorance




D.H. Wilkinson
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• THANK YOU

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Kumar Bhasin, Phys. Rev. C65 (2002)

• Incorporation of both s p waves in n-9Li
  potential
• Ground state energy and 3 excited states above
  the
• 3-body breakup threshold were predicted

• Er Er G
• (Ex) (T)
• 0.038 0.03(0.04) 0.056
• 1.064 1.02(0.07) 0.050
• 2.042 2.07(0.12) 0.500

• The resulting coupled integral equations for the
  spectator
• functions have been computed using the method of
  rotating
• the integral contour of the kernels in the
  complex plane.

Data from Gornov et al. PRL81 (1998)

• Dynamical content of the two body input
  potentials in the
• three body wave function has also been analyzed
  through
• the three-dimensional plots.

b-decay to two channels studied 11Li to
high lying excited state of 11Be
11Li to 9Li deuteron channel
18.3 MeV, bound (9Lipn) system Gamow-Teller
b-decay strength calculated
Branching ratio (1.3X10-4) calculated
Mukha et al (1997), Borge et al (1997)
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Kumar Bhasin PRC65, (2002)
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Appearance of Resonance in n-19 C Scattering

• The equation for the off-shell scattering
  amplitude in n-19 C
• ( bound state of n-18 C) can be written as
• where a k(p) is the off-shell scattering
  amplitude, normalized such that

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• In the present model, the singularity in the
  present model appears in the two body propagator