transfer reactions with halo nuclei barry davids, triumf ect* 2 nov 2006
TRANSCRIPT
Transfer Reactions Transfer Reactions with Halo Nucleiwith Halo Nuclei
Barry Davids, TRIUMFBarry Davids, TRIUMF
ECT*ECT*
2 Nov 20062 Nov 2006
SS1717(0): Remaining Issues(0): Remaining Issues
Cyburt, Davids, and Jennings examined Cyburt, Davids, and Jennings examined theoretical and experimental situation in 2004theoretical and experimental situation in 2004
Extrapolation is model-dependentExtrapolation is model-dependent Even below 400 keV, GCM cluster model of Even below 400 keV, GCM cluster model of
Descouvemont and potential model based on Descouvemont and potential model based on 77Li + n scattering lengths differ by 7%Li + n scattering lengths differ by 7%
ExtrapolationExtrapolation
The DataThe Data
Concordance?Concordance?
Using a “pole” model, fit radiative capture Using a “pole” model, fit radiative capture data below 425 keVdata below 425 keV
Allows data to determine shape, consistent Allows data to determine shape, consistent with cluster and potential modelswith cluster and potential models
Junghans et alia result: 21.4 ± 0.7 eV bJunghans et alia result: 21.4 ± 0.7 eV b All other radiative capture: 16.3 ± 2.4 eV bAll other radiative capture: 16.3 ± 2.4 eV b Transfer reaction ANC determinations: Transfer reaction ANC determinations:
17.3 ± 1.8 eV b and 17.6 ± 1.7 eV b17.3 ± 1.8 eV b and 17.6 ± 1.7 eV b
Mirror ANC’sMirror ANC’s
Timofeyuk, Johnson, and Mukhamedzhanov have Timofeyuk, Johnson, and Mukhamedzhanov have shown that charge symmetry implies a relation shown that charge symmetry implies a relation between the ANC’s of 1-nucleon overlap integrals in between the ANC’s of 1-nucleon overlap integrals in light mirror nucleilight mirror nuclei
Charge symmetry implies relation between widths of Charge symmetry implies relation between widths of narrow proton resonances and ANC’s of analog narrow proton resonances and ANC’s of analog neutron bound statesneutron bound states
Tested by Texas A & M group for Tested by Texas A & M group for 88B-B-88Li systemLi system Ground state agreement excellentGround state agreement excellent 11++ 1st excited state shows 2.5 1st excited state shows 2.5discrepancy between discrepancy between
theory and experiments (Texas A & M and Seattle)theory and experiments (Texas A & M and Seattle)
The ExperimentThe Experiment
Measure ANC’s of the valence neutron in Measure ANC’s of the valence neutron in 88Li Li via the elastic scattering/transfer reaction via the elastic scattering/transfer reaction 77Li(Li(88Li,Li,77Li)Li)88Li at 11 and 13 MeVLi at 11 and 13 MeV
Interference between elastic scattering and Interference between elastic scattering and neutron transfer produces characteristic neutron transfer produces characteristic oscillations in differential cross sectionoscillations in differential cross section
Amplitudes of maxima and minima yield ANCAmplitudes of maxima and minima yield ANC
CalculationsCalculations
DWBA calculations performed with FRESCO DWBA calculations performed with FRESCO by Natasha Timofeyuk and Sam Wrightby Natasha Timofeyuk and Sam Wright
88Li + Li + 77Li Optical potentials from Becchetti (14 Li Optical potentials from Becchetti (14 MeV MeV 88Li on Li on 99Be, modified to be appropriate Be, modified to be appropriate for for 77Li), two from Potthast (energy-dependent Li), two from Potthast (energy-dependent global fit to combined global fit to combined 66Li+Li+66Li and Li and 77Li+Li+77Li data Li data from 5-40 MeV)from 5-40 MeV)
77Li + n binding potentials taken from Esbensen Li + n binding potentials taken from Esbensen & Bertsch and from Davids and Typel& Bertsch and from Davids and Typel
Calculations by Sam WrightCalculations by Sam Wright
Advantages of the MethodAdvantages of the Method
Identical initial and final states => single vertex is Identical initial and final states => single vertex is involvedinvolved
Statistical precision greater (compared with distinct Statistical precision greater (compared with distinct initial and final states)initial and final states)
Single optical model potential neededSingle optical model potential needed Elastic scattering measured simultaneouslyElastic scattering measured simultaneously More than one beam energy allows evaluation of More than one beam energy allows evaluation of
remnant term in DWBA amplituderemnant term in DWBA amplitude Absolute normalization of cross section enters only as Absolute normalization of cross section enters only as
a higher-order effect in ANC determinationa higher-order effect in ANC determination
Experimental SetupExperimental Setup
Target, Beam, & DetectorsTarget, Beam, & Detectors
Two annular, segmented Si detectorsTwo annular, segmented Si detectors 25 µg 25 µg cm-2 7-2 7LiF targetLiF target LEDA detector covers lab angles from 35-61°LEDA detector covers lab angles from 35-61° S2 detector covers 5-15° in the labS2 detector covers 5-15° in the lab 77Li cm angular coverage from 10-30° and 70-Li cm angular coverage from 10-30° and 70-
122°122° 88Li beam intensities of 2-4 Li beam intensities of 2-4 10 1077 s s-1-1
Online Spectrum from S2 DetectorOnline Spectrum from S2 Detector
Ground state structure of Ground state structure of 99Li Li (N=6 new closed shell?)(N=6 new closed shell?)
9Li(d,t)8Li
5 0 0 0
4 0 0 0
3 0 0 0
2 0 0 0
1 0 0 0
0
210- 1- 2
8Ligs8Liex1
8Liex2
PRELIMINARY ONLINE SPECTRUM
Q-value for d(9Li,t)8Li [MeV]
E ~ 1.7A MeV
R. Kanungo et al.
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0 10 20 30 40 50 60 70 80θt [deg]
Et
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8Ligs
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8Liex2
1111Li Transfer StudiesLi Transfer Studies
1111Li is the most celebrated halo nucleus but isnLi is the most celebrated halo nucleus but isn’t ’t well well understood understood because of its soft Borromean because of its soft Borromean structurestructure
In particular, the correlation between two halo neuIn particular, the correlation between two halo neutrons is trons is insufficiently studied experimentallyinsufficiently studied experimentally
Two-neutron transfer reactions are known to be thTwo-neutron transfer reactions are known to be the best tool for studying pair correlatione best tool for studying pair correlations of nucleons s of nucleons in nucleiin nuclei
TRIUMF, for the first time in the world, can provide TRIUMF, for the first time in the world, can provide a low energy beam of a low energy beam of 1111Li with Li with sufficient intensity sufficient intensity for such studies.for such studies.
1111Li Halo Wave FunctionLi Halo Wave Function Admixture of 2sAdmixture of 2s1/21/2 and 1p and 1p1/21/2 waves dominate the waves dominate the
halo wave functionhalo wave function Change of shell structure in nuclei far from the stability linChange of shell structure in nuclei far from the stability lin
ee ? How about other waves such as 2d? How about other waves such as 2d5/25/2 and other higher and other higher orbitals? orbitals? --> pa--> pairing near the continuumiring near the continuum
The spectroscopic factor of (2sThe spectroscopic factor of (2s1/21/2))22 would refle would reflect the strength of other componentsct the strength of other components
Unfortunately, but interestingly, Unfortunately, but interestingly, 1010Li is not bouLi is not bound nd The single particle structure of halo neutrons is difficult to The single particle structure of halo neutrons is difficult to
study. sstudy. s1/21/2 does not make clear resonance state. does not make clear resonance state. MeasurementMeasurements of neither the fragment momentum distribution s of neither the fragment momentum distribution
nor the single particle transfer reactions (p,d) and (d,p) have nor the single particle transfer reactions (p,d) and (d,p) have provided conclusive resultsprovided conclusive results
Cross SectionCross Section Calculations by Ian Calculations by Ian ThompsonThompson
direct two-neutron transfer only including two-step transfer
QuickTime˛ Ç∆TIFFÅià≥èkǻǵÅj êLí£ÉvÉçÉOÉâÉÄ
ǙDZÇÃÉsÉNÉ`ÉÉÇ å©ÇÈÇΩÇflÇ…ÇÕïKóvÇ≈Ç∑ÅB
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1. Bertsch-Esbensen, 2. Thompson-Zhukov, 3. Yabana (No three body correlation)
1.6 A MeV 11Li(p, t)
Correlation of Neutrons in HalosCorrelation of Neutrons in Halos Interesting suggestion from three Interesting suggestion from three
body calculationbody calculation Mixing of di-neutron and cigar -type Mixing of di-neutron and cigar -type
configurations in configurations in 66HeHe
6He+4He, Elab = 151 MeV
potential scattering
di-neutroncigar type2n transfer
θcm[ ]deg0 306090120150
10310110-110-310-5
Recent Density Correlation Recent Density Correlation StudiesStudies
rc-2n=rc+r2n
r2nrc
rn-n
<r1•r2>
Three MethodsThree Methods HBT interferometry measurementHBT interferometry measurement
Fragmentation, fusion of coreFragmentation, fusion of core
Electromagnetic dissociationElectromagnetic dissociation
Matter and charge radiiMatter and charge radii
€
R(p1,p2) =< n >2
< n(n −1) >
σ Rd2σ
dp1dp2dσ
dp1
dσ
dp2
−1
€
RI (p1,p2) = ± ˜ F I (p1 − p2) / ˜ F I (0)2
€
dB(E1) =∫3
4π
Ze
A
⎛
⎝ ⎜
⎞
⎠ ⎟2
< (r1 + r2)2 >
€
dB(E1) =∫3
4π
Ze
A
⎛
⎝ ⎜
⎞
⎠ ⎟2
< rc−2n2 > ?
1111Li resultLi result
Experiment RadiiExperiment Radii Experiment HBTExperiment HBT Experiment EMDExperiment EMD
[fm][fm] [fm][fm] [fm][fm]
6He6He
<r<rmm22>>1/21/2 2.43±0.032.43±0.03
<r<rpp22>>1/21/2 1.912±0.0181.912±0.018
<r<rnn22>>1/21/2 2.65±0.042.65±0.04
<r<rnn22>>1/21/2-<r-<rpp
22>>1/21/2 0.739±0.0470.739±0.047
<r<r2n2n22>>1/21/2 3.22±0.073.22±0.07
<r<r-2n-2n22>>1/21/2 3.84±0.063.84±0.06
<r<rn-nn-n22>>1/21/2 3.91±0.283.91±0.28 5.9±1.25.9±1.2
<r<rn1n1rrn2n2> [fm> [fm22]] 2.76±0.632.76±0.63
11Li11Li
<r<rmm22>>1/21/2 3.55±0.103.55±0.10
<r<rpp22>>1/21/2 2.37±0.042.37±0.04
<r<rnn22>>1/21/2 3.90±0.133.90±0.13
<r<rnn22>>1/21/2-<r-<rpp
22>>1/21/2 1.53±0.131.53±0.13
<r<r2n2n22>>1/21/2 6.28±0.326.28±0.32
<r<rc-2nc-2n22>>1/21/2 6.15±0.526.15±0.52 5.01±0.325.01±0.32
<r<rn-nn-n22>>1/21/2 7.52±1.727.52±1.72 6.6±1.56.6±1.5
<r<rn1n1rrn2n2> [fm> [fm22]] 11.2±8.211.2±8.2
7.0: shimoura7.0: shimoura
13: Ieki13: Ieki
ISAC@TRIUMF
ISAC I
ISAC II
Too Low Beam Energy?Too Low Beam Energy? 1.61.6AA MeV is appropriate for the study. MeV is appropriate for the study.
The effect of Coulomb barrier is extremely sThe effect of Coulomb barrier is extremely small for halo neutrons.1.6A MeV is much himall for halo neutrons.1.6A MeV is much higher than the separation energy (~180 keV) gher than the separation energy (~180 keV) ..
Energy-momentum matching is not bad becEnergy-momentum matching is not bad because of the narrow internal momentum distrause of the narrow internal momentum distribution of the halo neutrons.ibution of the halo neutrons.
66AA MeV is conventional transfer reaction MeV is conventional transfer reaction energy and thus analysis tools were well energy and thus analysis tools were well developed.developed.
gassiplex
K
MAYAMAYA
1111Li(p,t)Li(p,t)99Li at TRIUMF Li at TRIUMF
The first run is planned at the end of The first run is planned at the end of November 2006November 2006
We expect 5000 (p,t) reactions to ground state We expect 5000 (p,t) reactions to ground state of of 99LiLi
Reactions populating the excited state of Reactions populating the excited state of 99Li Li are also expectedare also expected
Will measure other channels such as (p,d)Will measure other channels such as (p,d) Be ready for data (Ian)Be ready for data (Ian)
AcknowledgementsAcknowledgements
77Li(Li(88Li,Li,77Li)Li)88Li: Derek Howell (M.Sc. Student, Li: Derek Howell (M.Sc. Student, Simon Fraser University)Simon Fraser University)
d(d(99Li,t)Li,t)88Li: Rituparna Kanungo (TRIUMF)Li: Rituparna Kanungo (TRIUMF) p(p(1111Li,t)Li,t)99Li: Isao Tanihata (TRIUMF) and Li: Isao Tanihata (TRIUMF) and
Hervé Savajols (GANIL)Hervé Savajols (GANIL)
Kinematics of p(Kinematics of p(1111Li, Li, 99Li)tLi)t
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0
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0 5 1 0 1 5 2 0 2 5 3 0
L a b o r a t o r y A n g l e [ d e g r e e s ]
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11Li + p --> t + 9Li --> d + 10Li
c m 0 d e g r e e
9Li g.s
9Li E*=2.691
10Li g.s.
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8He
11Li+p -->4He+8He
[ [ [[
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11Li+12C -> 9Li+14C
9Li when (14C gs)
9Li when (14C 6.09)
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L a b o r a t o r y A n g l e [ d e g r e e s ]
[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[ [[[[ [[ [[ [[ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [
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9Li g.s
9Li E*=2.691
10Li g.s.c m 0 d e g r e e
Energy of deutron [MeV]
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8He
Energy of 4He [MeV]
B BB
BB
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Laboratory angle [degrees]
6A MeV
1.6A MeV
Typical eventsTypical events
P P A C
M A Y A
C4H10 gas
20 Si Array
20 CsI Array
Differences between Differences between 66He and He and 1111LiLi
1111Li is much less bound than Li is much less bound than 66HeHe 66He: mostly 1pHe: mostly 1p3/23/2 wave wave
1111Li has mixed waves of 1pLi has mixed waves of 1p1/21/2, 2s, 2s1/21/2, …, … The core of The core of 1111Li (Li (99Li) may be much softer than Li) may be much softer than
that of that of 66He (He (44He)He)
66He resultsHe results Experiment
[fm] 3-body. [fm]
Varga [fm]
Esbensen [fm]
Funada [fm]
Zhulov [fm]
<rm2>1/2 2.43±0.03 2.48 2.46 2.45
<rp2>1/2 1.912±0.018 1.80
<rn2>1/2 2.65±0.04 2.67
<rn2>1/2-<rp
2>1/2 0.808±0.047 0.87 <r2n
2>1/2 3.23±0.07 3.42 <r -2n
2>1/2 3.84±0.06 3.606 3.592(3.63) 3.51 3.54 <rn-n
2>1/2 3.93±0.25 4.762 5.413(4.62) 4.55 4.58 <rn1rn2> [fm2] 2.70±0.97 0.110 -1.59(0.54) 0.292 0.325
<rn2>1/2
<rp2>1/2
r r 2c n
<rm2>1/2
n1
n2
r -di n
r -n n=2r -di n
r 1n
r 2n
6He
HBT measurementHBT measurementRn-n= 5.9 ± 1.2 fm
Rn-n= 6.6 ± 1.5 fm
Rn-n= 5.4 ± 1.0 fm
EMD EMD 1111LI (70LI (70AA MeV)+Pb -> MeV)+Pb ->99Li+n+nLi+n+n
E(9Li-n)
E(9
Li-n
)
1MeV
1MeV
Nakamura et al. 2006
He and Li RadiiHe and Li Radii
BB
J
H
F
Ñ ÑÑ
Ñ
Ñ
É
É
É
É
É
Ç
Ç
Ç
Ç
Ç
Å
Å
ÅÅ
Å
-0.5
0
0.5
1
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2
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3
3.5
4
5 6 7 8 9 10 11 12
Mass Number A
B Rm(He)
J Rp(He)
H Rn(He)
F Nskin(He)
Ñ Rm(Li)
É Rp(Li)
Ç Rn(Li)
Å Nskin(Li)
[mb]
1000
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600
400
2008Li 9Li 11Li
σR
σΔZ
Charge changing crs. Li
[mb]
1000
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600
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2008Li 9Li 11Li
σR
σΔZ
Charge changing crs. Li
He
Li
RMS radii and the configurationRMS radii and the configuration
€
< re2 >=< rp
2 > + < Rproton2 > +
N
Z< Rneutron
2 >
< Rproton2 >= 0.801± 0.032
< Rneutron2 >= −0.120± 0.005
• Relation between ms radii
€
Ai<rim2>=Zi<rip2>+Ni<rin2> (2)
Neutr onradii<rn2>,<rsn
2>canbedetermi nedfro m(2).
•T hehaloradiusI
€
A<rm2>=Ac<rcm2>+Ah<rh2> (3)
•Coremotioninthehalonucleu :s <rc2>isthemsradiusofthecenterofthecorein
thehalonucleus.
€
<rp2>=<rsp2>+<rc2>→<rc2>=<rp2>−<rsp2> (4)
€
<rcm2>=<rc2>+<rsm2><rcn2>=<rc2>+<rsn2>
(5)
Usingthoseequations,wecanobtain<rc2>,<rcm
2>,<rcn2>.Themsradiusofhalo
distributi onthen<rh2>canbedetermi nedusingeq.(3).
• Core(rc) movement and two-neutron center-off-mass (r2n=rn1+rn2) movement. rn1
and rn2 are positions of halo neutrons from the center of mss of the halo nuclei.
€
Acrc=−Ahr2n=−Ah(rn1+rn2)2 (6)
Us ingeq.(6)<r2n2>areobtained.
•Dista ncebetweentwohaloneutrons(rn-n=rn1-rn2)andd -i neutronmsradi <us rd -i n2>.
€
rn−n=2rdi−n=rn1−rn2→<rn−n2 >=4<rdi−n2 > (7)•T hehaloradiusII
€
<rh2>=<r2n2>+<rdi−n2 > (8)Usingthisequationand<r2n
2>,<rh2>wecanobtai nthed -i neutronmsradius<rd -i n
2>and
thusthemsseparationoftwo-hal oneutrons<rn-n2>.
•Correlati onofthehaloneutrons:
€
Ac2<rc2>=<(rn1+rn2)2>=<rn12>+<rn22>+2<rn1⋅rn2> (9)
€
<rn−n2 >=<(rn1−rn2)2>=<rn12>+<rn22>−2<rn1⋅rn2> (10)Fro meqs.(9)and(10),
€
<rn1⋅rn2>=14(<rc2>−<rn−n2 >) (11)
Wegotthecrosstermofthecoordinatebetweentwoneutrons<rn1•rn2>.
there are two little drift chambers before MAYA, to monitor the beam. cathode
anode:amplification
area.
wall of CsI detectors
the projectile makes reaction with a nucleus of the gas.
the recoil product leaves enough energy to induce an image of its trajectory in the plane of the segmented cathode.
the light scattered particles do not stop
inside, and go forward to a wall made of 20 CsI detectors, where
they are stopped, and identified.
segmented cathode
MAYA is essentially an ionization chamber, where the gas plays also the role of reaction target. It could be used with H2, d2, C4H10, between 0-2 atm.
t1
tn
Φwe measure the drift time up to each amplification wire. The angle of the reaction
plane is calculated with these times.
MAYMAYAA