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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[MeV]

8Ligs

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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

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ǙDZÇÃÉsÉNÉ`ÉÉÇ å©ÇÈÇΩÇflÇ…ÇÕïKóvÇ≈Ç∑ÅB

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ǙDZÇÃÉsÉNÉ`ÉÉÇ å©ÇÈÇΩÇflÇ…ÇÕïKóvÇ≈Ç∑ÅB

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

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4π

Ze

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⎛

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⎞

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< 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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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.

X X X

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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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0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0

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

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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

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Ç

Ç

Ç

Ç

Ç

Å

Å

ÅÅ

Å

-0.5

0

0.5

1

1.5

2

2.5

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

800

600

400

2008Li 9Li 11Li

σR

σΔZ

Charge changing crs. Li

[mb]

1000

800

600

400

2008Li 9Li 11Li

σR

σΔZ

Charge changing crs. Li

He

Li

RMS radii and the configurationRMS radii and the configuration

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< re2 >=< rp

2 > + < Rproton2 > +

N

Z< Rneutron

2 >

< Rproton2 >= 0.801± 0.032

< Rneutron2 >= −0.120± 0.005

• Relation between ms radii

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Ai<rim2>=Zi<rip2>+Ni<rin2> (2)

Neutr onradii<rn2>,<rsn

2>canbedetermi nedfro m(2).

•T hehaloradiusI

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A<rm2>=Ac<rcm2>+Ah<rh2> (3)

•Coremotioninthehalonucleu :s <rc2>isthemsradiusofthecenterofthecorein

thehalonucleus.

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<rp2>=<rsp2>+<rc2>→<rc2>=<rp2>−<rsp2> (4)

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<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.

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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>.

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rn−n=2rdi−n=rn1−rn2→<rn−n2 >=4<rdi−n2 > (7)•T hehaloradiusII

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<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:

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Ac2<rc2>=<(rn1+rn2)2>=<rn12>+<rn22>+2<rn1⋅rn2> (9)

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<rn−n2 >=<(rn1−rn2)2>=<rn12>+<rn22>−2<rn1⋅rn2> (10)Fro meqs.(9)and(10),

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<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