Transcript Precise Determination of the 8Li Valence Neutron ANC

Transfer Reactions
with Halo Nuclei
Barry Davids, TRIUMF
ECT*
2 Nov 2006
S17(0): Remaining Issues



Cyburt, Davids, and Jennings examined
theoretical and experimental situation in 2004
Extrapolation is model-dependent
Even below 400 keV, GCM cluster model of
Descouvemont and potential model based on
7Li + n scattering lengths differ by 7%
Extrapolation
The Data
Concordance?





Using a “pole” model, fit radiative capture data
below 425 keV
Allows data to determine shape, consistent
with cluster and potential models
Junghans et alia result: 21.4 ± 0.7 eV b
All other radiative capture: 16.3 ± 2.4 eV b
Transfer reaction ANC determinations:
17.3 ± 1.8 eV b and 17.6 ± 1.7 eV b
Mirror ANC’s





Timofeyuk, Johnson, and Mukhamedzhanov have
shown that charge symmetry implies a relation
between the ANC’s of 1-nucleon overlap integrals in
light mirror nuclei
Charge symmetry implies relation between widths of
narrow proton resonances and ANC’s of analog
neutron bound states
Tested by Texas A & M group for 8B-8Li system
Ground state agreement excellent
1+ 1st excited state shows 2.5s discrepancy between
theory and experiments (Texas A & M and Seattle)
The Experiment



Measure ANC’s of the valence neutron in 8Li
via the elastic scattering/transfer reaction
7Li(8Li,7Li)8Li at 11 and 13 MeV
Interference between elastic scattering and
neutron transfer produces characteristic
oscillations in differential cross section
Amplitudes of maxima and minima yield ANC
Calculations



DWBA calculations performed with FRESCO
by Natasha Timofeyuk and Sam Wright
8Li + 7Li Optical potentials from Becchetti (14
MeV 8Li on 9Be, modified to be appropriate
for 7Li), two from Potthast (energy-dependent
global fit to combined 6Li+6Li and 7Li+7Li
data from 5-40 MeV)
7Li + n binding potentials taken from Esbensen
& Bertsch and from Davids and Typel
Calculations by Sam Wright
Advantages of the Method






Identical initial and final states => single vertex is
involved
Statistical precision greater (compared with distinct
initial and final states)
Single optical model potential needed
Elastic scattering measured simultaneously
More than one beam energy allows evaluation of
remnant term in DWBA amplitude
Absolute normalization of cross section enters only as
a higher-order effect in ANC determination
Experimental Setup
Target, Beam, & Detectors






Two annular, segmented Si detectors
25 µg cm-2 7LiF target
LEDA detector covers lab angles from 35-61°
S2 detector covers 5-15° in the lab
7Li cm angular coverage from 10-30° and 70122°
8Li beam intensities of 2-4  107 s-1
Online Spectrum from S2 Detector
Ground state structure of 9Li
(N=6 new closed shell?)
R. Kanungo et al.
9Li(d,t)8Li
E ~ 1.7A MeV
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10
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t [deg]
80
8Li
5000
ex2
4000
8Li
3000
ex1
8Li
gs
2000
PRELIMINARY ONLINE SPECTRUM
1000
0
-2
-1
0
1
2
Q-value for d(9Li,t)8Li [MeV]
11Li
 11Li



Transfer Studies
is the most celebrated halo nucleus but isn’t
well understood because of its soft Borromean
structure
In particular, the correlation between two halo
neutrons is insufficiently studied experimentally
Two-neutron transfer reactions are known to be
the best tool for studying pair correlations of
nucleons in nuclei
TRIUMF, for the first time in the world, can
provide a low energy beam of 11Li with sufficient
intensity for such studies.
11Li

Admixture of 2s1/2 and 1p1/2 waves
dominate the halo wave function



Halo Wave Function
Change of shell structure in nuclei far from the stability
line? How about other waves such as 2d5/2 and other
higher orbitals? --> pairing near the continuum
The spectroscopic factor of (2s1/2)2 would
reflect the strength of other components
Unfortunately, but interestingly, 10Li is not
bound


The single particle structure of halo neutrons is difficult
to study. s1/2 does not make clear resonance state.
Measurements of neither the fragment momentum
distribution nor the single particle transfer reactions
(p,d) and (d,p) have provided conclusive results
Cross Section Calculations by Ian
Thompson
direct two-neutron transfer only
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including two-step transfer
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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 Halos

Interesting suggestion from three
body calculation

Mixing of di-neutron and cigar -type
configurations in 6He
Recent Density Correlation
Studies
rc
r2n
rn-n
rc-2n=rc+r2n
<r1•r2>


Three Methods

HBT interferometry measurement

Fragmentation, fusion of core
d 2s
2 sR
n
dp1dp 2
R(p1 ,p 2 ) 
1
d
s
d
s
 n(n 1) 
dp1 dp 2
2
˜
˜
RI (p1,p2 )   FI (p1  p2 ) / FI (0)

Electromagnetic dissociation
2
2


3
Ze
3  Ze 
2
 dB(E1)     (r1  r2 ) 2   dB(E1)  4  A   rc2n 
4  A 

Matter and charge radii

?
11Li
result
Experiment Radii
[fm]
Experiment HBT
Experiment EMD
[fm]
[fm]
6He
<rm2>1/2
2.43±0.03
<rp2>1/2
1.912±0.018
<rn2>1/2
2.65±0.04
<rn2>1/2-<rp2>1/2
0.739±0.047
<r2n2>1/2
3.22±0.07
<ra-2n2>1/2
3.84±0.06
<rn-n2>1/2
3.91±0.28
<rn1rn2> [fm2]
2.76±0.63
5.9±1.2
11Li
<rm2>1/2
3.55±0.10
<rp2>1/2
2.37±0.04
<rn2>1/2
3.90±0.13
<rn2>1/2-<rp2>1/2
1.53±0.13
<r2n2>1/2
6.28±0.32
<rc-2n2>1/2
6.15±0.52
<rn-n2>1/2
7.52±1.72
5.01±0.32
6.6±1.5
ISAC@TRIUMF
ISAC II
ISAC I
Too Low Beam Energy?

1.6A MeV is appropriate for the study.
The effect of Coulomb barrier is extremely
small for halo neutrons.1.6A MeV is much
higher than the separation energy (~180 keV) .
 Energy-momentum matching is not bad because
of the narrow internal momentum distribution
of the halo neutrons.


6A MeV is conventional transfer reaction
energy and thus analysis tools were well
developed.
MAYA
K
11Li(p,t)9Li





at TRIUMF
The first run is planned at the end of
November 2006
We expect 5000 (p,t) reactions to ground state
of 9Li
Reactions populating the excited state of 9Li
are also expected
Will measure other channels such as (p,d)
Be ready for data (Ian)
Acknowledgements
 7Li(8Li,7Li)8Li:


Derek Howell (M.Sc. Student,
Simon Fraser University)
d(9Li,t)8Li: Rituparna Kanungo (TRIUMF)
p(11Li,t)9Li: Isao Tanihata (TRIUMF) and
Hervé Savajols (GANIL)
11Li + p --> t + 9Li
--> d +10Li
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8He
5
0
0
Energy of deutron [MeV]
X [ X
Energy of 4He [MeV]
X
[
11Li+p -->4He+8He
11Li+ 12C -> 9Li+ 14C
Energy of t [MeV]
Kinematics of
11
9
p( Li, Li)t
B
B
B
B
B
B
B
B
B
B
10
20
30
40
50
Laboratory angle [degrees]
60
1.6A MeV
0
20
40
60
80
100
120
La b o ra to ry An g le [d e g re e s ]
140
160
180
cm 0 degree
Typical events
20 CsI
Array
C4H10 gas
20 Si
Array
PPAC
MAYA
Differences between 6He and 11Li
 11Li



is much less bound than 6He
6He: mostly 1p
3/2 wave
11Li has mixed waves of 1p , 2s , …
1/2
1/2
The core of 11Li (9Li) may be much softer than
that of 6He (4He)
6He
results
6He
<r n2>1/2
<r m2> 1/2
n1
<r p2>1/2
rn1
a
rc2n
ra
rn2
rdi-n
rn-n=2rdi-n
n2
HBT measurement
Rn-n= 5.9 ± 1.2 fm
Rn-n= 6.6 ± 1.5 fm
Rn-n= 5.4 ± 1.0 fm
11LI
(70A MeV)+Pb ->9Li+n+n
E(9Li-n)
1MeV
EMD
Nakamura et al. 2006
E(9Li-n)
1MeV
He and Li Radii
4
Ç
Ñ
Li
3.5
Radii and Skin thickness [fm]
3
H
2.5
B
É
Ñ
Ç
2
Ç
Ñ
É
B
Ç
Ñ
É
Ç
Ñ
É
É
J
1.5
Å
He
B
Rm(He)
J
Rp(He)
H
Rn(He)
F
Nskin(He)
Ñ
Rm(Li)
É
Rp(Li)
Ç
Rn(Li)
Å
Nskin(Li)
1
F
0.5
Å
Å
Å
0
Å
-0.5
5
6
7
8
9
Mass Number A
10
11
12
RMS radii and the configuration
 re2  rp2    R 2proton  
 R 2proton  0.801 0.032
2
 Rneutron
 0.120 0.005

N
2
 Rneutron

Z
•
Relation between ms radii
2
Ai  rim
 Zi  rip2  Ni  rin2 
Neutron radii <rn2>, <rsn2> can be determi ned from (2).
(2)
• The halo radius I

2
A  rm2  Ac  rcm
 Ah  rh2 
• Core motion in the halo nuc leus:

the halo nuc leus.
2
 rp2  rsp
   rc2 
(3)
<rc2> is the ms radius of the center of the core in
2
 rc2  rp2    rsp

2
2
 rcm
 rc2    rsm

2
2
 rcn
 rc2    rsn

Using thos e equa tions, we can obtain <r 2>, <r 2>, <r 2> .
c
cm
cn
distribution then <rh2> can be determi ned using eq.(3).

(4)
(5)
The ms radius of halo
•
Core(rc) move ment and two-neu tron center-off-mass (r2n=rn1+rn2) move ment.
rn1
and rn2 are positi ons of halo neu trons from the center of mss of the halo nuc lei.
Ac rc  Ah r2n  Ah
(rn1  rn2 )
2
(6)
Using eq.(6) <r2n2> are obtained .
• Distance between two halo neu trons (rn-n=rn1-rn2) and di- neu tron ms radius< rdi-n2>.

2
2
rnn  2rdin  rn1  rn2
 rnn
 4  rdin

(7)
• The halo radius II
2
2
 rh2  r2n
   rdin

(8)

Using this equa tion and <r2n2>, <rh2> we can obtain the di- neu tron ms radius <rdi-n2> and
thus the ms separation of two-halo neu trons <rn-n2>.

• Correlation of the halo neu trons :
2
2
Ac2  rc2  (rn1  rn2 ) 2  rn1
   rn2
 2  rn1  rn2 
2
2
2
 rnn
 (rn1  rn2 ) 2  rn1
   rn2
 2  rn1  rn2 
From eqs.(9) and (10),

1
2

r

r

( rc2    rnn
)
n1 n2

4
We got the cross term of the coordinate between two neu trons <rn1•rn2>.

(9)
(10)
(11)
MAY
A
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.
there are two little drift
chambers before MAYA, to
monitor the beam.
the projectile makes reaction
with a nucleus of the gas.
cathode
wall of CsI
detectors
anode:
amplification
area.
segmented
cathode
the recoil product leaves enough energy to induce an image of its
trajectory in the plane of the segmented cathode.
we measure the drift time up to each
amplification wire. The angle of the reaction
plane is calculated with these times.
Φ
t1
tn
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.