michigan state university · 2011. 9. 21. · two nucleon correlations and pairing. jlab, may 09...
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michigan state university
Jlab, May 09
national superconducting cyclotron lab
Jlab, May 09
rare isotopes at nscl
Jlab, May 09
why rare isotopes
Jlab, May 09
facility for rare isotope beams
Jlab, May 09
rare isotopes at frib
Jlab, May 09
rare isotopes at frib
Jlab, May 09
Direct Reactions: current status and future directions
Jlab, May 09
F.M. Nunes
in collaboration with: A. Deltuva, A.C. Fonseca, P. Capel, E. Cravo, R.C. Johnson, P. Mohr, A.M. Moro, A.M. Mukhamedzhanov,
D. Pang, N.C. Summers, I.J. Thompson
funded by: NSF and DOE
Jlab, May 09
why do reactions? elastic
[Summers and Nunes, PRC 76 (07) 014611]
traditionally used to extract optical potentials, rms radii,
density distributions.[Lapoux et al, PRC 66 (02) 034608]
Jlab, May 09
why do reactions? inelastic
[Summers et al, PLB 650 (2007) 124]
traditionally used to extract electromagnetic transitions
or nuclear deformations
Jlab, May 09
why do reactions? transfer
g.s. SF = 0.33 ± 0.09 (d5/2)
1st SF = 0.30 ± 0.08 (s1/2)
example:84Se(d,p)85Se
[ISF white paper, A. Gade ]
compilation of one nucleonspectroscopic factors
[J. Thomas et al, PRC 76, 044302 (2007)]
traditionally used to extract spin,parity and spectroscopic
factors
Jlab, May 09
11Li(p,t)9Li@ 3 A MeV
why do reactions? transfer
measured both ground state and excited state 9Li
[Tanihata et al, PRL 100, 192502 (2008)]
traditionally used to study two nucleon correlations and
pairing
Jlab, May 09
why do reactions? breakup
23O(Pb,Pb)22O+n+g[Nociforo et al, PLB 605 (2005) 79]
n
23O + g n + 22O208Pb
22
O23O
two nucleon correlation function
14Be g n+n+12Be
[Marques et al, PRC 64 (2001) 061301]
Pb
C
Jlab, May 09
14C(n,)15C has impact on:
• neutron-induced CNO cycle
• heaviest element in non-homogenous BB
• abundancies from the r-process in SN
why do reactions? astrophysics
Jlab, May 09
• direct measurement
why do reactions? astrophysics
14C(n,)15C
• Coulomb dissociation
n
208Pb
14
C
low relative energy
15C
• transfer reaction
14C(d,p)15C
Outline
Jlab, May 09
(d,p) reactions the combined method (n,) versus (d,p)
breakup reactions CDCC method results for 14C(n,)15C eXtended CDCC results for 11Be on 9Be
breakup and transfer Faddeev vs CDCC
future directions
inelastic excitation and breakup
SF versus ANC: definitions
Jlab, May 09
)()( rihiCrI llj
Rr
ABN
0
2 )(||r
AB
AB
lj rIdrS
Spectroscopic factor (SF)
Asymptotic normalization coefficient (ANC)
)()( rihibr lnlj
Rr
nljN
)()( rArI nljnljAB
approximation2
2
2
nljb
CAS
lj
nlj
B
nlj B=A+n
(d,p) reactions: standard analysis
Jlab, May 09
dppd
BAAB
rI
rI
)'(
)(
Overlap functions
Spectroscopic factor
d
dS
d
dDW
jj
)(
exp
exp
Experimental xs related to DWBA xs
BpAd
)( postUUVV
IVIM
pBpAnp
ipdABf
distorted wave Born approximation (DWBA)
ABABj IINS
(d,p) reactions: standard method
Fit to Elastic scattering of deuteron
Optical potentialFrom transfer angular distribution
JpFrom normalization of angular distribution
Spectroscopic factor
Uncertainties: optical potentialsreaction mechanism beyond DWBAsingle particle parameters
Jlab, May 09
optical potential uncertainties
Jlab, May 09 Liu et al, PRC 69, 064313 (2004)
12C(d,p)13C : systematic extraction
Uncertainties: optical potentialsreaction mechanism beyond DWBAsingle particle parameters
ADWA
ADWA
reaction mechanism: beyond DWBA
Jlab, May 09
12C
13C
0+
2+
½-
½+
2-way transfer
Delaunay et al, PRC 72 (2005) 014610
12C(d,p)13C: couplings
Uncertainties: optical potentialsreaction mechanism beyond DWBAsingle particle parameters
Jlab, May 09
ipdABf IVIM
adiabatic distorted wave approximation (ADWA)
deuteron optical potential includes deuteron breakupwithin the adiabatic and zero-range approximation
)2/()2/()( dpdndd EUEUEU
finite-range correctionsWales and Johnson NPA274(1976)168
Johnson and Soper potential
d
dS
d
dAD
jj
)(
exp
exp
Experimental xs related to ADBA xs
Johnson, AIP 791, 132 (2005)
reaction mechanism: beyond DWBA
single particle uncertainties
Uncertainties: optical potentialsreaction mechanism beyond DWBAsingle particle parameters
Jlab, May 09
?
(d,p) and overlap functions
Jlab, May 09 ISF whitepaper (2006)
(d,p) reactions: combined method
From sub-Coulomb transfer reaction obtain ANC
From higher energy transfer reaction obtain SF consistent with ANC
Combined method provides a handle on single particle parameters!
Jlab, May 09
2)M)(M()( outin
th CbSb
22 SbC
Mukhamedzhanov and Nunes, Phys. Rev. C 72, 017602 (2005)
22 M)( out
th Cb
(d,p) reactions versus (n,)
Jlab, May 09
Are the SF extracted from (d,p) consistent with those from neutron capture?
Requirements:
• data for transfer below and above the Coulomb barrier
• data from neutron capture
(d,p) reactions and (n,): benchmark with 48Ca
Jlab, May 09
s-wave to p-wave E1 transition significant contribution from interior
thermal capture data with 6% accuracy
scattering length known
48Ca(n,)49Ca
sub-Coulomb with 10% accuracy many data sets up to Ed=56 MeV
48Ca(d,p)49Ca
(d,p) reactions and (n,): benchmark with 48Ca
Jlab, May 09
Dependence on nucleon optical potentials Single particle parameters for IAB(r)
48Ca(d,p)49Ca: validity of ADWA
[Mukhamedzhanov, Nunes and Mohr, Phys. Rev. C 77, 051601R (2008)]
(d,p) reactions and (n,): benchmark with 48Ca
Jlab, May 09
SFs and ANCs from 48Ca(d,p)49Ca sub-Coulomb
[Mukhamedzhanov, Nunes and Mohr, Phys. Rev. C 77, 051601R (2008)]
(d,p) reactions and (n,): benchmark with 48Ca
Jlab, May 09
SFs and ANCs from 48Ca(d,p)49Ca
[Mukhamedzhanov, Nunes and Mohr, Phys. Rev. C 77, 051601R (2008)]
(d,p) reactions and (n,): benchmark with 48Ca
Jlab, May 09
SFs and ANCs from 48Ca(d,p)49Ca and 48Ca(n,)49Ca
(n,)@ 25 meV
11.053.0 SF
(d,p)@ 2 MeV and 56 MeV
25.055.0 SF
[Mukhamedzhanov, Nunes and Mohr, Phys. Rev. C 77, 051601R (2008)]
(d,p) reactions: conclusions
Jlab, May 09
benchmark with (n,) SFs extracted from (d,p) and (n,g) are consistent (for the one case)
crucial to have a peripheral reaction from which ANC is extracted(this removes the single particle ambiguity)
results suggest that (d,p)@30 MeV is ideal to study 48Ca(n,)49Ca thermal neutron capture s ]p is well suited for extracting SF
transfer with unstable nuclei
Jlab, May 09
• Extended tails: finite range more important!
• Uopt very different from Ucore
remnant more important!
• Continuum! Continuum! Continuum!
Outline
Jlab, May 09
(d,p) reactions the combined method (n,) versus (d,p)
breakup reactions CDCC method results for 14C(n,)15C eXtended CDCC results for 11Be on 9Be
breakup and transfer Faddeev vs CDCC
future directions
inelastic excitation and breakup
Breakup reactions: CDCC theory
Jlab, May 09
n15C + g n + 14C
208Pb
14C
15C
•Projectile treated as 2-body system•3-body Hamiltonian for reaction
vcrvc
vcvTcTR
VTh
hVVTH
fix VcT and VvT
from elasticscattering
0),(),(
0)()(
kljkljvc
nnnnvc
rkrkh
rrh
l = core-valence relative angular momentum
j = projectile total angular momentum
binding energy for bound states
resonances and scattering phaseshifts for continuum
Vcn fixed by
Breakup reactions: CDCC theory
Jlab, May 09
s1/2 p1/2 p3/2 d3/2 d5/2 f5/2 f7/2
Ev
c
0
8
15C
s1/2
d5/2
i
i
k
klji
i
lji dkrkkwN
r1
),()(2
)(, p
•Discretize continuum into bins•average wavefuntion over a bin
wi(k) chosen so that the
bin wavefunctions are realand normalized correctly using
i
i
k
kii dkkwN
1
2|)(|
Breakup reactions: CDCC theory
Jlab, May 09
1)()()()( ''
' RuRVRuERVT JJJJLR
)()(),(
)ˆ()(),()ˆ()()( '''
vTvTcTcT
JMLJMLJ
RVRVRrV
RYrRrVRYrRV
•Solve set of radial coupled equations
•Where the coupling potential from state to state ’ is
and the cluster target potentials include both Coulomb and Nuclear parts
•We have N coupled channels, each labeled by the set of quantum numbers
)( Ljli
Breakup reactions and ANC
Jlab, May 09
• breakup reactions are very peripheral• cross sections depend essentially on the ANC
of the bound state• for low relative energies, small residual
dependence on continuum properties
[Capel and Nunes, Rev. C 73, 014615 (2006)]
2CBU
[Capel and Nunes, Rev. C 75, 054609 (2007)]
Breakup reactions and (n,): methodology
Jlab, May 09
CDCC + set of single particle parameters extract ANC from 2 minimum error from =min
21
Nakamura
Nakamura et al, NPA722(2003)301c
Reifarth et al, PRC77,015804 (2008)
Summers and Nunes, PRC78(2009)069908
04.032.1 ANC fm-1/2
208Pb(15C,14C+n)208Pb@68 MeV/u
• Reifarth
14C(n,)15C
Yao, JPG33 (2006) 1
Outline
Jlab, May 09
(d,p) reactions the combined method (n,) versus (d,p)
breakup reactions CDCC method results for 14C(n,)15C eXtended CDCC results for 11Be on 9Be
breakup and transfer Faddeev vs CDCC
future directions
inelastic excitation and breakup
Core excitation in breakup
Jlab, May 09
JIjs ;,
r
x
I
lj
0+0+
0+
0+2+
2+
projectile fully coupled
11Be example
Core excitation in breakup
Jlab, May 09
JIjs ;,
r
x
I
lj
0+2+
0+
0+0+
2+
Dynamical excitation
11Be example
Core excitation in breakup: XCDCC results
Jlab, May 09
Comparison with other models
9Be(11Be,10Be)X @ E=60 MeV/A
CDCC
Stripping cross section taken from eikonal
calculations (J.A. Tostevin 2005)
Data: Aumann et al., PRL84, 35 (2000)
[Summers, Nunes and Thompson, PRC 73 (2006) 031603R]
Outline
Jlab, May 09
(d,p) reactions the combined method (n,) versus (d,p)
breakup reactions CDCC method results for 14C(n,)15C eXtended CDCC results for 11Be on 9Be
breakup and transfer Faddeev vs CDCC
future directions
inelastic excitation and breakup
Breakup and transfer coupled
Jlab, May 09
Faddeev Formalism
CDCC Formalism
each Faddeev component includes correct asymptotics for the corresponding transfer channel
breakup is split in all Faddeev components
limitation of Faddeev-AGS calculations:
convergence with Coulomb is hard (regularization techniques needed to improve)
number of channels increases rapidly with partial waves
Breakup and transfer coupled
Jlab, May 09
Deuteron breakup on 12C @ 56 MeV
[Deltuva et al, PRC 76, 064602]
Breakup and transfer coupled
Jlab, May 09
11Be breakup on protons @ 39 MeV/u
[Deltuva et al, PRC 76, 064602]
breakup: summary of recent activities
Jlab, May 09
Continuum discretized coupled channels method (CDCC) nuclear and Coulomb to all orders
several applications to exotic nuclei: good description of data scaling with square of ANC: breakup can be used to extract ANC
Coulomb dissociation can be used to extract peripheral (n,)
new methodology based on extracting the ANC
14C(n,)15C from Coulomb dissociation consistent with direct capture data
Include core excitation in breakup consistently
CDCC was extended to include coupled channel bins (XCDCC)
results for breakup of 11Be on 9Be show core excitation is important
Breakup and transfer on the same footing
CDCC and Faddeev calculations were compared
excellent agreement for cases where transfer coupling is weak mismatches for the case of 11Be on protons
Outline
Jlab, May 09
(d,p) reactions the combined method (n,) versus (d,p)
breakup reactions CDCC method results for 14C(n,)15C eXtended CDCC results for 11Be on 9Be
breakup and transfer Faddeev vs CDCC
future directions
inelastic excitation and breakup
facility for rare isotope beams
Jlab, May 09
future directions
Jlab, May 09
future: microscopic overlap functions for reactions
6He
fully microscopic (built from NN interaction) fully antisymmetrized correct asymptotic behaviour
0 4 8 12 16-0.12
-0.08
-0.04
0.00
0.04
0.08
0.120 4 8 12 16
1E-9
1E-6
1E-3
1
K = 2, s
K = 2, p
K = 0, s
K = 6, d
K = 6, f
O(
) [f
m-3
]
[fm]
Two nucleon correlations in 6He
pro
bab
ilit
y
[thesis of Ivan Brida]
Overlap functions in 6He
Jlab, May 09
future: large scale computation
dimension: NJ~102 J channelsNR~102-103 radial steps
NC~10-103 (?) channels
XCDCC equations system of coupled linear equations • parallelization in terms of projectile-target J• solve for each J the matrix equations• use AMD cluster (128 nodes with 4 cores/node and 8 GB per node)• typically use 20-40 CPUs
parallelize the system of coupled equations (NC)
radial grid not easy to parallelize – differential equations
• memory ~ NR.NC2
• time ~ NR.NC3 .NJ
•Our present limit: memory per node!
swapping
Jlab, May 09
state of the art few-body methods (XCDCC,4B-CDCC, AGS4B) results so far have involved < 100 processors more degrees of freedom ] larger scale computation system of linear coupled eqns need to be parallelized memory sharing should be investigated
future: large scale computation
or something completely different…?
Jlab, May 09
thanks to:
my collaborators: A. Deltuva, A.C. Fonseca, P. Capel, E. Cravo, R.C. Johnson, P. Mohr, A.M. Moro, A.M. Mukhamedzhanov,
D. Pang, N.C. Summers, I.J. Thompson
and funding agencies: NSF and DOE
in the beginning 08
and Max Gimblett