michigan state university · 2011. 9. 21. · two nucleon correlations and pairing. jlab, may 09...

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