F. M. NunesNSCL, Michigan State University

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Recent developments in the study of halo breakup

In collaboration with: Neil Summers (MSU) and Ian Thompson (Surrey)

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structure versus reactions

data = reaction x structure

Usually not this simple: reaction and structure are entangled!

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Importance

of breakup

breakup and driplines

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11Be(p,p’)10Be+n

[Shrivastava et al, PLB 596 (2004) 54][Shrivastava et al, PLB 596 (2004) 54]

low energy continuum experiments

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23O(Pb,Pb)22O+n+g[Nociforo et al, PLB 605 (2005) 79][Nociforo et al, PLB 605 (2005) 79]

9Be(17C, 16C )X

[Maddalena et al., PRC63(01)024613]

low energy continuum experiments

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breakup with CDCC: three body reaction

core

valence

target

rR

•Projectile treated as 2-body system•3-body Hamiltonian for reaction

vcrvc

vcvTcTR

VTh

hVVTH

0),(),(

0)()(

kljkljvc

nnnnvc

rkrkh

rrh

l = core-valence relative angular momentumj = projectile total angular momentum

is single particle/cluster wavefunction defined by potential Vvc

binding energy for bound states

resonances and scattering phaseshifts for continuum

fixed by

fix VcT and VvT from elasticscattering

Summers @ NSCL2004

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continuum discretization

i

i

k

klji

ilji dkrkkw

Nr

1

),()(2

)(,

•Discretize continuum into bins•average wavefuntion over a bin with weight wi(k)

exc

g.s.

s1/2 p1/2 p3/2 d3/2 d5/2 f5/2 f7/2

Evc

0

20

wi(k) chosen so that thebin wavefunctions are realand normalized correctly using

i

i

k

kii dkkwN

1

2|)(|

•label the quantum numbers

for each bin by i,lj

Summers @ NSCL2004

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CDCC equations

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

Summers @ NSCL2004

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• F.M. Nunes and I.J. Thompson, Phys.Rev.C59, 2652 (1999).• B. Davids, et al., Phys.Rev.C 63, 065806 (2001).• J.A. Tostevin, F.M. Nunes, and I.J. Thompson, Phys.Rev.C 63, 024617 (2001).• J. Mortimer, I.J. Thompson, and J.A. Tostevin, Phys.Rev.C 65, 064619 (2002).• A. Moro et al., Phys. Rev. C 67, 047602 (2003).• T. Egami, et al., Phys.Rev.C 70, 047604 (2004).

CDCC results for breakup

8B breakup into p+7Be

•K. Rusek and K.W. Kemper, Phys.Rev.C 61, 034608 (2000).•T. Matsumoto, et al., Phys.Rev.C 70, 061601(R) (2004).•K. Ogata et al., Phys. Rev. C 73, 051602 (2006).

6He breakup into nn+4He

6Li breakup into d+4He•N. Keeley and K. Rusek, Phys. Letts B 375, 9 (1996).•K. Rusek and K.W. Kemper, Phys.Rev.C 61, 034608 (2000).•C. Signorini et al., Phys. Rev. C 67, 044607 (2003).

11Be breakup into n+10Be• J.A. Tostevin et al., Phys. Rev. C 66, 024607 (2002).• M. Takashina, et al., Phys.Rev.C 67, 037601 (2003).• A. Shrivastava et al., Phys. Lett. B596, 54 (2004).

• N.C. Summers and F.M. Nunes, Phys. Rev.C 70, 011602(R) (2004).

7Be breakup into 3He+4He

15C breakup into n+14C•J.A. Tostevin et al., Phys. Rev. C 66, 024607 (2002).

•H.B. Jeppesen et al., Nucl. Phys. A 748, 374 (2005).

9Li(d,p)10Li(continuum)

•Obertelli et al., Phys. Letts B 633, 33 (2006)

26Ne(d,p)27Ne(continuum)

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mistake?

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core excitation: eXtended CDCC

[Summers, Nunes and Thompson, PRC 73 (2006) 031603R][Summers, Nunes and Thompson, PRC 73 (2006) 031603R]

JIjs ;,

r

I

lj

Standard Approximations

Single particle projectile

Spectator core XCDCC includes

Coupled configuration of projectile

Dynamical excitation of core

0+

n

10Be

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breakup of 11Be

JIjs ;,

r

I

lj0+0+

0+

0+2+

2+

projectile fully coupled

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breakup of 11Be

JIjs ;,

r

I

lj

0+2+

0+

0+0+

2+

Dynamical excitation

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coupled channel model for 11Be

JIjs ;,

r

I

lj

[Nunes, Thompson and Tostevin, NPA 703 (2002) [Nunes, Thompson and Tostevin, NPA 703 (2002) 593]593]

coupled channel equation (i=l,j,I)

deformation of the core introduced via Rws

core matrix elements = rotational model

)(),( corevcrproj hrVTH

pJIjsla rYrr )](])([[)(),(

)()()()( ''

' rrVrerVT pppp Ja

aa

Jaa

Jaaa

Jaa

lr

)](1[)( 202 rYRrR ws

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continuum discretization

a

p

k

k

annanni

inJ JIjslrdkrkkw

Nr

i

i

P;,),(|,),()(

2)(

1

:

•Discretize coupled channel continuum into bins

quantum numbers

for each bin by n l,j,I

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computational problem

)()()()( ''

' RRVRERVT TTTT JJJJLR

TvtvtctctTJ JRVRVJRV ;')(),(;)('

•We have a very very large number of coupling potentials to calculate

•Second order coupled differential equation (enhanced numerov method)

parallelized for each channel J

parallelized

•Our present limit on the cluster is memory per node!

•Memory ~ NR.NC2

•Dimension: NR=400-5000 radial steps NC=50-1800 channels

NJ=30-200 J channels

•Code in F90 + MPI

•Time ~ NR.NC3 .NJ

(L,Jp,Jt,J,i,n)

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applications of XCDCC

p(11Be,10Be+n+)p @ E~60 MeV/u

breakup on a protons

elastic+inelastic+transfer+breakup

breakup on a heavy target at intermediate energies208Pb(11Be,10Be+n+) 208Pb @ E~40-60 MeV/u

breakup on a light target9Be(11Be,10Be+n+) 9Be @ E~60 MeV/u

knockout

inelastic+breakup

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computation details for HPC-cluster

NC

under the approximation of no spin of the neutron

Breakup on 9Be @ E=60 MeV/A

NR=5000 NC=500 NJ=100 NCPUS=4 walltime=5.5 d mem=65Gb

Breakup on a heavy target @ E=40 MeV/A

NR=400 NC=1800 NJ=30 NCPUS=16 walltime=4 d mem=120Gb

Breakup on a protons @ E=40 MeV/A

[Summers, Nunes and Thompson, PRC[Summers, Nunes and Thompson, PRC7474, 014606 (2006)], 014606 (2006)]

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breakup of 11Be on 9Be

Comparison with other models

measurement at MSU: neutron was not detectedIncludes stripping as well as breakup

9Be(11Be,10Be)X @ E=60 MeV/A

[Summers, Nunes and Thompson, PRC 73 (2006) 031603R][Summers, Nunes and Thompson, PRC 73 (2006) 031603R]

CDCC

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breakup of 11Be

Stripping is not sensitive to deformation

[Batham, Thompson and Tostevin, PRC[Batham, Thompson and Tostevin, PRC7171 064608 064608 (2005)](2005)]

• Eikonal model including dynamical rotational excitations of 16C core

• Inclusive cross section of rotational states of 16C

• Assumed 17C(3/2+) [1d5/22+] ground state - pure single particle state with excited 2+ core

• Enhanced breakup cross section due to deformed 16C+Target interaction

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breakup of 11Be

Stripping cross section taken from eikonal calculations (J.A. Tostevin 2005)

9Be(11Be,10Be)X @ E=60 MeV/A

XCDCC breakup

Data: Aumann Data: Aumann et al.et al., PRL84, 35 (2000), PRL84, 35 (2000)

[Summers, Nunes and Thompson, PRC 73 (2006) 031603R][Summers, Nunes and Thompson, PRC 73 (2006) 031603R]

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elastic 11Be+p

data: Lapoux et al, GANIL

data: Shrivastava et al., Phys. Lett. B 596 (2004) 54.

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breakup 11Be on p

data: Shrivastava et al., Phys. Lett. B 596 (2004) 54.

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inelastic 11Be+Pb

Data: Pain Data: Pain et al.et al., GANIL, GANIL

GANILGANIL

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inelastic 11Be+Pb

Data: Pain Data: Pain et al.et al., GANIL, GANIL

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• XCDCC provides an important step forward for understanding reactions with exotic beams

• can be applied to a wide range of energies• includes nuclear and Coulomb on equal footing

• consistent core excitation is also now possible• results for 11Be show that is has predictable power

still some discrepancies to understand…

Conclusions

Experimentalists: Need less integrated data!!

Theorists: Need better structure model for projectile!!

Experimentalists: elastic! elastic! elastic!

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Thanks

Only possible due to: Neil Summers (Rutgers)