1

Direct Reactions in/forDirect Reactions in/for Nuclear Astrophysics Nuclear Astrophysics

Carlos BertulaniCarlos Bertulani(University of Arizona)(University of Arizona)

2

Nuclear Astrophysics

TeV/nucleon keV/nucleon

??? ???Exotic stellar site

Quark matter in compact stars,Big Bang

Typical stellar site

Stellar evolution

Nuclear many-body problem: one of the hardest problems of all physics!• Interactions are complicated• Nucleons = composite particles• Requires large computation

Nuclear many-body problem: one of the hardest problems of all physics!• Interactions are complicated• Nucleons = composite particles• Requires large computation

3

Typical problems

BpBe 87 ),( γ BpBe 87 ),( γ

OC 1612 ),( γ OC 1612 ),( γ OC 1612 ),( γ OC 1612 ),( γ

4

Electron screening:Electron screening: (a)(a) in starsin stars (theoretical)(theoretical) (b) on earth(b) on earth (experimental+theoretical)(experimental+theoretical)

Atomic, QED, or nuclear effects?

NO

Stopping power tables wrong? YES

CB, Balantekin, Hussein, NPA 1997

CB, de Paula, PRC 2000, 2004

5

Solutions with direct reactions at 50-200 Solutions with direct reactions at 50-200 MeV/nucleonMeV/nucleon(A) Trojan horse

(B) ANC

Baur, PLB 1986

Akram Mukhamedzhanov, 1991

A(a=b+x,b+c)C A(x,c)C

Talk by Bob Tribble, Tuesday

(C) Knockout reactions CB, McVoy, PRC

1992Zdk

dZdk

dbest probe of ψ

Spectroscopic factorsSpectroscopic factors

CB, Hansen, PRC 2004

input for nuclear reactions in astrophysicsinput for nuclear reactions in astrophysics

Hansen, Tostevin, ARNPS 2003

Claudio Spitaleri, Catania

6

Shoemaker-Levy comet

)( ),(1

c b a

E

ddE

Edn

EddE

d

l

l

)(

),(1c b a

E

ddE

Edn

EddE

d

l

l

Theory

cba k

kbc

2

2

cba k

kbc

2

2

CB, Baur, Rebel, CB, Baur, Rebel, 19861986

Coulomb Coulomb dissociationdissociation

Kiener et al., Z. Phys. Kiener et al., Z. Phys. 19931993

(easier than this)

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Standard Standard calculationscalculations

rMJJM

MJJM

00

00

;* rrr

1 – Use a 1 – Use a nuclear modelnuclear model. Expand trans. dens. into multipoles. Expand trans. dens. into multipoles

1a – e.g. a 1a – e.g. a potential modelpotential model (Woods Saxon + Coulomb + (Woods Saxon + Coulomb + spin orb.)spin orb.)

)()(2

10

2

1

ˆ

16

0

00

00000

*2

00000

00;

rRrRrI

j

J

J

jjjJMMJ

j

jJer

Jjl

JljE

C

lljJIeffMJJM

x

C

2 – Use an 2 – Use an optical potentialoptical potential, or build from folding (M3Y, JLM, , or build from folding (M3Y, JLM, etc.)etc.) sEtrdrdEU NNTP ,, 212

31

3 rrr

3 – Plug in 3 – Plug in DWBA amplitudeDWBA amplitude

RRR

YrRUrRrddm

f PTJMN ,

2)()*(33

2)(

8

4 – Repeat all for 4 – Repeat all for Coulomb interactionCoulomb interaction

00)( , MJYrJMESf x

JMC r

5 – Add all5 – Add all

M

JMN

JMC

x

ffJdEd

d J2

)()(

0 12

1

s,d

p3/2

s,dp,f

p3/2

E1E2

capturecapture break-break-upup

E1

9

Motobayashi et al, PRL 1994

Application to Application to 7Be(p,)8B

talk by Motobayashi

10

Discussions with John Bahcall, Discussions with John Bahcall, 19941994

11

page page 22

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Nuclear Nuclear interaction:interaction:

BpBe 87 ),( γ BpBe 87 ),( γ

from

PbBPbB 78 ep PbBPbB 78 ep

50 MeV/nucleon

Data: Kikuchi, PLB 97 Calc: C.B., NPA 1998

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Higher order Higher order transitionstransitions

dElmEEe

BEe

jtiE

jlm

tiE

j ,

,/

00/

00

dElmEEe

BEe

jtiE

jlm

tiE

j ,

,/

00/

00

Continuum Continuum discretizationdiscretization

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Higher order transitions + E1-E2 Higher order transitions + E1-E2 interferenceinterference

PbBPbB 78 ep PbBPbB 78 ep

C.B., Z. Phys. 1996• small effect higher-

order transitions in

dEdd /• small E1-E2 interference in dEdd /

• but large E1-E2 interference in momentum distirbutions

Esbensen, Bertsch, NPA 1996

Used by Davids, PRL 1999 to filter E2 from S17(0)

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0,22 rRUk

b

z

00 2 VEVU

z

ezS zik

,

,,,

bR

rbrR

SikS

EVU

zz

2

02

Relativistic Relativistic effectseffects

jlJM

zSedik

f

ezSzVzSiv

i

zkkiz

;

,2

,,,

'

0,

KKQ

bbQ

bbb

Q.b

jlJM

zSedik

f

ezSzVzSiv

i

zkkiz

;

,2

,,,

'

0,

KKQ

bbQ

bbb

Q.b

V0

Eikonal

Relativistic CDCC

CB, PRL 2005

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0 2 4 6 8 10

[degrees]

0.010

0.100

E = 1.25 - 1 .5 M eV

E = 0.5 - 0.75 M eV

0.01

0.10

1.00

.d

/d

[b/r

ad]

relativistic corrections

DATA: Kikuchi et al, DATA: Kikuchi et al, 19971997

88B dissociation on lead at 50 B dissociation on lead at 50 MeV/nucleonMeV/nucleon

4-10% effect4-10% effect

0 0.5 1 1.5 2E [M eV]

0

40

80

120

160

d/d

E

[m

b/M

eV]

perturbation theory

R-CDCC

NR-CDCCwith non-relativistic V0

DATA: Davids et al, DATA: Davids et al, 20022002

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Summary on CD method Summary on CD method forfor

BpBe 87 ),( γ BpBe 87 ),( γ

S17 (0) = 18 ± 1.1 eV.b S17 (0) = 18 ± 1.1 eV.b

CD method has proven useful to extract S17(0) (and other S-(and other S-factors)factors)

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Attempts Attempts forfor

OC 1612 ),( γ OC 1612 ),( γ

Fleurot, PhD Thesis, 2002

PbCPbO 1216 PbCPbO 1216 80 MeV/nucleon

dotted:dotted: nuclearnuclear

dashed:dashed: CoulombCoulomb

solid:solid: nuclear + Coulomb + nuclear + Coulomb + interf.interf.

see also contribution by C. Angulo

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)(ˆ)( ,)()()(

aaAaaAA rrrg

)()(~)( rOSrIrg llll

rrgr,rENr,rHdr all0''''

)(ˆ)'(ˆ' )()()()( rN

Hrr,r

N

H aaAaaA

Trying to reconcile structure and Trying to reconcile structure and reactionsreactionsWhat do we need?

What can we do in practice?

Hill-Wheeler, 1953

e.g. NCSM

What are the effective interactions in H = T + ½∑vik ??

MANY YEARS OF INVESTIGATION

talk by C. Forssen

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r

rWCrR l

ljlj2/1,)(

r

rWCrR l

ljlj2/1,)(

Fix: correct Coulomb tail at large r’s

bad asymptoticsbad asymptoticsbad asymptoticsbad asymptotics

No-Core-Shell-ModelNo-Core-Shell-Model(with correction for asymptotics)

Navratil, C.B., Caurier, PLB 2005

PRC 2006

Many-body bound Many-body bound statestate

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Knockout reactions with Knockout reactions with NCSMNCSM

m

ljmCC

innn

lj

C

strip

NCSM

C SerddzSbdl

SC

kd

d 2222

2

21

122

1rbb rk

m

ljmCC

innn

lj

C

strip

NCSM

C SerddzSbdl

SC

kd

d 2222

2

21

122

1rbb rk

With NCSM wavefunctions (10 ћ)

• l=1, j=1/2, I7Be=3/2: C2S=0.085

• l=1, j=3/2, I7Be=1/2: C2S=0.280

• l=1, j=3/2, I7Be=3/2: C2S=0.958

8B (41 MeV/nucleon) + 9Be 7Be + X 8B (41 MeV/nucleon) + 9Be 7Be + X

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8B (938 MeV/nucleon) + 12C 7Be + X

σstr = 99.39 mb

exp = 94 ± 9 mb

8B (938 MeV/nucleon) + 12C 7Be + γ + X

σstr = 15.31 mb

exp = 12 ± 3 mb

DATA: Cortinal-Gil et al, 2002DATA: Cortinal-Gil et al, 2002

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7Be(p,g)8B S-factor with NCSM

SS1717 = 22 ± 1 = 22 ± 1 eV.beV.b

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Future: Charge Future: Charge ExchangeExchange

2AB

2AB

(p,n) (n,p) (d,2He) ... (Z, Z±1)

2200~ ABab

d

d

22

00~ ABabd

d

needed for A~50-60

based onTadeucci et al, NPA 1981

e- + (Z,A) (Z-1, A) + e

Z Z+1

Lenske, Wolter, Bohlen, PRL 1989CB, NPA 1993

Obtained from

Remco Zegers - MSU

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Electron-ion collider ELISe Electron-ion collider ELISe (GSI)(GSI)

skins and halosskins and halos

soft multipole vibrationssoft multipole vibrations

σee’ (q)

GDR

SGDR11Li

H.Simon@gsi.de

Δrnp

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2~ qf

ddE

dl

e

Ershov, PRC 2005

),,,( llnll raSqff very strong dependence on effective range expansion parameters, al, rl

CB, PLB 2005

Electron-ion collider ELISe Electron-ion collider ELISe (GSI)(GSI)

H.Simon@gsi.de

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ikkra

kT ...

211

1~)(

20

ikkra

kT ...

211

1~)(

20

2/

1~)(

EiEEES

R 2/

1~)(

EiEEES

R

2//1

cot2

0

2

pra

Hmipc

C

2//1

cot2

0

2

pra

Hmipc

C

Kong, Ravndal, 2000

van Kolck, 1997Gegelia, 1998Kaplan, Savage, Wise, 1998

in progress

EE

R ''

EE

R ''

CB, Hammer, van Kolck, 2002

Reconciling Nuclear Physics with Reconciling Nuclear Physics with QCDQCD

Hen 4 Hen 4

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Summary• Problems in nuclear astrophysics

• Screening: confusing

• too small cross sections

• Many reactions will never be measured directly

• Using direct reactions

• Coulomb excitation • Charge-exchange • Knockout & transfer reactions, …• Need ISOL and fragmentation facilities

• Needed theory

• reactions in general • bridge internal (structure) to external (reactions) • understand Nuc. Phys. from fundamental theory QCD

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and for the LHC …