direct reactions in/for nuclear astrophysics

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)

7

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

12

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

13

Higher order Higher order transitionstransitions

dElmEEe

BEe

jtiE

jlm

tiE

j ,

,/

00/

00

dElmEEe

BEe

jtiE

jlm

tiE

j ,

,/

00/

00

Continuum Continuum discretizationdiscretization

14

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)

15

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

16

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

17

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)

18

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

19

)(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

20

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

21

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

22

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

23

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

SS1717 = 22 ± 1 = 22 ± 1 eV.beV.b

24

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

25

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

26

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

27

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

28

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

29

and for the LHC …