Indirect methods for nuclear astrophysics with radioactive nuclear beams

Livius TracheTexas A&M University

Nuclear Structure Workshop

Weizman Institute of Science, Apr. 11-12, 2011

2

M. Smith & E. Rehm

Two big problems:1. - reactions in stars involve(d) radioactive nuclei ⇒ use RNB2. - very small energies and very small cross sections ⇒indirect methods

mass, T1/2resonances

site, path?!mass, T1/2

+ fissionbarriers ?!

3

Indirect methods in NPA with RNB

Indirect methods in NPA with or w/o RNB A. Coulomb dissociation B. Transfer reactions (ANC method) C. Breakup of loosely bound nuclei D. Spectroscopy of resonances: β-decay, transfer

reactions, resonant elastic scatt., etc Decay spectroscopy

E. Trojan Horse Method …

= studied at TAMU

12C 13C

13N 15N

15O

14N

17O

17F

16O

18F

18O14O

19Ne18Ne

13O

11C

12N

8B

7Be

9C 10C

10B

11N

11B9B

8Be

22Ne21Ne

9Be

23Na

17Ne

16F15F

22Na20Na

24Al23Al 25Al

24Mg23Mg22Mg21Mg20Mg

19Na

19F

20Ne

25Si24Si 26Si

15C14C

27Al26Al

28Si27Si 29Si

26Mg25Mg

27P26P 28P 30P29P 31P

28S27S 29S 31S30S 32S

32Ar31Ar 33Ar 35Ar34Ar 36Ar

31Cl30Cl 32Cl 34Cl33Cl 35Cl

34S33S= planned

12O

16Ne

22Al

23Si

25P

21Al

30Si

(p,n) possible

stable

used at TAMU

(p,2n) possible

21Na

also 38Ca, 46V, 57Cu, 62Ga, …

14F

4

5

Indirect methods for nuclear astrophysics

Need good additional knowledge

(data)

Measurement at lab energies

Comparison with (reaction)

calculations

Extract (nuclear structure)

information

Calculate astrophysical S-factoror reaction rates

Compare with direct measurements

6

Coulomb Dissociation vs direct• After pioneering 6Li->α+d

(Karlsruhe) and 7Li->α+t (TAMU) …

• CD of 8B->7Be+p at GSI, GANIL, MSU, RIKEN, …

• CD gives results comparable with direct capture 7Be(p,γ)8B measurements

• Important: uncertainties are totally different => reliable data for input in solar model

• More CD: w. other nuclei –determine the energy dependence of S(E), including resonances and their location and strength

A

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ANC in peripheral reactions: radiative proton capture, transfer and breakup

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

1 10 100 1000

radius (fm)

Pot

(MeV

)

rrW

CrS lnljnljnlj

)2()( 2/1,2/1 κ

ϕ η +−→

Bound state for r>RN

in – scattering wf

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

1 10 100 1000

radius (fm)

Pot

(MeV

)

rrW

CrS lnljnljnlj

)2()( 2/1,2/1 κ

ϕ η +−→

Bound state for r>RN

in – scattering wf

Transfer or breakup vs proton capt in 8B

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 10 20 30 40 50 60

radius (fm)w

fct,

prob

ab

wave fct

transfer

Whittaker

pr capt

)()ˆ()()ˆ()( rrYrrYVT coul ϕεϕ −=+

Shape in asymptotic region given by Whittaker fct. Only normalization (ANC) unknown and needed!

(p,γ) happens here

transfer happens here

B,C

breakup happens here

8

B. Transfer reactions: the ANC method

Transfer reaction B+d→A+a peripheral (absorption)

• Transfer matrix element:

2 22 2( ) ( )

A A d d

A A d d

A A d d

DWl j l j

Bpl j apl j

A dBpl j apl j

dd

Cb b

Cσσ

=Ω ∑

NA: proton-nucleus also peripheral

( )2

, ( )ABpp Cγσ ∝

ANC - independent on binding potential geometry!OMP knowledge crucial for reliable absolute values!Semi-micr proc. JLM interaction (LT ea, PRC, 2000)

( ) ( )A df Bp ap iM I V Iχ χ− += ∆

I CW r

rBpA

r R

BpA l Bp Bp

Bp

Bp NA≈

>− +η

κ, ( )12

2

1 1 1 2 2 2

DWBAnlj

i fn l j n l j

S Sd dd d

σσ

→

Ω

=Ω ∑

(Christy and Duck, 1963Parker and Tombrello, 1964)

Depend on geom (r0,a) of proton-binding potential < 20-40%

Depend on OMP* n Factors !!!

9

From MARS group at Texas A&M University

Transfer reactions. Major results:– ANC technique firmly established for transfer reactions

• Proton transfer for 7Be(p, γ)8Β, 11C(p,γ)12N, 12N(p, γ)13O, 13N(p, γ)14O, 9Be(p, γ)10B, 13C(p, γ)14N, 14N(p, γ)15O, 15N(p, γ)16O

• Use of neutron transfer and mirror symmetry for ANC proposed and tested:– (7Li,8Li) for (7Be,8B) → 7Be(p, γ)8B ( S17)– (22Ne,23Ne) for (22Mg,23Al) →22Mg(p, γ)23Al– (17O,18O) for (17F,18Ne) →17F(p, γ)18Ne

• Optical Model Potentials for nucleus-nucleus collisions from double-folding procedure using JLM eff inter. Needed in DWBA. Established with stable beams and tested for RNBs: 7Be, 8B, 11C, 12N, 13N, 17F, …

10

Cross sections for (p,γ) fromp-transfer reactions with RNB from MARS

12 C

12 N

Melamine target

(Faraday Cup)

∆ E - det . (PSSD)

Er - det .

12 C

12 N

Melamine target

(Faraday Cup)

∆ E - det . (PSSD)

.

12C @23 MeV/uH2 cryotarget

12N @12 MeV/u99% pure, 4 mm diaMelamine target

Four telescopesystem (“the cross”):∆E – PSD 65, 110 µm

E – 500 µm

11

Example 12N @12 MeV on N6C3H6 and C

• Primary beam: 12C @ 23 MeV/u 150 pnA• Secondary beam: 12N @12 MeV/u 2x105 pps

• Elastic θcm =8-60 deg.• Fit OMP from folding JLM– no param adjust!• Transfer 14N(12N,13O)13C – fit w. DWBA extract ANC• 12N(p,γ)13O rate evaluated from ANC

C2p1/2 (13O g.s.)=2.53±0.30 fm-1

12

Transfer & elastic @12 MeV/uTAMU MARS 12N beam 2⋅105 pps

14N(12N,13O) proton-transfer react ⇒ 12N(p,γ)13O (rap proc)

A. Banu et al, Phys Rev C 79, 025805 (2009)

ANC, S-factor 0-2 MeVReaction rate

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Neutron transfer – 14N(7Li,8Li)13CStudy mirror reaction – neutron transfer with stable beam to obtain information on 8LiUse charge symmetry 8Li - 8B

Results:C2

tot(8B)= 0.455 ± 0.047 fm-1

S17(0) = 17.6 ± 1.7 eV b&

Mixing ratio C2(p1/2)/C2(p3/2)=0.13(2)

LT e.a., PRC 67, June 2003

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23Al from n-transfer: (22Ne,23Ne) for (22Mg,23Al)

Mirror symmetry:Snlj(23Al)=Snlj(23Ne)

C2=Sb2 → C2(23Al)=[b2(Al)/b2(Ne)]C2(23Ne)

Astrophysical motivation:22Mg(p,γ)23Al

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* OMPs from the entrance/exit channels DWBA.

* The Angular distribution for:

Transfer Reaction p1/2d5/2 (Q=0.254 MeV)

* The reaction is Peripheral

0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.60.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

S

&

C2

b (23Ne) [fm-1/2]

p1/2d5/2( )5 / 2

2 23 -10.86 0.08 0.12 fmdC Ne = ± ±

( )5 / 2

5 / 2 5 / 2

2 23

3

3 1

23 2

( Al) 4.63

( Al) ( Ne

0.77 *10 fm

)

d

d dS S

C −= ±

= ⇒

T. Al-Abdullah ea, PRC 2009

# Transfer Reaction:13C(22Ne,23Ne)12C

# Elastic Scattering:1. 22Ne+13C2. 22Ne+12C

Beam @ 12 MeV/A

Targets 100 μg/cm2

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7Be on melamine

TAMU exps @ 12 MeV/u

ORNL exps @ 10 MeV/u

G. Tabacaru ea,PRC 73, 025808 (2006)

J. Blackmon ea, PRC 73, 034606 (2005)

A. Banu ea, PRC 79, 2009.

Optical Model Potentialsfor Nucleus-Nucleus collisions

for RNBs

Essential to make credible DWBA calc needed in transfer studies

Have established semi-microscopic double folding using JLM effective interaction:

• Established from exps with stable loosely bound p-shell nuclei: 6,7Li, 10B, 13C, 14N … @ 10 MeV/u

• Independent real and imaginary parts, energy and density depend.

• Parameters: renormalization coeff. (Nv~0.4-0.5, Nw=1.0)

• Predicts well elastic scatt for RNBs: 7Be, 8B, 11C, 12N, 13N, 17F

• Good results for transfer reactions (tested where possible)

L. Trache ea, PRC 61 (2000), F Carstoiu ea PRC 70 (2004)

12N on melamine

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H burning

Ne-Na cycle

12C 13C

13N 15N

15O

14N

17O

17F

16O

19F18F

18O14O

19Ne18Ne

13O

11C

12N

8B

7Be

9C 10C

10B

11N

11B9B

8Be

20Ne 22Ne21Ne

9Be

23Na

17Ne

16F15F

22Na21Na20Na

24Al23Al 25Al

24Mg23Mg22Mg21Mg20Mg

19Na

(p,γ)(p,α)(β+ ν)

= studied at TAMU

CNO, HCNO

7Be(p,γ)8B (solar neutrinos probl.):p-transfer: S17(0)=18.2±1.7 eVbDirect meas: S17(0)=20.8±1.4 eVb

Comp with direct meas: 16O(3He,d)17F vs. 16O(p,γ)17FGagliardi e.a. PRC 1999 vs. Morlock e.a. PRL 1997

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ANC family tree

(courtesy Michael Wiescher)

ANC method (references):

• Xu, Gagliardi, Tribble, Mukhadmedzhanov, Timofeyuk, PRL 73, 2027 (1994)• A.M. Mukhadmedzhanov et al., PRC 56, 1302 (1997)• C.A. Gagliardi et al., PRC 59, 1149 (1999)• L. Trache, F. Carstoiu, C.A. Gagliardi, R.E. Tribble, PRL 87, 271102 (2001)

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Breakup (one-nucleon removal r.)

Momentum distributions → nljCross section → ANC (only!!!)Gamma rays → config mixing

Need: Vp-target & Vcore-targetand reaction mechanism

Calc: F. Carstoiu; Data: see later

C

Spectroscopic factors:

calcnljS

σσ exp=

or ANC:

calcnljnlj bC

σσ exp22 =

Need good experimental data! Need good, reliable, calculations!!!

20

One-nucleon removal = spectroscopic tool

Example of momentum distributions – all types!E. Sauvan et al. – PRC 69, 044503 (2004).Cocktail beam: 12-15B, 14-18C, 17-21N, 19-23O, 22-25F@ 43-68 MeV/nucleon.

normal halo2s1/2

Config mixing

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Example: Summary of the ANC extracted from 8B breakup with different interactions

Data from:F. Negoita et al, Phys Rev C 54, 1787 (1996)B. Blank et al, Nucl Phys A624, 242 (1997)D. Cortina-Gil e a, EuroPhys J. 10A, 49 (2001).R. E. Warner et al. – BAPS 47, 59 (2002).J. Enders e.a., Phys Rev C 67, 064302 (2003)

All available breakup cross sections on targets from C to Pb and energies 27-1000 MeV/u give consistent ANC values!

Summary of results: LT ea, PRL 87, 2001LT ea, PRC 67, 2004

7Be(p,γ)8B (solar neutrinos probl.):p-transfer: S17(0)=18.2±1.7 eVbBreakup: S17(0)=18.7±1.9 eVbDirect meas: S17(0)=20.8±1.4 eVb

22

NeNa cycle

Explosive H-burning in novae: “22Na puzzle”

- what are the stellar reaction rates for the 22Mg(p,γ)23Al and 22Na(p,γ)23Mg?

- novae: explosive H-burning of accreting material in binaries star-WD. ~ 30/yr. - γ rays from the decay of long-lived isotopes like 26Al have been detected- E=1.275 MeV γ ray following the decay of 22Na predicted, but not observedby space gamma-ray telescopes

22Na depletion in novae: how does it happen?

24Si140 ms

- what about 23Al(p,γ)24Si?

23

Questions to nuclear structure: “23Al structure and consequences on 22Mg(p,γ)23Al reaction rate”

23Ne

1/2+

5/2+

23Al

- a case of “level inversion” towards p-rich nuclei ?• g.s. of mirror nuclei 23

10Ne13 vs. 2313Al10

- what are the gound state spin and parity of 23Algs ?

Sp = 142 keV

X. Z. Cai et al., PRC 65, 024610 (2002)

22Mg(p,γ)23Al astrophys S- factordirect capture only

y = 62.815x2 + 1173x + 2016.6

0.E+00

1.E+04

2.E+04

3.E+04

4.E+04

5.E+04

6.E+04

7.E+04

0 0.5 1 1.5 2 2.5 3

Ep (MeV)

S-f

acto

r (e

V b

)

2s1/2 E1

1d5/2 E1

1d5/2 E1+E2

Poly. (1d5/2 E1+E2)

Nuclear physics input to NA!!!- is 23Al a proton-halo nucleus ?

1017 keV550 keV

gs gshugeThomas-Ehrman effect ?!

24

32S primary beam

444

183

95 MeV/u, ~ 400 W

MCP

LDCTrifoil

Gamma-ray detectors:8 EXOGAM clovers 4% effic.12 NaI crystals 6% effic.

E491 exp. @ GANIL

Cocktail beam(mid-target energies):

24Si 53 MeV/u 23Al 50 MeV/u

22Mg 47 MeV/u21Na 43 MeV/u20Ne 39 MeV/u

• large angular acceptances:4° (horiz. & vertic. planes)

• broad momentum acceptance:∆p/p = 7%

A. Banu et al., NIC10 Symposium2008 & PRC, submitted

With Nigel Orr et al.

25

26

23Al→22Mg+pProton removal

(sought)

GANIL E491 exp

12C(22Mg,22Na)12NCharge exchange

(new & unexpected)

27

Results from 23Al breakup23Al breakup (inclusive)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-300 -200 -100 0 100 200 300

PzCM [MeV/c]

cs [m

b/M

eV/c

]

exp. data

theory (1d5/2)

theory (2s1/2)

config. mixing of 23Al ground state

42+-> 41

+

1

2+-> 0+

41+-> 2+

22Mg0+

2+

41+

42+

1247

2061

1985

Γ(23Al)~200 MeV/c and Jπ=5/2+

A. Banu et al, PRC, submitted

28[46] T. Gomi, T. Motobayashi et al, JPG 31 (2005)

Complementarities: Coulomb and nuclear dissociation

29

Results for 24Si breakup24Si breakup

0

0.05

0.1

0.15

0.2

0.25

0.3

-300 -200 -100 0 100 200 300

PzCM [MeV/c]

cs [m

b/M

eV/c

]

exp.data

theory

23Al(p,g)24Si react rate

1E-101E-09

1E-081E-07

1E-061E-05

0.0001

0.0010.01

0.11

0 0.5 1 1.5 2

Temp [GK]

reac

t rat

e [c

m3/

mol

/sec

]

direct capture tog.s.

Astroph S-factor for 23Al(p,γ)24Si

S fa

ctor

[evb

]

3.00E+02

4.00E+02

5.00E+02

6.00E+02

7.00E+02

8.00E+02

9.00E+02

1.00E+03

1.10E+03

1.20E+03

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ecm [MeV]

th

SFσσ exp=

SF = 2.5-2.9(spect. factor)

C2(24Sigs) = 62.4 ± 7.1 fm-1

=> first exp det of direct comp of 23Al(p,γ)24Si

30

= breakupE491 exp

12C 13C

13N 15N

15O

14N

17O

17F

16O

18F

18O14O

19Ne18Ne

13O

11C

12N

8B

7Be

9C 10C

10B

11N

11B9B

8Be

22Ne21Ne

9Be

23Na

17Ne

16F15F

22Na20Na

24Al23Al 25Al

24Mg23Mg22Mg21Mg20Mg

19Na

19F

20Ne

21Na

25Si24Si 26Si

16N

15C14C

13B

12Be

27Al26Al

28Si27Si 29Si

26Mg25Mg

27P26P 28P 30P29P 31P

28S27S 29S 31S30S 32S

32Ar31Ar 33Ar 35Ar34Ar 36Ar

31Cl30Cl 32Cl 34Cl33Cl 35Cl

34S33S

March 2009

12O

17Ne

22Al

23Si

25P

21Al

30Si

31

Summary A-C

Indirect methods w RNB – valuable tool for nuclear astrophysicsAccuracies of 10-15% can be obtainedQ: Good enough?!For better accuracies more work needed, including systematic studies and development of structure and reaction theories (and codes): Work close to proton drip line makes continuum

important, antisym, etc…Combination of methods is importantQ: what are most imp reactions ?!

32

Collaborators

R.E. Tribble, A. Banu, CA Gagliardi, AM Mukhamedzhanov, M McCleskey, E Simmons, B. Roeder –Texas A&M UniversityF. Carstoiu – IFIN-HH BucharestE491 exp: TAMU & N. Orr et al. (LPC Caen), P. Chomaz et al.

(GANIL Caen), W. Catford et al. (Univ of Surrey), M. Chartier et al. (Univ of Liverpool), R. Lemmon, M. Labiche (Daresbury), M. Freer et al.(Univ of Birmingham), F. Negoita (IFIN Bucharest)

Q: Spectroscopic factors vs ANC?!

33

According to some:

34

Reduction factors! Are they safe(ly determined)?!Spectroscopic factors are not observables, right?!

While others say…

35

Sauvan ea, PRC 69, 2004GANIL data

36

MARS

Primary beam 24Mg @ 48A MeV – K500 CyclPrimary target LN2 cooled H2 gas p=1.6 atm Secondary beam 23Al @ 40.2A MeV

24Mg 48A MeV

Purity: 90%, or >99% after en degraderIntensity: ~ 4000 ppsFirst time - very pure & intense 23Al

23Al 40A MeV

In-flight RB production

(p,2n) reaction