Recent Results for proton capture S-factors from

measurements of Asymptotic Normalization Coefficients

R. Tribble

Texas A&M University

OMEG03

November, 2003

Nuclear Astrophysics Issues

• CNO cycle

- energy producing cycle following p-p chain

- important in wide range of stellar environments,

including our Sun

CNO CyclesCNO Cycles

13C

13N

12C

14N

15O

15N

17O

17F

16O

18F

18O 19F 20Ne

(p, ) (p, α) (p, )

(e+,ν)

(p, )

(p, α)

(p, )

(e+,ν)

( p, )

(e+,ν)

(p, )

(p,α)

(e+,ν)

(p,α)

(p, ) (p, )

I II III

IV

Nuclear Astrophysics Issues

• CNO cycle reaction- 14N(p,)15O (ANCs from (3He,d) reaction)

• HCNO cycle- turns on as temperature and/or density increase

- yields higher energy release, precursor to runaway

NaNa

NeNe

FF

OO

NN

CC

33 44 55 66 77 88 99 1010

CNOHot CNO (T9=0.2)Hot CNO (T9=0.4)Breakout Reactions

http://csep10.phys.utk.edu/guidry/NC-State-html/cno.html

Hot CNO Cycle and Hot CNO Cycle and 1313N(p,N(p,))1414OO

Nuclear Astrophysics Issues

• CNO cycle reaction- 14N(p,)15O (ANCs from (3He,d) reaction)

• HCNO cycle reaction- 13N(p,)14O (ANCs from (13N,14O) reaction)

• Ne-Na cycle reaction- next cycle, 21Ne likely source of neutrons

21 22

21 22

20 23 24

( , )

Na Ne

Ne

Ne p N

Na Al

a

Important in second generation stars

Ne – Na Cycle

Nuclear Astrophysics Issues

• CNO cycle reaction- 14N(p,)15O (ANCs from (3He,d) reaction)

• HCNO cycle reaction- 13N(p,)14O (ANCs from (13N,14O) reaction)

• Ne-Na cycle reaction- 20Ne(p,)21Na (ANCs from (3He,d) reaction)

• S17 – yet a different measurement!

Direct Radiative proton capture

M S E Ee2 2[ ( ) ]

M is: M O r rA B p Bp Bp B B p p i Bp ( , , ) ( ) ( ) ( ) ( )^

( )

Integrate over ξ: M I r O r rBpA

Bp Bp i Bp ( ) ( ) ( )^

( )

Low B.E.: I r CW r

rBpA

Bp

r R

BpA l Bp Bp

Bp

B NA( )

( ),

1

2

2

Find: capture BpAC( ) 2

Radiative Capture of Charged ParticleRadiative Capture of Charged Particle

22/12/1

0

2/12/1

int

)(

)(2

2)(

ff

LB

BAp

r

piR rxHrkIiEE

ieM

OH

r

rkW

CvNiEE

ieM LB

lBAp

r

piRch

2

2)(

2

1,

2/12/1

iGFO

Real, ? Complex, ANC

observed

r>RN

r<RN

2)1,('

2)2,('

)1,(1,0

2)1,(2,0

)1,(2,0

MRcc

ERcc

EDjl

ERjl

EDjl UUUUUE

iiiiii

Capture through subthreshold states

well known problem for many years

E

V

Subthreshold state

resonanceExamples:

12C(,)16O

13C(,n)16O

14N(p,)15O

20Ne(p,)21Na

Subthreshold Capture

M dr r r e SeLl

ikr ikr

rf

o

( )

p radiative capture:

near threshold – S matrix is:

S e ek k i k

k k i ki i p

2 22

02

202

( )

( )

P

W r

rC

k bound sta te ik

k resonance sta te

l

l, / ( )

( )

( )

1 22

0

0

2

02

0

02

2

0 2

0

where:

M I V If BpA

apd

i ( ) ( )

Transfer Reaction

Transition amplitude:

Peripheral transfer:

I CW r

rBpA

r R

BpA l Bp Bp

Bp

Bp NA

,

( )12

2

dd

C C

b bBpl jA

apl jd

Bpl j apl jl j l jDWA A d d

A A d d

A A d d

( ) ( )2 2

2 2

ANC’s measured by our groupstable beams

• 9Be + p 10B [9Be(3He,d)10B;9Be(10B,9Be)10B]• 7Li + n 8Li [12C(7Li,8Li)13C]• 13C + p 14N [13C(3He,d)14N;13C(14N,13C)14N]• 14N + p 15O [14N(3He,d)15O]• 16O + p 17F [16O(3He,d)17F]• 20Ne + p 21Na [20Ne(3He,d)21Na]

beams 10 MeV/u

S factor for 14N(p, )15O

• ANC’s 14N(3He,d)15O

(d) Rez/TAMU (27 MeV)

(e) TUNL (20 MeV)

• NRC to subthreshold state at Ex = 6.79 MeV

• Subthreshold resonance width from Bertone, et al.

• R-Matrix fits to data from Schröder, et al.

d/d

cm

S factor for 14N(p, )15O

• C2(Ex6.79 MeV) fm-1 [non-resonant capture to this state dominates S factor]

• S(0) = 1.40 ± 0.20 keV·b for Ex6.79 MeV

• Stot(0) 1.70 ± 0.22 keV·b

S factor dominated by direct captureto the subthreshold state

Contribution from the tail of the subthreshold resonance: 3/ 2 , 504 keVRE

is negligible

New reaction rate at .007 < T9 < 0.1 lower (up to 2) than NACRE.(Impacts stellar luminosity at transition period to red giants and ages of globular clusters.)

S factor for 14N(p, )15O

width is small

S factor for 20Ne(p, )21Na

• Ne - Na cycle reaction

• Subthreshold state dominates rate

2s1/2 at Ex = 2.425 MeV, =7.1± 0.6 keV

Experimental results andDWBA analysis

20Ne(3He,d)21Na

(0) 4550 800keVbS (0) 3500keVbS

present work

C. Rolfs and W. S. Rodney, NPA 241,460 (1975)

Higher reaction rate for increases the abundance of and, correspondingly, the number of neutrons from

21Na 21Ne21 24( , )Ne n Mg

fitting parameter; new measurement would help!

S C2

For subthreshold resonance (dashed line)

ANC’s measured by our group radioactive (rare isotope) beams

• 7Be + p 8B [10B(7Be,8B)9Be] [14N(7Be,8B)13C]

• 11C + p 12N [14N(11C,12N)13C] • 13N + p 14O [14N(13N,14O)13C] • 17F + p 18Ne [14N(17F,18Ne)13C]

{ORNL (TAMU collaborator)}

beams 10 - 12 MeV/u

1313N(p,N(p,))1414OO

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

0 200 400 600 800 1000

Ec.m. (keV)

S (k

eV*b

)

)),((

)23.0(90.0

)),(,),(

,),(,),((

72.036.3

)),(,),((

9.03.37

1413

208131420814141

143121413

131314314

OndN

S

PbNpOPbnONH

OnHeCOpN

eV

NpNpOtHeN

keVtot

D.Decrock et al., PRC48, 2057(1993)

ANC’s for13N + p 14O

• reaction:

14N(13N,14O)13C

K500: 13C beam 195 MeV

MARS: 13N beam 153 MeV

1414N(N(1313N,N,1414O)O)1313CC

DW

O

N

N

C

N

C

DW

O

N

N

C

N

CO

N

bb

C

bb

C

C

2

11

2

11

2

2

11

2

11

2

11

2

31

2

11

2

2

11

2

31

2

31

2

2

11

exp

14

13

14

13

14

13

14

13

14

13

14

1314

13

C2 = 29.0 ± 4.3 fm-1

DWBA by FRESCO

(ANC for p)CN 1314

S Factor for S Factor for 1313N(p,N(p,))1414OO

• DC/Decrock_dc = 1.4

• Constructive/Decrock_tot =1.4

• Constructive/Destructive =4.0 ( expected constructive interference for lower energy tail, useful to check)

For Gamow peak at T9=0.1,

Transition from CNO to Transition from CNO to HCNOHCNO

• 13N(p,)14O vs decay

• 14N(p,)15O vs decay

Crossover at T9 0.2

For novae find that 14N(p,)15O slowerthan 13N(p,)14O; 14N(p,)15O dictatesenergy production

XH=0.77

ANC’s measured by our group stable beams (mirror symmetry)

• 7Be + p 8B [13C(7Li,8Li)12C]

• 22Mg + p 23Al [13C(22Ne,23Ne)12C]

[underway now]

ANC’s for 7Be + p 8Bfrom mirror reaction 13C(7Li,8Li)12C

• separate p1/2 and p3/2

• Fits ANC’s7Li + n Li:

• C2(p3/2) = .384±.038 fm-1

• C2(p1/2) = .048±.006 fm-1

7Be + p B:

• C2(p3/2) = .405±.041 fm-1

• C2(p1/2) = .050±.006 fm-1

p1/2

p3/2

S17(0) = 17.6±1.7 eVb

Collaborators

• TAMU: A. Azhari, H. Clark, C. Gagliardi, Y.-W. Lui, A. Sattarov, X. Tang, L. Trache, A. Zhanov

• INP (Czech Republic): V. Burjan, J. Cepjek, V. Kroha, J. Piskor, J. Vincour

• IAP (Romania): F. Carstoiu

TAMU Upgrade Plans

• Further develop RIB capability

• Produce accelerated RIB’s at intermediate energies

[white paper at http://cyclotron.tamu.edu/]

TAMU Upgrade Plans

• Stage I - commission K150(88”) cyclotron

- ECR source injection- commission beam lines to existing apparatus

• Stage II- isotope production stations completed- production of rare isotopes

• Stage III- K500 acceleration of rare isotope beams

Proposed Layout

B

A

BA

B

A

++1 -n ECRION GUIDE

CB

A

A

B

B

ION SOURCE

HEAVY ION

AB

ABB A

LIGHT ION

A

ION GUIDE

RADIATION EFFECTSFACILITY

SOLENOID

TAMU UpgradeStage I – Performance K150 beams

Isotope E I Isotope E I

MeV/u pA MeV/u pA

p 50 27 20Ne 26 3

d 30 20 22Ne 24 0.5

3He 40 10 34S 18 0.7

4He 30 10 40Ar 16 1.4

6Li 30 7 40Ca 16 1.5

7Li 22 8 59Co 10 0.9

10B 30 4 78Kr 9 0.6

11B 24 5 86Kr 8 0.6

16O 30 2 129Xe 5.6 0.5

(Simultaneous operation of K150 and K500 into different experimental areas.)

TAMU UpgradeStage III Performance

Ion Guide (heavy ions) into K500

Isotope Max. Energy Intensity

Mev/u pps

9Li 45 3 x 106

12Be 45 5 x 106

38S 36 5 x 105

44S 26 2 x 102

42Ar 39 7 x 105

62Fe 38 4 x 104

8B 70 2 x 106

14O 63 1 x 105

22Mg 57 6 x 104

27P 62 2 x 103

62Ga 47 4 x 102

64Ga 45 2 x 104

neutron-rich isotopes

proton-rich isotopes

TAMU Upgrade Plans

• Cost $4 M

• Proposal submitted - 12/1/03

• Time line 2 years for stage I - II

2 more years for completion and first experiment