Nuclear astrophysics data needs for

charged-particle reactions

C. Iliadis (University of North Carolina)

In which sites are charged-particle reactions important?

For any object in the Universe that produces nuclear energy

For which processes would we like to know the reaction rates?

Big bangHydrogen burningHelium burningAdvanced burning (carbon/neon/oxygen/silicon)s-process (neutron sources)p-process . . .

A list of “experimental” charged-particle reaction rate compilations:

Brussels (Angulo, Descouvemont)*Chapel Hill (Iliadis) Karlsruhe (KADoNIS) Livermore (Hoffman, Rauscher, Heger, Woosley) Los Alamos (Hale, Page)*MSU (Schatz) NACRE (Angulo et al.) NETGEN (Arnould, Goriely, Jorissen)*Notre Dame (Wiescher)*Oak Ridge (Smith, Hix, Bardayan et al.) . . .

*: REACLIB format

Published “experimental” charged particle reaction rate evaluations:

CONCLUSION: • About 66 reactions from CF88 have not been evaluated since!• Many of these are still used in our rate libraries (e.g., REACLIB)

Caughlan and Fowler, ADNDT 40, 283 (1988) 159 A=1-30

Angulo et al., NP A656, 3 (1999) 86 A=1-28

Iliadis et al., ApJS 134, 151 (2001) 55 A=20-40

Descouvemont et al., ADNDT 88, 203 (2004) 10 A=1-7

Reference: # of reactions: Mass range:

How an incorrect reaction rate was derived from “correct” input information:

10-100

10-90

10-80

10-70

10-60

10-50

10-40

10-30

10-20

10-10

100

0.5 0.6 0.70.80.91 2 3

( )Temperature GK

12 (C12 , )C n

23Mg

( )REACLIB fit

. (1977)Dayras et al

What is needed in terms of experimental input information?

NA σv =8

πm01

⎛

⎝⎜⎞

⎠⎟

1/2NA

(kT )3/2Eσ(E)e−E /kTdE

0

∞

∫Reaction rate:

Measured Er and

Unobserved resonances

Nonresonant σ (R-matrix)

Insufficient resonanceinformation

Energy

S-fa

ctor

1

2

4

3

Measured Er and

Unobserved resonances

Nonresonant σ (R-matrix)

Insufficient resonanceinformation

Energy

S-fa

ctor

1

2

4

3

Region 1: Absolute resonance strengths and cross sections

QuickTime™ and aTIFF (LZW) decompressor

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Paine et al., PR C17, 1550 (1978)

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Iliadis et al., A=20-40 evaluation

Recommended absolute resonance strengths as a backbone for reaction rate evaluations:

These recommended values are independent of target or beam properties!

Measured Er and

Unobserved resonances

Nonresonant σ (R-matrix)

Insufficient resonanceinformation

Energy

S-fa

ctor

1

2

4

3

Consider the simplest case: only one particle channel and the -ray channel are open

≡ΓaΓ

Γa + Γ

Γa=Γ

low energy⏐ →⏐ ⏐ ⏐ Γa = f(known)⋅f(unknown) : C2S

The "spectroscopic factor" C2S can be measured indirectly by transfer reactions (stripping or direct capture)

Region 2: “Indirect” experimental information is crucial forlow-energy resonances

Er

C

A+aX+x

a

y

25Mg + p→ + 26Al

25Mg+ 3He→ d+ 26Al25Mg+ (d+ p)→ d+ 26Al

Ey

Inte

nsit

y of

yC2S large

C2S small

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Reliability of indirect measurements:(see also talks tomorrow by Rauscher/Descouvemont)

• Orsay/spectroscopic factors (Vernotte et al.)• Texas A&M/ANC’s (Tribble, Mukhamedzhanov et al.) . . .

Measured Er and

Unobserved resonances

Nonresonant σ (R-matrix)

Insufficient resonanceinformation

Energy

S-fa

ctor

1

2

4

3

Region 3: Extrapolation of nonresonant cross sections

(see talk tomorrow by Descouvemont)

Examples:

7Be(p,)8B12C(,)16O14N(p,)15O . . .

S-f

acto

r

Energy

Gamow peak

R-matrix model

Measured Er and

Unobserved resonances

Nonresonant σ (R-matrix)

Insufficient resonanceinformation

Energy

S-fa

ctor

1

2

4

3

Region 4: Matching of experimental and Hauser-Feshbach rates

In recent evaluations (Angulo 1999, Iliadis 2001), experimental and theoreticalrates are matched at Tmax which is found from the condition: E0(Tmax)+n(Tmax) =Emax

Energy

S-f

acto

r

Experimental cutoff at high energy Emax

E0

Gamow peak

Fowler & Hoyle, ApJS 9, 201 (1964)

Blue: Gamow peakRed: effective window

0

1

2

3

0.5 1 1.5 2 2.5 3 3.5 4

Temperature (GK)

35Cl(p,)36Ar

0.0

0.5

1.0

1.5

2.0

20 22 24 26 28 30 32 34 36

Mass number A

T=2.5 GK

0.0 100

5.0 104

1.0 105

1.5 105

2.0 105

0 2 4 6 8 10 12

NA

<σ>v

( )Temperature GK

30 ( ,Si p)31P

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Reaction rate errors: NACRE as a milestone

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Iliadis et al., ApJS 134, 151 (2001)

See also:Thompson and Iliadis, NPA 647, 259 (1999)[Error analysis for resonant thermonuclearReaction rates]

Download from:www.tunl.duke.edu/~astro/Software/Software.html

Mathematical model for error analysisif values and uncertainties for Er, and C2S are know

A new reaction rate evaluation effort:

Charged-particle rates in the A=40-60 region

Parpottas (U. of Cyprus)Iliadis (UNC)

SILICON BURNING

(T =3.6 GK , ρ =3⋅107 g/cm3)

φij =ri→ j −rj→ i

max(ri→ j ,rj→ i )

φij ≤0.01 (approximate equilibrium)

0.1 <φij <1 (no equilibrium)

The future:

• Use recommended standard resonance strengths and cross sections• Refine indirect methods (C2S, ANC’s)• Apply a sound mathematical model to derive rate errors• Use primary data to calculate reaction rates

• A unified reaction rate evaluation effort would be important for our field• A modular reaction rate library generator like NETGEN is useful