Continuum shell model Continuum shell model calculations for nucleon capture calculations for nucleon capture

at astrophysical energiesat astrophysical energies

Janina GrineviJanina Grineviciuteciute

Western Michigan UniversityWestern Michigan University

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H burningH burning pp chain pp chain

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77Be(p,Be(p,))88B B

Production rate of Production rate of 88Be solar neutrinos:Be solar neutrinos:• accuracy of stellar modelsaccuracy of stellar models• neutrino mixing and nature of weak neutrino mixing and nature of weak

interactioninteraction

desired reaction rate uncertainty less desired reaction rate uncertainty less than 5%than 5%

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Dependance on temperature of energy production ratesDependance on temperature of energy production rates

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CNO cycleCNO cycle

figure taken from H. Schatz (2004)figure taken from H. Schatz (2004)

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4 CNO cycles4 CNO cycles

figure taken from H. Schatz (2004)figure taken from H. Schatz (2004)

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1414N(p,N(p,))1515O O

Slowest reaction in CNO cycleSlowest reaction in CNO cycle• controls duration of hydrogen burningcontrols duration of hydrogen burning• determines main sequence turnoff – determines main sequence turnoff –

globular cluster agesglobular cluster ages• determines CNO neutrino flux in the Sundetermines CNO neutrino flux in the Sun

Initial abundance of C, N,O is mostly Initial abundance of C, N,O is mostly converted into converted into 1414NN

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Turn off luminosity – age of globular clustersTurn off luminosity – age of globular clusters

CNO cycle

pp chain

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Proton capture reactionsProton capture reactions

Crossections are extremely low Crossections are extremely low

measure as low in energy as measure as low in energy as possible, thenpossible, then extrapolate to Gamow window

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12C(p,)13N

Cro

ss s

ectio

n, b

arns

12 c(p,g)

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12C(p,g) S-factor12C(p,g) S-factor

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RCCSM advantages R.J.PhillpottRCCSM advantages R.J.Phillpott

• Provides coupled-channels solutions for Provides coupled-channels solutions for

bound and unbound wave functionsbound and unbound wave functions

• Wave functions antisymmetric and contain Wave functions antisymmetric and contain

no spurious componentsno spurious components

• Bound states and continuum states are Bound states and continuum states are

orthogonalorthogonal

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RCCSM coordinatesRCCSM coordinates

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RCCSM inputRCCSM input

• Oscillator size parameter Oscillator size parameter =mw/=mw/

• Desired states of the A-1 core nucleiDesired states of the A-1 core nuclei

• Realistic translationally invariant Realistic translationally invariant

interactioninteraction

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InteractionInteraction

• A fit to Cohen-Kurath interaction and Reid A fit to Cohen-Kurath interaction and Reid

soft core g-matrix elementssoft core g-matrix elements

• Spin orbit forceSpin orbit force

• Tensor forceTensor force

• Skyrme interactionSkyrme interaction

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Channel wave functions within channel radius aChannel wave functions within channel radius acc

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CalculationsCalculations

• Oscillator size parameter, interactionOscillator size parameter, interaction

• R matrix radiiR matrix radii

• Calculate matrix elements of interactionCalculate matrix elements of interaction

• CM transformationCM transformation

• R matrix techniques to get f and d coefficientsR matrix techniques to get f and d coefficients

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7Be(p,g)7Be(p,g)

Dean Halderson (2006)Dean Halderson (2006)

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15O levels15O levels

www.tunl.duke.edu/nucldatawww.tunl.duke.edu/nucldata

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1414N(p, N(p, ) level scheme) level scheme

Gamow peak at 26.5 keVfor T6=15

figure taken from A. Formicola et al. (2004)figure taken from A. Formicola et al. (2004)

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The The 1515O positive parity spectrumO positive parity spectrum

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S factor for the transition to the 3/2S factor for the transition to the 3/2++ (6.79MeV) state in (6.79MeV) state in 1515OO

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1/21/2++22 1/2 1/2-- transition transition

• Initial stateInitial state

• g.s.g.s.

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Total S factorTotal S factor

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Angular distribution and analyzing powerAngular distribution and analyzing power

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ConclusionsConclusions

• Transition to 3/2+ agrees well with Transition to 3/2+ agrees well with existing dataexisting data

• No significant contributions from No significant contributions from subthreshold resonancesubthreshold resonance

• Low energy S factor is nearly flatLow energy S factor is nearly flat• S(30) = 1.625 keVbS(30) = 1.625 keVb