A thick target method for astrophysical nuclear reaction rates

Thick-Target Methods for

Astrophysical Reaction Rates

R. J. (Jerry) Peterson

University of colorado

Jerry.Peterson@Colorado.edu

An efficient and direct path from accelerator beams to reaction rates.

*Does not need delicate thin targets *Integrates over all energies to zero

*Measures population of final long-lived states. *Calculable model-dependent uncertainties

Reaction Rates

[AB] = R(T) [A] [B]

Example—

C(p,)

N (g.s.), the first step of

the stellar CNO cycle.

[

N] = R(T) [proton] [

C]

Units—R(T) =NA < v>, in cm3 mole-1 sec-1.

(E)= radiative capture cross section to g.s. v=relative velocity

NA=Avogadro’s number

Uses- CNO cycle, explosive

nucleosynthesis, plasma

diagnostics, symmetry studies.

The thin target

method-– The usual thin target method uses a sample with energy loss much less than the beam energy. At low beam energies, rates of energy loss are high and thin samples are very difficult to make and handle.

– E0

–

Danger! A(p,) and A+1(p,n) reactions give the same final nucleus

Resonancessteps

(example—Isobaric analog resonances) and (p,n) channel gives steeper slopes

We can fit cross sections from yields, here the IAS of the 93_Mo

A trick to avoid using cross sections

themselves-Tests

•

C(p,)

N (10 minute, +)

•

Li(p,)

Be (53 days, )

1.Measure prompt gamma rays, and

2.Count

N/

Be produced, offline.

This was done for

C(p,n)

N, counting both 13N

and neutrons [D.A.Lind et al., Phys. Rev. C11,

2099 (1975)]

Test— R(T) agree for thin/thick target

methods

Inverse kinematics

The thick target method may be used in inverse

kinematics, with a heavy ion beam.

Example p(

C,gamma)

N, with a 6 MeV

C beam

on a proton target, which has the same center

of mass energy as the proton beam on

C at

500 keV. Stop the

C in a target with hydrogen,

and count the

N. If the yields agree, a new

class of experiments is available with

radioactive beams.

With a radioactive

beam--p(13N,gamma)14O , 70.6 sec halflife, + emitter, with the

511 keV annihilation line to measure the yield of 14O.

This is an important step in the CNO cycle which began with 12C(p,)13N.

The Almaty group has mastered the technology of

Zirconium Hydride targets, with good proton content, able to handle the heat and charge of the beam.

When the method can be shown to work, a new set of experiments will become available for nuclear

Conclusion--• Use of a thick, stopping target for low-energy nuclear reaction analysis is simple, reliable, and effective.

Many stellar and other nuclear reaction rates have been measured using a cyclotron in harmonic

modes-• Protons—N. A. Roughton et al., Atomic Data and Nuclear Data Tables 23, 177 (1980)

• Alphas- N. A. Roughton et al., Atomic Data and Nuclear Data Tables 28, 341 (1983).

• This method should be used more widely, and is likely to be useful with radioactive beams.