46
C. R. Brune
2 Astrophysical Scenarios
The transition from isolated resonances to the continuum will be important when
the level density is modest. This situation is most easily realized in lighter nuclei,
in the range 20 A 50. In nuclear astrophysics, this leads us to consider
proton- and α-induced reactions in the rapid proton capture process (rp-process)
and in type-II supernovae. The rp-process primarily consists of a sequence of
(p, γ ) reactions, (α, p) reactions, and β + decays which occur on the surface of
an accreting neutron star, with a relevant temperature range of 0.5–2.0 GK. In the
type-II (core-collapse) supernova scenario, these reactions may occur during the
oxygen and silicon burning phase before the explosion, or in the α-rich freeze-out
immediately afterword. Here, the relevant temperature range is 1.5–5 GK.
We focus here on the 34 Ar(α, p) 37 K reaction which is thought to be an important
reaction for regulating flow to higher masses in the rp-process [2, 3]. The timereversed reaction has recently been measured at the ATLAS facility at Argonne
National Laboratory [4]. An indirect study of the compound-nuclear levels in
38 Ca has been performed using the 40 Ca(p, t) 38 Ca reaction at iThemba [5]. The
properties of 38 Ca levels have also been studied using the elastic scattering of
protons from 37 K [6]. Finally, measurements of the 34 Ar(α, p) 37 K reaction have
been performed for E c.m = 5.7 and 6.1 MeV with the ReA3 facility at the
National Superconducting Cyclotron Laboratory (K. Schmidt, K. Chipps, private
communication). The reaction rate in the rp process is determined by the cross
section for 1 E c.m. 4 MeV, considering the aforementioned temperature range.
It should be noted that none of the direct measurements to date have been performed
in the astrophysically relevant energy range.
3 Overview of Our Approach
The Breit–Wigner formula for the cross section connecting channels c and c is
given by
σ cc =
π
k 2 ω J
c c
(E − E R ) 2 + 2 /4
,
(1)
where k is the incoming wavenumber, E is the incoming energy, ω J is a statistical
factor, c are the partial widths, E R is the resonance energy, and =
c c is the
total width. The channel label c represents the particle pair type, the total angular
momentum J , the orbital angular momentum, and channel spin. The corresponding
HF (energy-averaged) result is [7]
σ cc =
π
k 2 ω J
T c T c
c T c
,
(2)
C. R. Brune
2 Astrophysical Scenarios
The transition from isolated resonances to the continuum will be important when
the level density is modest. This situation is most easily realized in lighter nuclei,
in the range 20 A 50. In nuclear astrophysics, this leads us to consider
proton- and α-induced reactions in the rapid proton capture process (rp-process)
and in type-II supernovae. The rp-process primarily consists of a sequence of
(p, γ ) reactions, (α, p) reactions, and β + decays which occur on the surface of
an accreting neutron star, with a relevant temperature range of 0.5–2.0 GK. In the
type-II (core-collapse) supernova scenario, these reactions may occur during the
oxygen and silicon burning phase before the explosion, or in the α-rich freeze-out
immediately afterword. Here, the relevant temperature range is 1.5–5 GK.
We focus here on the 34 Ar(α, p) 37 K reaction which is thought to be an important
reaction for regulating flow to higher masses in the rp-process [2, 3]. The timereversed reaction has recently been measured at the ATLAS facility at Argonne
National Laboratory [4]. An indirect study of the compound-nuclear levels in
38 Ca has been performed using the 40 Ca(p, t) 38 Ca reaction at iThemba [5]. The
properties of 38 Ca levels have also been studied using the elastic scattering of
protons from 37 K [6]. Finally, measurements of the 34 Ar(α, p) 37 K reaction have
been performed for E c.m = 5.7 and 6.1 MeV with the ReA3 facility at the
National Superconducting Cyclotron Laboratory (K. Schmidt, K. Chipps, private
communication). The reaction rate in the rp process is determined by the cross
section for 1 E c.m. 4 MeV, considering the aforementioned temperature range.
It should be noted that none of the direct measurements to date have been performed
in the astrophysically relevant energy range.
3 Overview of Our Approach
The Breit–Wigner formula for the cross section connecting channels c and c is
given by
σ cc =
π
k 2 ω J
c c
(E − E R ) 2 + 2 /4
,
(1)
where k is the incoming wavenumber, E is the incoming energy, ω J is a statistical
factor, c are the partial widths, E R is the resonance energy, and =
c c is the
total width. The channel label c represents the particle pair type, the total angular
momentum J , the orbital angular momentum, and channel spin. The corresponding
HF (energy-averaged) result is [7]
σ cc =
π
k 2 ω J
T c T c
c T c
,
(2)