40
I. J. Thompson
0.995
1.000
1.005
SAMMY
FRESCO
CONRAD
AMUR
0.995
1
1.005
EDA
0.995
1
1.005
0.995
1
1.005
0.995
1
1.005
0.995
1
1.005
6
8
1 0
1 2
1 4
0.995
1
1.005
6
8
1 0
1 2
1 4
0.995
1
1.005
θ lab = 23.192°
θ lab = 26.738°
θ lab = 45.530°
θ lab = 29.418°
θ lab = 30.836°
θ lab = 36.999°
θ lab = 39.951°
θ lab = 42.620°
Ratio to AZURE2 cross section
Laboratory Energy (MeV)
Tombrello and Parker (1963)
3 He(α,α)
3 He
Fig. 2 Comparison of calculations to AZURE2 results for the 3 He(α, α) 3 He reaction using the
energies and angles of the [15] data
5 An “Optical” R-matrix Model
At higher incident energies, there are more and more inelastic or transfer two-body
channels. Numbers of partial waves increase, but this is still manageable using
standard R-matrix theory. But when breakup channels begin to open, these are more
difficult to model as they need three-body dynamics. Sometimes these can be well
approximated by cascaded two-body channels [16], or by using hyper-spherical
harmonics to model the three-body kinematics in full detail. In the meantime, we
could perhaps settle for using damping widths Γ α to describe loss of flux to outside
the two-body model space in generalization of the Reich–Moore approximation.
Such damping widths Γ α describe loss of flux to outside the model space like an
optical model, generalizing Reich–Moore for missing particle channels, as in
R αα (E) =
P
p=1
γ pα γ pα
e p − E + iΓ α /2
.
(3)
This could be allowed, as mentioned earlier, if there are specific physical channels
missing from the model (never for bound states). Then the missing flux (from the
I. J. Thompson
0.995
1.000
1.005
SAMMY
FRESCO
CONRAD
AMUR
0.995
1
1.005
EDA
0.995
1
1.005
0.995
1
1.005
0.995
1
1.005
0.995
1
1.005
6
8
1 0
1 2
1 4
0.995
1
1.005
6
8
1 0
1 2
1 4
0.995
1
1.005
θ lab = 23.192°
θ lab = 26.738°
θ lab = 45.530°
θ lab = 29.418°
θ lab = 30.836°
θ lab = 36.999°
θ lab = 39.951°
θ lab = 42.620°
Ratio to AZURE2 cross section
Laboratory Energy (MeV)
Tombrello and Parker (1963)
3 He(α,α)
3 He
Fig. 2 Comparison of calculations to AZURE2 results for the 3 He(α, α) 3 He reaction using the
energies and angles of the [15] data
5 An “Optical” R-matrix Model
At higher incident energies, there are more and more inelastic or transfer two-body
channels. Numbers of partial waves increase, but this is still manageable using
standard R-matrix theory. But when breakup channels begin to open, these are more
difficult to model as they need three-body dynamics. Sometimes these can be well
approximated by cascaded two-body channels [16], or by using hyper-spherical
harmonics to model the three-body kinematics in full detail. In the meantime, we
could perhaps settle for using damping widths Γ α to describe loss of flux to outside
the two-body model space in generalization of the Reich–Moore approximation.
Such damping widths Γ α describe loss of flux to outside the model space like an
optical model, generalizing Reich–Moore for missing particle channels, as in
R αα (E) =
P
p=1
γ pα γ pα
e p − E + iΓ α /2
.
(3)
This could be allowed, as mentioned earlier, if there are specific physical channels
missing from the model (never for bound states). Then the missing flux (from the