4.5 Problems
149
2. Open Channels for F + H 2 : How many open rovibrational channels are there
for scattering energies at E = 0.7, 0.9, 1.1, 1.3, 1.5 eV for the F + H 2 system
assuming J = 0?
3. Coupled Channels: Consider the H + H 2 system. You have decided to include
the lowest nine values of the rotational angular momentum j = 0, 1 . . . 8 for each
of lowest four vibrational states ν = 0, 1, 2, 3. How many coupled channels will
be used for J = 0, J = 4, J = 8, J = 12, J = 16, and J = 100. How many of
these coupled channels will be open at E = 0.7, 0.9, 1.1, 1.3, 1.5 eV?
4.5.2 Quantitative Problems
1. ABC or APH3D: Use the APH3D or ABC (http://ccp6.ac.uk/downloads.htm)
programs to calculate the reaction probabilities for H 3 and F + H 2 for J = 0
and J = 1. Use total energies in the range E = 0.3 eV to E = 1.5 eV. Do your
answers agree with published results?
2. TD_APH3D: Use the TD_APH3D program to calculate the reaction probabilities
for H 3 and F + H 2 for J = 0. Use total energies in the range E = 0.3 eV to
E = 1.5 eV. Do your answers agree with published results?
3. Infinite Order Sudden Approximation—IOSSUD: The infinite order sudden
approximation is quite useful for calculating approximate inelastic nonreactive
results. This approximation is valid when the total energy is large compared to
the rotational energy spacing. It is equivalent to holding the orientation angle γ
fixed between the atom and diatom during the collision. That is the molecule
does not significantly rotate during the collision process. Use the JWKB phase
shift program to calculate the phase shifts η l (γ) at 11 scattering angles for the
He + C O 2 molecule assuming it is a rigid rotor. The orbital angular momentum
quantum number should vary from 0 to 100 for each angle. Then calculate the
integrated cross section by averaging over the orientation angles
σ =
1
2
1
−1
σ(γ) d cos(γ),
(4.73)
where
σ(γ) =
4π
k 2
l=100
l=0
(2l + 1) sin
2
δ l (γ)
(4.74)
The total differential cross can also be calculated as
I (θ) =
1
2
1
−1
I (γ) d cos(γ)
(4.75)
149
2. Open Channels for F + H 2 : How many open rovibrational channels are there
for scattering energies at E = 0.7, 0.9, 1.1, 1.3, 1.5 eV for the F + H 2 system
assuming J = 0?
3. Coupled Channels: Consider the H + H 2 system. You have decided to include
the lowest nine values of the rotational angular momentum j = 0, 1 . . . 8 for each
of lowest four vibrational states ν = 0, 1, 2, 3. How many coupled channels will
be used for J = 0, J = 4, J = 8, J = 12, J = 16, and J = 100. How many of
these coupled channels will be open at E = 0.7, 0.9, 1.1, 1.3, 1.5 eV?
4.5.2 Quantitative Problems
1. ABC or APH3D: Use the APH3D or ABC (http://ccp6.ac.uk/downloads.htm)
programs to calculate the reaction probabilities for H 3 and F + H 2 for J = 0
and J = 1. Use total energies in the range E = 0.3 eV to E = 1.5 eV. Do your
answers agree with published results?
2. TD_APH3D: Use the TD_APH3D program to calculate the reaction probabilities
for H 3 and F + H 2 for J = 0. Use total energies in the range E = 0.3 eV to
E = 1.5 eV. Do your answers agree with published results?
3. Infinite Order Sudden Approximation—IOSSUD: The infinite order sudden
approximation is quite useful for calculating approximate inelastic nonreactive
results. This approximation is valid when the total energy is large compared to
the rotational energy spacing. It is equivalent to holding the orientation angle γ
fixed between the atom and diatom during the collision. That is the molecule
does not significantly rotate during the collision process. Use the JWKB phase
shift program to calculate the phase shifts η l (γ) at 11 scattering angles for the
He + C O 2 molecule assuming it is a rigid rotor. The orbital angular momentum
quantum number should vary from 0 to 100 for each angle. Then calculate the
integrated cross section by averaging over the orientation angles
σ =
1
2
1
−1
σ(γ) d cos(γ),
(4.73)
where
σ(γ) =
4π
k 2
l=100
l=0
(2l + 1) sin
2
δ l (γ)
(4.74)
The total differential cross can also be calculated as
I (θ) =
1
2
1
−1
I (γ) d cos(γ)
(4.75)