9.4 Calculation of Spectra and Reaction Cross Sections in the Coupled-. . .
469
and 1
+
1 below the neutron emission threshold. Neutron separation energies from
the ground state and excited states are S n = 2.032 MeV and S n = 1.052 MeV,
respectively, in good agreement with the experimental data. The 3
+
1 resonance peak
can be seen in M1 and E2 transitions. As in the 7 Be(p, γ ) 8 B reaction (see Fig. 9.4),
E1 and M1 transitions are almost the only contributors to the total neutron radiative
capture cross section, the E2 transition cross section being three orders of magnitude
smaller. The peak around 200 keV comes from the 3
+
1 resonance. Its width is about
30 keV, so that the cross section varies quickly therein.
Coupled-channel Gamow shell model calculation underestimates the data of
Imhof et al. [91]. The extrapolation of the calculated neutron radiative capture cross
section at low E CM is done using the expansion:
σ (E CM ) =
4.541
√
E CM
− 2.360 + 3.387
E CM ,
(9.175)
which yields: σ (GSM-CC) = 25.41 μb at E CM = 25 keV. A simplified calculation
of the radiative capture cross sections of 7 Be(p, γ ) and 7 Li(n, γ ), i.e. using a small
model space, is effected in Exercise XI.
Exercise XI
One will calculate in this exercise the low-lying spectrum of 8 Li and 8 B and the
cross sections of the radiative capture reactions 7 Be(p, γ ) and 7 Li(n, γ ). While it
is not strictly necessary, nevertheless it is preferable to run codes using a parallel
machine with at least 5–10 cores, as calculations can take a few hours otherwise.
A. To avoid too large model space dimensions, sd partial waves are represented by
four harmonic oscillator states. Briefly state the advantages and disadvantages
of the use of a few harmonic oscillator states to represent sd partial waves.
Explain why the basic features of considered radiative capture cross sections
can still be qualitatively reproduced in this approximate picture.
B. Run the Gamow shell model code to obtain the bound or resonance states of
8 Li and 8 B with 2p-2h truncations in the nonresonant continuum and without
truncation.
Explain why the nucleon emission widths of the first resonance states of
8 Li and 8 B are not correct when using 2p-2h truncations, whereas they are
close to experimental data in the absence of model space truncation.
C. Run the Gamow shell model coupled-channel code to obtain the resonant
spectrum of 8 Li and 8 B.
State why it is close to that calculated in B without model space
truncations.
469
and 1
+
1 below the neutron emission threshold. Neutron separation energies from
the ground state and excited states are S n = 2.032 MeV and S n = 1.052 MeV,
respectively, in good agreement with the experimental data. The 3
+
1 resonance peak
can be seen in M1 and E2 transitions. As in the 7 Be(p, γ ) 8 B reaction (see Fig. 9.4),
E1 and M1 transitions are almost the only contributors to the total neutron radiative
capture cross section, the E2 transition cross section being three orders of magnitude
smaller. The peak around 200 keV comes from the 3
+
1 resonance. Its width is about
30 keV, so that the cross section varies quickly therein.
Coupled-channel Gamow shell model calculation underestimates the data of
Imhof et al. [91]. The extrapolation of the calculated neutron radiative capture cross
section at low E CM is done using the expansion:
σ (E CM ) =
4.541
√
E CM
− 2.360 + 3.387
E CM ,
(9.175)
which yields: σ (GSM-CC) = 25.41 μb at E CM = 25 keV. A simplified calculation
of the radiative capture cross sections of 7 Be(p, γ ) and 7 Li(n, γ ), i.e. using a small
model space, is effected in Exercise XI.
Exercise XI
One will calculate in this exercise the low-lying spectrum of 8 Li and 8 B and the
cross sections of the radiative capture reactions 7 Be(p, γ ) and 7 Li(n, γ ). While it
is not strictly necessary, nevertheless it is preferable to run codes using a parallel
machine with at least 5–10 cores, as calculations can take a few hours otherwise.
A. To avoid too large model space dimensions, sd partial waves are represented by
four harmonic oscillator states. Briefly state the advantages and disadvantages
of the use of a few harmonic oscillator states to represent sd partial waves.
Explain why the basic features of considered radiative capture cross sections
can still be qualitatively reproduced in this approximate picture.
B. Run the Gamow shell model code to obtain the bound or resonance states of
8 Li and 8 B with 2p-2h truncations in the nonresonant continuum and without
truncation.
Explain why the nucleon emission widths of the first resonance states of
8 Li and 8 B are not correct when using 2p-2h truncations, whereas they are
close to experimental data in the absence of model space truncation.
C. Run the Gamow shell model coupled-channel code to obtain the resonant
spectrum of 8 Li and 8 B.
State why it is close to that calculated in B without model space
truncations.