1. University of Johannesburg
Comparison of coupled-channel studies of nucleon scattering from the oxygen isotopes with the shell model
S. Karataglidis,
University of Johannesburg

2. MCAS Collaboration K. Amos, D. van der Knijff, University of Melbourne
L. Canton, INFN/Padova
J. P. Svenne, University of Manitoba
P. R. Fraser, Curtin University

3. Introduction
The structures of 17O and 17F are critical in the synthesis of elements beyond carbon,
within the stellar environment. The CNO cycle:
CN:
NO:
OF:

4. Nuclear Structure 17O and 17F are mirror nuclei.
Both are formed by coupling a single nucleon to an 16O core.
First three positive parity states give the single particle energies in the sd-shell.
19O and 19F formed by coupling a single nucleon to an 18O core.
However…
16O is not a simple closed core system: minimum of 4ħω admixtures required in the shell model. (Brown and Green, 1966).
Coupling of the single nucleon to the 16O core then leads to more complicated structures.

5. Low-energy scattering: MCAS
We seek to obtain S matrices and evaluate:
Total elastic scattering cross sections:
Total reaction cross sections:
The MCAS approach is built upon:
Finite-rank separable representations of realistic interactions;
Scattering matrices for separable Schrödinger interactions;
Sturmian functions (Weinberg states) to define form factors.

6. Multi-channel T matrices
Solution of coupled Lippmann-Schwinger equations:
Expand the potential matrix:
Optimal functions, , involve Sturmians :

7. Multi-channel S matrices
Separable expansion of multi-channel Vcc’ ⇒ multi-channel S matrix (c,c’ are open
channels, specified by Jπ):
Matrix elements (Sturmian basis) , with:

8. Shell model, mass-17 Positive parity: (0+2)ħω;
Negative parity: (1+3)ħω.
WBP interaction of Warburton
and Brown.

9. MCAS, mass-17 Vibrational model: 0+ (gs), 0+ (6.05 MeV),
3- (6.13 MeV), 2+ (6.92 MeV)
1- (7.12 MeV).
(Preliminary results.)

10. Low-energy neutron
scattering cross section from
16O. (Preliminary results.)

11. Spectrum, 19O, (19Na)
Spectrum of 19O, below
n+18O threshold.

12. Spectrum of 19O showing
scattering states.

13. Conclusions
Calculated the low-energy spectra of 17O and 17F from both the shell model and MCAS, assuming a vibrational model for 16O.
Preliminary results indicate spectra of mass 17 nuclei well-reproduced.
Preliminary results for the low-energy neutron scattering from 16O, leading to 17O, reproduce the resonance structure.
Spectrum of 19O, as n+18O (vibrational model) requires further investigation with MCAS. There are two indicators: spurious 3/2+, and the 9/2+ state coming above threshold.