Tetrahedral intrinsic structure of Oxygen-16

revisitedChris Halcrow

University of Leeds

INPC 2019 — Glasgow

Joint work with C. King and N. S. Manton

This is the tetrahedral 16-Skyrmion, it has alpha-particles on each vertex.

Plan: model Oxygen-16 by including vibrational and rotational excitations of tet.

It has three vibrational modes:

This is the tetrahedral 16-Skyrmion, it has alpha-particles on each vertex.

Plan: model Oxygen-16 by including vibrational and rotational excitations of tet.

It has three vibrational modes:

• A vibration — symmetric stretching (1-Dimensional)

This is the tetrahedral 16-Skyrmion, it has alpha-particles on each vertex.

Plan: model Oxygen-16 by including vibrational and rotational excitations of tet.

It has three vibrational modes:

• A vibration — symmetric stretching (1-Dimensional)

• E vibration — two particles move down, two up (2D).

This is the tetrahedral 16-Skyrmion, it has alpha-particles on each vertex.

Plan: model Oxygen-16 by including vibrational and rotational excitations of tet.

It has three vibrational modes:

• A vibration — symmetric stretching (1-Dimensional)

• E vibration — two particles move down, two up (2D).

• F vibration — one vertex moves away, leaving a triangle of particles behind (3D).

Skyrme model suggests that the E-vibration is most important, as its frequency is much lower than A- and F-vibrations. Also, it connects the tetrahedron to the square, dynamically.

timeincreasing

A vibrational wavefunction, concentrated at the tetrahedra.

A vibrational wavefunction, concentrated at square configurations.

A vibrational wavefunction, concentrated at the tetrahedra and the squares.

Physical states are combinations of these vibrational wavefunctions with rotational (or spin) wavefunctions, and harmonic wavefunctions from the A- and F-vibrations.

The allowed combinations depend on the symmetries of the wavefunctions.

The energy for a spin state is

E = Evib + 12~!AnA + 1

2~!FnF + Erot<latexit sha1_base64="btLO58tTPzGThZG30FodLZ8KO10=">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</latexit><latexit sha1_base64="btLO58tTPzGThZG30FodLZ8KO10=">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</latexit><latexit sha1_base64="btLO58tTPzGThZG30FodLZ8KO10=">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</latexit><latexit sha1_base64="btLO58tTPzGThZG30FodLZ8KO10=">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</latexit>

The energy spectrum, up to 20 MeV. Colours represent number of A, E and F excitations

A comparison of our model (coloured symbols) to experiment (black dots).

The model successfully describe many (~70) states.

Explains the gap between lowest spin 2 states; due to the square configuration.

Predict another 4- state near 15 MeV

Predicts many high-spin, unnatural-parity states.

Biggest issue is 0- state.

References

Oxygen-16:

C. J. Halcrow, C. King and N. S. Manton, Phys. Rev. C 95, 031303 (2017) Int. J. Mod. Phys. E 28, No. 3 (2019) 1950026

Carbon-12 in the Skyrme Model:

P. H. C. Lau, N. S. Manton, Phys. Rev. Lett. 113, 232503 (2014)

J. I. Rawlinson, Nucl. Phys. A 975 (2018) 122

[arXiv:1608.05048] [arXiv:1902.09424]

[arXiv:1408.6680]

[arXiv:1712.05658]