Abstract Introduction: We present an extensive theoretical investigation of the electron impact excitation of doubly-ionized titanium (Ti III) to meet the needs of spectral analysis and plasma modeling. OBJECTIVES: The main objective of this work is to extend the currently scarce database of both structure and collision data for Ti III. METHODS: The calculation was performed in the close-coupling approximation using theB-splineR-matrix method. The multi-configuration Hartree–Fock method in combination withB-spline configuration interaction expansions and the non-orthogonal orbitals technique is employed for accurate descriptions of the target wave functions and adequate accounts of the various interactions between the target states. Relativistic effects are treated at the semi-relativistic Breit-Pauli approximation level. RESULTS: The present close-coupling expansion includes 138 fine-structure levels of Ti III belonging to the , , , ( ), ( ), , and configurations. Comprehensive sets of radiative and electron collisional data are reported for all of the possible transitions between the 138 fine-structure levels. Thermally averaged collision strengths are determined using a Maxwellian distribution for a wide range of temperatures from K to K. The accuracy of the calculated radiative parameters is validated by comparing with available values from the NIST database and previous literature. CONCLUSION: Given the lack of sufficient currently available experimental and theoretical data, the electron impact excitation cross sections of the Ti III fine-structure levels presented here are systematic, extensive, and internally consistent, thus making them suitable for many modeling applications.
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Four-dimensional aspects of tight contact 3-manifolds
We conjecture a four-dimensional characterization of tightness: A contact structure on a 3-manifold Y is tight if and only if a slice-Bennequin inequality holds for smoothly embedded surfaces in . An affirmative answer to our conjecture would imply an analogue of the Milnor conjecture for torus knots: If a fibered link L induces a tight contact structure on Y, then its fiber surface maximizes the Euler characteristic among all surfaces in with boundary L. We provide evidence for both conjectures by proving them for contact structures with nonvanishing Ozsváth–Szabó contact invariant.
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- Award ID(s):
- 1709016
- PAR ID:
- 10231071
- Publisher / Repository:
- Proceedings of the National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 118
- Issue:
- 22
- ISSN:
- 0027-8424
- Page Range / eLocation ID:
- Article No. e2025436118
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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