In a boron-10-enriched/boron-11-enriched hexagonal boron nitride stack, STEM vibrational EELS revealed out-of-plane optical (ZO) energy transitions wider than the reported atomically sharp interface. Logistic-fitted transition widths were greater near the Brillouin-zone center than near its boundary. The isotope-composition boundary and momentum-dependent phonon-energy transition describe different properties. [Li et al. (2023)](https://www.nature.com/articles/s41467-023-38053-z)

Source: https://www.nature.com/articles/s41467-023-38053-z

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A sharp isotope interface can have broader ZO transitions

In the simple Earth–Sun–star diagram, stellar parallax p uses the one-AU Earth–Sun baseline and is half the ideal two-view angle from opposite orbital viewpoints. These viewpoints change a nearby star’s apparent position relative to more distant stars.

Because stellar parallax angles are tiny, small-angle geometry gives p (radians) ≈ baseline/distance, with both lengths in matching units. Equivalently, d (pc) ≈ 1/p (arcsec). Keep these angular units consistent with the chosen formula.

Apparent displacement decreases with distance, and even nearby shifts are tiny. Analyst deduction: measuring such shifts depends on angular resolution; the supplied evidence gives no universal distance cutoff.

Primary sources:
- https://www.astro.ucla.edu/~wright/distance.htm
- https://www.esa.int/Science_Exploration/Space_Science/Gaia/Parallax

Annual stellar parallax: the one-AU angle convention

Proxima Centauri’s Hubble-based projected path, released in 2013, illustrates two contributions: the star’s drift across the sky and a scalloped annual component caused by Earth’s orbit.

In the 2013 HST spatial-scanning draft’s one-direction fit, position, parallax and proper motion are estimated together. Known viewing geometry fixes the annual component’s shape and phase; observations at multiple epochs distinguish its parallax amplitude from the star’s drift. Three epochs are necessary for that described fit, but insufficient in practice because image registration adds parameters.

Analyst deduction: a displacement between two images should not automatically be treated as pure parallax. Proxima’s path illustrates the distinction, while the HST epoch requirement belongs to the particular fitting method described.

Primary sources:
- https://science.nasa.gov/asset/hubble/proper-motion-path-of-proxima-centauri/
- https://assets.science.nasa.gov/content/dam/science/missions/hubble/releases/2014/04/STScI-01EVSR8SCX5TPX51VK9KXY2QPA.pdf

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