• Trialpha Hoyle State pixel-art physics T-shirt, black tee, front view

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Trialpha

The Hoyle State Physics

\[{}^{4}\mathrm{He} + {}^{4}\mathrm{He} \rightleftharpoons {}^{8}\mathrm{Be}, \qquad {}^{8}\mathrm{Be} + {}^{4}\mathrm{He} \to {}^{12}\mathrm{C}^{*}\,(7.654\ \mathrm{MeV},\ 0^{+})\]
$29.99 USD
$29.99 USD
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Size guide S–5XL · inches

Trialpha juggles three helium nuclei inside a star. For a moment they become carbon, and that is why you exist.

The Physics

Stars make carbon by fusing three helium-4 nuclei (alpha particles), which only works well because carbon-12 has an excited state at just the right energy. The Hoyle state sits at 7.654 MeV, spin-parity 0⁺, about 0.38 MeV above the 7.275 MeV three-alpha threshold. It almost always falls apart again; only rarely does it settle down into ordinary carbon.

3 ⁴He → ¹²C*(7.654 MeV, 0⁺) → ¹²C + γγ (rarely)

  • ⁴He: helium-4 nucleus, alpha particle
  • ¹²C*: excited carbon-12 nucleus
  • MeV: mega-electronvolt, 1.602 × 10⁻¹³ J
  • 0⁺: spin 0, positive parity
  • γ: gamma-ray photon

In 1953 Fred Hoyle predicted a carbon level near 7.7 MeV; a Caltech team measured 7.68 ± 0.03 MeV, and Cook, Fowler and Lauritsen assigned it 0⁺ in 1957.

On the shirt

Front: Trialpha, the pixel-art character, with the title. Back: the three-alpha reaction, the resonance energy and threshold, the 1953 prediction and measurement and the 1957 assignment. Printed on a unisex tee.

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Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

पैमाने के लिए: साइज़ M की चौड़ाई 20 in (50.80 cm) है, यानी लगभग 3.143 × 1034 प्लांक लंबाई (lP = 1.616255 × 10−35 m)। इंच-टेप ज़्यादा जल्दी काम करेगा।

Measurements in inches, ±1.5 in tolerance.

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Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

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The physics

I juggle three helium nuclei in the core of an old star. Two of them stick for a moment as beryllium-8, which falls apart in about 10⁻¹⁶ seconds. If a third arrives in time, we can become carbon.

That only works well because carbon-12 has an excited state at just the right energy: 7.654 MeV, spin 0, positive parity, sitting 0.38 MeV above the energy of three separate alphas. Almost every time, it falls apart again into three alphas. Only rarely does it drop to ordinary carbon by giving off gamma rays or an electron–positron pair, and those rare drops make the carbon.

In 1953 Fred Hoyle argued that stars need such a level near 7.7 MeV. A Caltech team looked and found it at 7.68 ± 0.03 MeV, and in 1957 Cook, Fowler and the Lauritsens showed it has spin 0 and positive parity. The carbon in you went through a state like mine.

Equations

\[{}^{4}\mathrm{He} + {}^{4}\mathrm{He} \rightleftharpoons {}^{8}\mathrm{Be}, \qquad {}^{8}\mathrm{Be} + {}^{4}\mathrm{He} \to {}^{12}\mathrm{C}^{*}\,(7.654\ \mathrm{MeV},\ 0^{+})\]
\[{}^{12}\mathrm{C}^{*} \to {}^{12}\mathrm{C} + \gamma\gamma \quad (\text{rarely; usually } {}^{12}\mathrm{C}^{*} \to 3\,{}^{4}\mathrm{He})\]
SymbolMeaningUnit
\({}^{4}\mathrm{He}\) helium-4 nucleus (alpha particle) \(\mathrm{1}\)
\({}^{8}\mathrm{Be}\) beryllium-8, unstable, lives about 10⁻¹⁶ s \(\mathrm{1}\)
\({}^{12}\mathrm{C}^{*}\) carbon-12 in its excited Hoyle state \(\mathrm{1}\)
\(\mathrm{MeV}\) mega-electronvolt, 1.602 176 634 × 10⁻¹³ J (exact) \(\mathrm{J}\)
\(0^{+}\) spin 0, positive parity \(\mathrm{1}\)
\(\gamma\) gamma-ray photon \(\mathrm{1}\)

Sources

  1. Hoyle (1954) On Nuclear Reactions Occurring in Very Hot Stars. I., Astrophys. J. Suppl. 1, 121
  2. Dunbar, Pixley, Wenzel & Whaling (1953) The 7.68-MeV State in C12, Phys. Rev. 92, 649
  3. Cook, Fowler, Lauritsen & Lauritsen (1957) B12, C12, and the Red Giants, Phys. Rev. 107, 508

Field notes

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