A note accompanying the reference transistor: the complete specification of the field effect γ ray valve introduced there, as a device, as an algebra, and as an instrument that has been sitting on Mössbauer benches for sixty years without ever being asked to compute.
A valve is four parts on one sight line:
- Source: ⁵⁷Co diffused into rhodium foil, 1 to 25 mCi (a standard commercial Mössbauer source). Emits the 14.4 keV line at natural width with recoil free fraction f_s ≈ 0.75 at room temperature.
- Channel medium: the absorber foil, 95 percent enriched ⁵⁷Fe, 1 to 2 µm, epoxy free mounted on 25 µm beryllium. Effective resonant thickness t_a = f_a n σ_0 d of order 5 to 15 for this geometry (with the strength split across the six magnetic hyperfine components in α iron): deep dips are routine.
- The GATE, in either of two forms:
- kinematic: a piezoelectric velocity transducer carrying source or absorber; one natural linewidth per 0.097 mm/s, full authority within ±10 mm/s, bandwidth from DC to tens of kHz (the ordinary Mössbauer drive);
- magnetic: a coil at the foil; roughly 0.7 linewidths per tesla on ⁵⁷Fe (the trim ring's ¹⁸¹Ta channels reach 42 per tesla and switch with millitesla; see the build note).
- DRAIN: whatever the sight line feeds: a coincidence cavity, another valve, or a boundary counter.
Measured behavior to expect (standard Mössbauer practice, quoted as ranges because they are geometry dependent): resonant transmission dips of 30 to 70 percent of the recoil free component; insertion loss from electronic absorption in the foil of 5 to 10 percent (mass attenuation near 63 cm² per gram at 14.4 keV, across 1 to 2 µm of iron); OFF to ON contrast on the resonant component of 3:1 to 10:1 per stage, compounding across stages in series.
Switching time: the channel cannot respond faster than the excited state lifetime (141 ns for ⁵⁷Fe), and in practice the gate is limited by the drive: kHz to tens of kHz kinematic, up to MHz for small magnetic swings. The valve is a microsecond class router, not a nanosecond one, until faster lines (⁶⁷Zn, ⁷³Ge class) or switched hyperfine media are engineered.
Let a valve's state be OPEN (detuned, transmitting) or CLOSED (on resonance, absorbing). For the resonant component of the stream:
- series composition is AND of openness: a stream survives a chain of valves only if every one is open; transmission is the product of stage transmissions, exactly the thinning algebra of the gate set;
- parallel composition is OR: split paths recombined pass flux if any path is open;
- NOT is built in: a closed valve is a complement on the resonant component (and its re emission is isotropic, so a closed valve is also a tap: the absorbed traffic reappears as 4π fluorescence, usable as a monitor port);
- velocity multiplexing: a single physical sight line carries several logical channels at once, one per Doppler offset; a valve tuned to offset v_i gates channel i and ignores the others. This is frequency division multiplexing inside one γ line, orthogonal to the energy division multiplexing between lines (gates/edm_channels.md); a Mössbauer drive is a channel selector the way a superheterodyne dial is.
What the algebra is for, honestly: valves route, modulate, select, and complement. They do not amplify (β = 1 and lossy), so valve networks obey the same law as the rest of the routine gate set: any feed forward function (Bernstein, theory Section 6), no unbounded recurrence. A valve network is the machine's switchboard; the gain socket is still the keystone's.
Driven with a waveform instead of a setpoint, the valve writes time structure onto the resonant component: sideband generation, pulse shaping, and phase control of single γ quanta by exactly this mechanism are demonstrated physics (the coherent γ optics literature: waveform control of recoilless photons through vibrating resonant absorbers). For the machine this is the fast input port made rigorous: an external problem enters as a drive waveform, and the valve imprints it onto nuclear traffic with no penetration of the vessel (magnetic flux coupling, per the build note).
- Temperature. The second order Doppler shift moves the ⁵⁷Fe line by 7×10⁻⁴ mm/s per kelvin near room temperature: about one natural linewidth per 130 K. Ten kelvin of gradient across a valve bank therefore costs under a tenth of a linewidth, which ordinary enclosure design provides; metrology grade setpoints trim the residual with the coils that exist anyway. Stated as a specification, not discovered as a mystery drift.
- Background. The valve gates the recoil free resonant component only; Compton scattered and non resonant photons pass regardless, a DC pedestal under the logic. Discrimination is by energy window (the 14.4 keV photopeak) and, where needed, by coincidence with the 122 keV feeding photon of the ⁵⁷Co cascade, which tags true source quanta. The pedestal costs contrast, is fully characterized by a one hour bench scan, and enters the error budget as a known constant, never as noise.
Every element above is decades old. The Mössbauer drive was built to measure hyperfine spectra, and the entire apparatus has spent its life as an instrument pointed at samples. Pointed instead at another valve, it is a logic element; arranged in series and parallel under the stream algebra, it is a switchboard; driven by waveforms, it is a modem between the electronic world and the nuclear one. The reference transistor's GATE terminal is not a proposal; it ships from catalogs with a calibration sheet. What has never shipped is the intent.