Being able to measure a few thousand electrons accurately means using the best parts for the job but it starts with picking the right technology. While many applications are agnostic to the underlying design of the op amp they use I am of the opinion that the only way to build a preamp is with an FET input stage; That mean using an FET input op amp or a discrete FET input stage to an op amp. BJT and MOSFET inputs have the advantage of lower voltage noise (BJT) and lower current noise (MOSFET) but the low input impedence of BJTs and the high voltage noise of MOSFETs seems to pretty much rule them out for anything that can be built at home. High performance CMOS IC preamps have been designed in the literature but I see no way to apply this and let me honest here, I don't understand how they do what they do.
The elephant in the room in that the voltage noise and input impedance specs are awesome. It's used by the radiation watch project and Peter's OpenCT2. With femtoamp input bias currents this should be the obvious choice. Nowhere in the datasheet can I find mention of an FET input stage, so I think the high input impedance is down to the internal compensation. This is doubtless a really good solution for pH electrodes and other slow ultra high impedance sources but the window between voltage and current noise for success in this project is narrow. The current noise for this op amp is around 100 times higher than I'd expect for an FET input and maybe tens of thousands of times higher than if it were dominated by the input current. The other thing to note is that while this chip has femtoamp bias currents the best sensors I'm looking at have hundreds of picoamps of leakage current which means replacing a 10 picoamp op amp with a 10 femtoamp op amp is of questionable value. I will certainly need to test one at some point to be sure but I'm ignoring it for now. About 5 USD.
It's the application note for the 4475 that started hobbyists using PIN diodes as replacements for Geiger tubes. On looking through the specs, this seems to be a pretty good candidate for spectroscopy but I've yet to see anyone use it this way. About 1 to 2 USD.
A 4475 without the feedback compensation. Higher bandwidth, higher slew rate, not unity gain stable. Might be ideal for the preamp. Might work well in parts of the shaper, but there really isn't a requirement for an FET input amplifier for the shaper. The 4475 and 4488 are where I'm pinning my hopes at the less expensive end of the design. About 1 USD.
The first version of the freshlab circuit uses this dirt cheap op amp for the preamp and the shaper. Higher noise and higher slew rate than the 4475. That circuit performs badly, but I'd be an idiot not to replicate it as a benchmark. Will the lower noise but lower slew rate 4475 be better or worse, and how the hell does a chip with such low bandwidth have such a high slew rate? Large variation in price but some under 15 cents.
Low noise, not FET input. This was used by the shapers in 2 or 3 documented projects (depending on if you take the 8011 to be equivalent) but circuit diagrams are not available. As a current feedback op amp they are difficult to design for. With a discrete FET this could work for a preamp. I felt this was my best option for the final design a few month s ago but difficulties in using them and questions over effects of current noise in the negative input have left me with doubts. For now these will be staying in the box. Approx 2-3 USD.
Low noise, low input capacitance, insane >1GHz gain bandwidth product, ideal and proven as part of a preamp (the freshlab high performance design used one). The only disappointing thing about this is the price (circa 10USD) which isn't so high as to exclude it but isn't so low as I can grab a bucketful and use it for every function in every prototype. I am hoping for better performance using a discrete low noise FET and a cheaper op amp. Both using the 657 and attempting to beat it are going to have to wait.
There are cavernous pit falls in trying to match spec sheet values to applications. Ultimately it must come to down to real tests, but I've done what I can to select good candidates and to keep the search space for the final design manageable.