The short answer is that you can put it on a breadboard, but it will require attention be paid to the first op-amp circuit. The first op-amp is used as a charg

The short answer is that you can put it on a breadboard, but it will require attention be paid to the first op-amp circuit. The first op-amp is used as a charge amplifier. A high energy charged particle will deposit a charge Q on un-grounded node of the reverse biased diode. The voltage on the output of the amplifier is V_out = -Q/C_feedback + V_bias, where v_bias is made with the voltage divider on the non-inverting input. The resistor R3 is only used to adjust the frequency response (and I assume stability) of the amplifier. It will low pass the signal at ~800 Hz. The problem and the reason they want you to use small low capacitance components is that in order to get a large charge to voltage conversion factor, C_feedback is small (5 pf). If you build the circuit on a breadboard and place the op-amp output and input on consecutive lanes then parasitic capacitance can easily add another ~10 pF to that and drop your amplification. To get around this, you'd have to lift up that leg of the capacitor and solder your connections to it instead. This will avoid stray capacitance from lowering your gain.