You will need to provide a voltage of at least the threshold voltage PLUS the minimum voltage of the LM334Z. If the LM334Z circuit by itself doesn’t work, that will be the first problem to figure out. Make sure you completely read through the datasheet www.ti.com/lit/ds/symlink/lm334.pdf?ts=1689139734…, there are example circuits in it for reference. For the resistor method, keep in mind that the current isn’t constant; the voltage is. Your current is dictated by your resistor and the voltage across it, which is the supply voltage minus the threshold voltage. If your threshold voltage changes as the dose increases (which is the typical behaviour), the voltage across the resistor will change, therefore your current will change, which will generate error in your reading. The only way to minimize this error is to apply a very high voltage (100’s to 1000’s of volts) to the resistor, such that a change in the threshold would become a rounding error.