amplifier - Shaping negative pulses to positive ones

I have built a scintillation detector. The detector outputs 0,1 ms 50-200 mV negative pulses from a photomultiplier (DC). The pulse shape is shown in the picture below.

To detect the pulses I need to change their properties (still DC however). Their new shape has to be pretty much identical, but more than 500 mV positive voltage (their duration can be 0,1 ms to 0,5 ms, but preferably 0,3 ms to 0,4 ms). The shape is, again, illustrated in the picture above.

Does anyone with more experience than me have a small form-factor schematic that will work? If I need to, I have a 5 V rail that I can power something with.

Thanks!

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Update: The op amp that I chose (TLE2081) has sufficient properties. However, I can't get my schematic to work. See the picture for my schematic.

The output I am getting is my Vcc+, which is odd. I am not getting the pulses that I was looking for. I think I did something wrong, does anybody have any ideas?

Thanks!