The bacteria that convert ammonia ions (NH₄⁺) to nitrate ions (NO₃⁻) are called nitrifying bacteria. This process is called nitrification and occurs in two steps:

1. Nitrification - Ammonia-oxidizing bacteria (AOB), such as *Nitrosomonas*, convert ammonia to nitrite (NO₂⁻).

2. Nitrite oxidation - Nitrite-oxidizing bacteria (NOB), such as *Nitrobacter*, convert nitrite to nitrate.

So, in summary, the nitrifying bacteria responsible for converting ammonia ions to nitrate ions are:

* Ammonia-oxidizing bacteria (AOB): *Nitrosomonas*, *Nitrosospira*, etc.

* Nitrite-oxidizing bacteria (NOB): *Nitrobacter*, *Nitrospira*, etc.