wp_ajax_{$this->action}

See hook in action

See this hook used in plugins:

Select Pluginadvanced-custom-fields.5.7.6advanced-custom-fields.5.7.7advanced-custom-fields.5.7.8advanced-custom-fields.5.7.9advanced-custom-fields.5.7.10advanced-custom-fields.5.7.12advanced-custom-fields.5.8.0advanced-custom-fields.5.8.1advanced-custom-fields.5.8.2advanced-custom-fields.5.8.3advanced-custom-fields.5.8.5advanced-custom-fields.5.8.7advanced-custom-fields.5.8.8advanced-custom-fields.5.8.9advanced-custom-fields.5.8.11advanced-custom-fields.5.8.12advanced-custom-fields.5.8.13advanced-custom-fields.5.8.14advanced-custom-fields.5.9.0advanced-custom-fields.5.9.1advanced-custom-fields.5.9.3advanced-custom-fields.5.9.4advanced-custom-fields.5.9.5advanced-custom-fields.5.9.6advanced-custom-fields.5.9.7advanced-custom-fields.5.9.8advanced-custom-fields.5.9.9advanced-custom-fields.5.10advanced-custom-fields.5.10.1advanced-custom-fields.5.10.2advanced-custom-fields.5.12advanced-custom-fields.5.12.1advanced-custom-fields.5.12.2advanced-custom-fields.5.12.3advanced-custom-fields.6.0.2advanced-custom-fields.6.0.3advanced-custom-fields.6.0.4advanced-custom-fields.6.0.5advanced-custom-fields.6.0.6advanced-custom-fields.6.0.7advanced-custom-fields.6.1.4advanced-custom-fields.6.1.6advanced-custom-fields.6.1.7advanced-custom-fields.6.2.0advanced-custom-fields.6.2.1advanced-custom-fields.6.2.2advanced-custom-fields.6.2.3advanced-custom-fields.6.2.4advanced-custom-fields.6.2.6.1advanced-custom-fields.6.2.7