How can a Storyboard triggered on a ControlTemplate be targeted to a generated child of the ControlTemplate?

Setting the Storyboard.TargetName doesn't work here. It throws 'targetButton' name cannot be found in the name scope of 'System.Windows.Controls.ControlTemplate'.

Is there another way to accomplish this?

<ControlTemplate x:Key="aTemplate"
                 TargetType="someType">
    <ControlTemplate.Triggers>
        <EventTrigger RoutedEvent="Mouse.MouseEnter">
            <EventTrigger.Actions>
                <BeginStoryboard>
                    <Storyboard>
                        <DoubleAnimation Storyboard.TargetName="targetButton ???"
                                         Storyboard.TargetProperty="Opacity"
                                         From="0" To="1" Duration="0:0:0.5" />
                    </Storyboard>
                </BeginStoryboard>
            </EventTrigger.Actions>
        </EventTrigger>
    </ControlTemplate.Triggers>
    <Grid>
        <Grid.RowDefinitions>
            <RowDefinition />
            <RowDefinition />
        </Grid.RowDefinitions>
        <StackPanel>
            <Label Content="..." />
          开发者_开发知识库  <Button Opacity="0"
                    x:Name="targetButton" />
        </StackPanel>
        <ContentPresenter Grid.Row="1" />
    </Grid>
</ControlTemplate>