Shadow with bright fade effect (Shader Problem!)

[MatheusMarkies]

Good Morning!
I need help creating an effect (similar to scattering) in the shadows.
Like this:

There is an outline in the shade with the color of the light a little stronger.

I tried to create a paracid effect by adding the color of the saturated light to the shadow fade area.
But it was asism:

float3 IncomingLight (Surface surface, Light light) {
    float3 color = float3(1,1,1);
    if (light.saturationRim > 0) {
        if (light.attenuation < 0.8) {
            if (light.attenuation > 0) {

        float3 hsv = RGBtoHSV(light.color);//HSV
        hsv.x = gmod(hsv.x + -0.02, 1.0);//Add HUE
        hsv.yz *= float2(light.saturationRim, 1.4);//Add Saturation
        float3 LightColor = saturate(HSVtoRGB(hsv));//RGB

        color = lerp(float3(0, 0, 0), LightColor, light.attenuation) * light.attenuation;
        }
    }
    }
    return saturate(dot(surface.normal, light.direction) * light.attenuation) * light.color + color;
}

I tried again by multiplying the color:

float3 IncomingLight (Surface surface, Light light) {
    float3 color = float3(1,1,1);
    if (light.saturationRim > 0) {
        if (light.attenuation < 0.8) {
            if (light.attenuation > 0) {

        float3 hsv = RGBtoHSV(light.color);//HSV
        hsv.x = gmod(hsv.x + -0.02, 1.0);//Add HUE
        hsv.yz *= float2(light.saturationRim, 1.4);//Add Saturation
        float3 LightColor = saturate(HSVtoRGB(hsv));//RGB

        color = lerp(float3(0, 0, 0), LightColor, light.attenuation) * light.attenuation;
        }
    }
    }
    return saturate(dot(surface.normal, light.direction) * light.attenuation) * light.color * color;
}

As you can see the ring is very strong and its edge should have a fade.
How can I create this effect in the right way?

[MatheusMarkies]

I managed to fix the effect and get a result closer to the expected.
SRP Shadows:

float3 IncomingLight(Surface surface, Light light) {
    float3 color = float3(1, 1, 1);
    if (light.saturationRim > 0) {

        float3 hsv = RGBtoHSV(light.color);//HSV
        hsv.x = gmod(hsv.x + -0.01, 1);//Add HUE
        hsv.yz *= float2(light.saturationRim, 1.4);//Add Saturation
        float3 LightColor = saturate(HSVtoRGB(hsv));//RGB
        LightColor = pow(LightColor, 0.3);

        color = lerp(float3(1, 1, 1), LightColor * 2, (1 - light.attenuation) * 0.7);
    }
    else {
        color = light.color;
    }

    return saturate(dot(surface.normal, light.direction) * light.attenuation) * (light.color + (color));
}