glsl – The right way to setup gradient lighting in OpenGL shader?

I setup easy single gentle supply lighting round campfire object.
Nonetheless, as might be seen, the transition between lightened space and unlighted one is sharp.

The GLSL fragment shader code:

uniform vec2 screenSize;
uniform vec2 lightSourceSize;
uniform vec2 lightSourceCoords;
uniform float lightIntensityCap;
uniform sampler2D textureSample;

void major(void)
{
    float horizontalDiff = -lightSourceSize.x / 2;
    float verticalDiff = lightSourceSize.y;

    float lightSourceX =
    (lightSourceCoords.x - horizontalDiff) / screenSize.x * 2 - 1;

    float lightSourceY =
    (-lightSourceCoords.y - verticalDiff) / screenSize.y * 2 + 1;

    vec2 lightSourcePos = vec2(lightSourceX, lightSourceY);

    float lightIntensity = 1.0/distance(lightSourcePos, pos.xy);

    if (lightIntensity >= lightIntensityCap) {
        lightIntensity = lightIntensityCap;
    }

    if (lightIntensity <= 1) {
        lightIntensity = 1;
    }

    if (distance(lightSourcePos, pos.xy) > 0.3) {
        lightIntensity = 1;
    }

    vec4 lightCol = vec4(lightIntensity, lightIntensity, lightIntensity, 1.0);
    fColor = texture(textureSample, fragmentUV).rgba * lightCol;

    if (fColor.a <= 0){
        discard;
    }
}

If I’ll take away

if (distance(lightSourcePos, pos.xy) > 0.3) {
    lightIntensity = 1;
}

the lightened space will broaden and the transition will probably be a lot smoother. How do I interpolate gentle depth and obtain clean transition for smaller space?