Draw an antialiased ring with fragment shader

Hello guys,

I just started to learn opengl. At the moment I try to draw antialiased ring which has a width of 1 pixel.
The outer edge looks pretty smooth, but inner edge is not.
Could you help to improve this?

https://i.imgur.com/YBlZpJC.png

Thats how my shader looks like:

uniform vec2  u_resolution;
uniform float u_width;
uniform vec4  u_color;

void main() {
    float alpha = u_color[3];
    float delta = 0.0;

    vec2 st = gl_FragCoord.xy/u_resolution;     // normalize resolution 0 to 1
    float pixel = 1.0 / u_resolution.x;         // normalized size of 1 pixel 
    st = st * 2.0 - 1.0;                        // set range from -1 to 1
    float len = dot(st, st);                    // compute squared vec len from center to coordinate
    float r2 =  1.0 - pixel;

    delta = fwidth(len);
    alpha = alpha - smoothstep(1.0 - delta, 1.0 + delta, len);
    if ( alpha == u_color[3])
        alpha = alpha- smoothstep(r2 + delta, r2 - delta, len);

    gl_FragColor = u_color * alpha;
}