Vial with optimized neck for improved side compression performance

A glass container, comprising:

• a glass tube with a first end, a second end, and a longitudinal axis Ltube therebetween, the glass tube has, in a direction from the first end to the second end, a top region, a junction region, a neck region, a shoulder region, and a body region, wherein the top region is at the first end and has an outer diameter (dt), the neck region has an outer diameter (dn) with dn<dt, the body region extends to the second end and has an outer diameter (db) with db>dt, and the glass tube in the body region has a thickness (lb);
• and
• a glass bottom closing the glass tube at the second end,
• wherein, when an outer surface of the body region is placed on a plane horizontal substrate, within any given cross-section of the glass container that is located in a plane centrically located in the glass container and comprising the longitudinal axis Ltube, f(x) defines a vertical distance between the plane horizontal substrate and the outer surface at a given position x and l(x) defines a thickness of the glass tube at a given position x, wherein the thickness of the glass tube l(x) is measured in a direction perpendicular to the longitudinal axis Ltube,
• wherein k(x)=|f″(x)/[1+f′(x)2]3/2| defines an absolute value of a curvature of f(x) at a given position x;
• and
• wherein, in an interval between x=P1 and x=P2 for any concave curvature in the interval, a minimum value for [l(x)/lb]3/k(x) is at least 0.35 mm, wherein P2 defines the x-position at which f(x) is ½×db−¼×dt−¼×dn and P1 is P2−dt/2+dn/2.