Changing distance to aim target cause LookAt jump/jitter

I have an archer in a third-person camera view. The camera rotates (aims) towards where the bow is pointing + added distance, which works well. I use Raycast to spot targets and shorten the aim distance to that target. Problem: when I change distance to target; the cameras rotation jumps towards the new target position. Is there a way to make the transition smooth using LookAt on the camera?

Bow code for updating aimTarget:

 void FixedUpdate() {
     float targetDistance = AIM_DISTANCE;
         
     RaycastHit hit;
     if (Physics.Raycast(transform.position, transform.TransformDirection(Vector3.forward), out hit, AIM_DISTANCE))
     {
         targetDistance = Vector3.Distance(hit.transform.position, transform.position);
     }
     aimAtPosition = transform.position+transform.TransformDirection(Vector3.forward) * targetDistance;
 }

 
 public Vector3 getBowTarget()
 {
     return aimAtPosition;
 }

Cameracode for looking at the target (positioning code omitted):

 transform.LookAt(bowScript.getBowTarget());