For an integral domain R  with quotient field Q  the group Ext R  1 (Q,R)  may be regarded as a Q  -vector space and hence it is isomorphic to the direct power Q (d)   for some finite or infinite cardinal number d  . It is shown that in the class of all Noetherian domains of Krull dimension 1 that are analytically unramified in at least one maximal ideal the above number d  is either arbitrarily infinite or of the form p t −1  , p  a prime. Further, a class of principal ideal domains is obtained, for which Ext R  1 (A,R)≅Q/R  for a suitable torsion-free R  -module A  .