Casimir self-energy of a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>δ</mml:mi><mml:mtext>−</mml:mtext><mml:msup><mml:mrow><mml:mi>δ</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> sphere

We extend previous work on the vacuum energy of a massless scalar field in the presence of singular potentials. We consider a single sphere denoted by the so-called"delta-delta prime"interaction. Contrary to the Dirac delta potential, we find a nontrivial one-parameter family of potentials such that the regularization procedure gives an unambiguous result for the Casimir self-energy. The procedure employed is based on the zeta function regularization and the cancellation of the heat kernel coefficient a_2. The results obtained are in agreement with particular cases, such as the Dirac delta or Robin and Dirichlet boundary conditions.