EFFECTS OF THE FINITE-SIZE OF THE ION (DD-MU)(-LEVELS OF THE MOLECULES (DD-MU)E AND (DD-MU)DEE() ON THE ENERGY)

The energy shift due to the finite size of the pseudonucleus (dd mu)(1 1)(+) in the molecules (dd mu)(11)e and (dd mu)(11)dee, the subscripts indicating the first excited stale with total angular momentum of one unit, is of importance in the theoretical estimation of the rate of d -d fusion catalyzed by negative muons. The energy shift in the molecul e (dd mu)(11)e is calculated using perturbation theory up to second or der. The finite-size shift is found to be 1.46 meV. This is significan tly larger than the value of 0.7 meV for this energy shift calculated by Bakalov [Muon Catalyzed Fusion 3, 321 (1988)] by a method similar t o the present method; recently found excellent agreement of theory wit h experimental results for the formation rate of the molecule (dd mu)( 11)dee was based on Bakalov's value with some modifications. The resul ts of a direct calculation of the finite size energy shifts in (dd mu) (11)dee using first-order perturbation theory are presented. The contr ibution from the quadrupole component of the (dd mu)(11) charge distri bution, which is not taken into account in the conventional scaling pr ocedure based on the finite-size energy shifts of (dd mu)(11)e, is fou nd to be of the order of 1 meV and to depend on the angular-momentum s tates of (dd mu)(11)dee. Sources of uncertainty in the current theoret ical estimates are also discussed.