Effects of the finite size of the ion (dd{mu}){sup +} on the energy levels of the molecules (dd{mu})e and (dd{mu})dee
- The Institute of Physical and Chemical Research (RIKEN), Wako-shi, Saitama 351-01 (Japan)
- Department of Physics, Kyushu University, Fukuoka 812 (Japan)
The energy shift due to the finite size of the pseudonucleus (dd{mu}){sub 11}{sup +} in the molecules (dd{mu}){sub 11}e and (dd{mu}){sub 11}dee, the subscripts indicating the first excited state 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 molecule (dd{mu}){sub 11}e is calculated using perturbation theory up to second order. The finite-size shift is found to be 1.46 meV. This is significantly larger than the value of 0.7 meV for this energy shift calculated by Bakalov [Muon Catalyzed Fusion {bold 3}, 321 (1988)] by a method similar to the present method; recently found excellent agreement of theory with experimental results for the formation rate of the molecule (dd{mu}){sub 11}dee was based on Bakalov{close_quote}s value with some modifications. The results of a direct calculation of the finite-size energy shifts in (dd{mu}){sub 11}dee using first-order perturbation theory are presented. The contribution from the quadrupole component of the (dd{mu}){sub 11} charge distribution, which is not taken into account in the conventional scaling procedure based on the finite-size energy shifts of (dd{mu}){sub 11}e, is found to be of the order of 1 meV and to depend on the angular-momentum states of (dd{mu}){sub 11}dee. Sources of uncertainty in the current theoretical estimates are also discussed. {copyright} {ital 1997} {ital The American Physical Society}
- OSTI ID:
- 632565
- Journal Information:
- Physical Review A, Vol. 56, Issue 4; Other Information: PBD: Oct 1997
- Country of Publication:
- United States
- Language:
- English
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