Numerical calculations of energy, nucleus size and coulomb decay rate for ddμ* resonance states in the variational approach using new wavefunctions

Abstract

This paper provides a theoretical complement to the experimental measurement of the population of excited dμ(2s) and dμ(1s) atoms in a deuterium. The population of these atoms plays an important role in a muon catalyzed fusion cycle. Symmetric and non-symmetric muonic molecular ions have been predicted to form in excited states in collisions between excited muonic atoms and hydrogen molecules. One example is the ddμ*, which is a muonic deuterium–deuterium symmetric ion in excited state and is initially produced in the interaction of dμ(2s) atoms with deuterium nuclei. Our calculations interpret the experimental findings in terms of the so-called side-path model. This model essentially deals with the interaction mentioned above in which the ddμ* ion undergoes Coulomb de-excitation where the excitation energy is shared between a dμ(1s) atom and one deuterium. The structure of ddμ* is studied here using the numerical, variational method and the given wavefunctions. Few resonance energies for ddμ* molecular states are calculated below the 2s threshold. For more precise assessment of the reliability of the given wavefunctions, the nucleus sizes and Coulomb decay rates for the zeroth, first and second vibrational meta-stable states of the mentioned ion are also calculated. The obtained results are close to those previously reported. The advantage of the given method over previous methods is that the used wavefunction has only two terms, which simplifies the calculations with the same results as those from the complicated coupled rearrangement channel method with a Gaussian basis set. These energies are the base data required for size, formation and decay rate calculations of the ddμ* ion.