Simple analytical expressions for mesomolecular matrix elements

Effect ofdtμquasinucleus structure on energy levels of the(dtμ)Xeeexotic molecule

“…Thus, under the above approximations, the radial wave function Φ nl (ρ) in the potential (19) coincides with the harmonic-oscillator wave function and the multipole matrix elements (16), (17), (18) are reduced to l-independent…”

“…The simple, though providing the required accuracy expressions for the multipole matrix elements (16), (17), and (18) are obtained using the following reliable approximations.…”

“…The asymptotic expression (24) has been widely used in description of the loosely bound states of mesic molecules and the asymptotic normalization constant C a was determined by a comparison with the exact three-body calculations [9,16,17]. For the same reasons, the asymptotic expressions are used for the continuum wave functions φ kλ (r), viz.,…”

“…As a result, the value ε 11 = 596meV [1,2,4] is obtained for the lowest hyperfine state by taking into account relativistic effects, hyperfine effects, finite nuclear size, and vacuum polarization. The asymptotic constant C a was determined in a number of papers [9,16,17] by a comparison of the asymptotic expression (24) with the three-body wave function. In the following, it is accepted the value C a = 0.874/ √ 2 obtained in the latest elaborated calculation [17] of the wave function in a wide asymptotic region of large distances between d and tµ.…”

Normalization of the asymptotic form of three-body (dtμ)+and (ddμ)+wave functions

“…At present, two different values for C for (dt's)ii exist in the literature. Menshikov [9] found C=0.812 using a wave function calculated from an expansion in terms of adiabatic states [10, 11] while Aissing, Monkhorst, and Petrov [12] found C=1.006 using a variational wave function [13] expanded in a basis set of I Slater-type functions. The two C values difFer by approximately 20%%uo.…”