Many-body forces are sometimes a relevant ingredient in various fields, such as atomic, nuclear or hadronic physics. Their precise structure is generally difficult to uncover. So, phenomenological effective forces are often used in practice. Nevertheless, they are always very heavy to treat numerically. The envelope theory, also known as the auxiliary field method, is a very efficient technique to obtain approximate, but reliable, solutions of many-body systems interacting via one-or two-body forces. It is adapted here to allow the treatment of a special form of many-body forces. In the most favourable cases, the approximate eigenvalues are analytical lower or upper bounds. Otherwise, numerical approximation can always be computed. Two examples of many-body forces are presented, and the critical coupling constants for generic attractive many-body potentials are computed. Finally, a semiclassical interpretation is given for the generic formula of the eigenvalues. *
A theoretical investigation of the atomic structure and radiative parameters involving the lowest states within the 6p 5 , 6p 4 7s and 6p 4 7p configurations of neutral astatine is reported for the first time in the present paper. Using different physical models based on the pseudo-relativistic Hartree-Fock approach, the influence of intravalence, core-valence and core-core electron correlation on the atomic parameters is discussed in detail. This work allowed us to establish the intermediate-coupling composition and to clearly fix the spectroscopic designation of six excited levels within the 6p 4 7s and 6p 4 7p configurations which had been located in previous experimental studies. In addition new tentative identifications of four levels belonging to the 6p 4 9p and 6p 4 10p configurations are reported in this work together with predicted level energies along the 6p 4 n p and 6p 4 n d Rydberg series up to n = 50.
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