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A detailed study of the spin forbidden transitions, 1s2 1S → 1snp 3P (n = 2,... 7) has been carried out for the first five members of the helium isoelectronic sequence. Non-relativistic time-dependent coupled Hartree-Fock (TDCHF) theory with a spin dependent perturbation has been used to this end. Transition energies for the various excited states generated, have been obtained and suitable analytic representations for these high lying Rydberg states have been given. Also, the magnetic quadrupolar (M2) transition rate has been calculated with the help of the wavefunctions so obtained. These compare favourably with existing data.

PurposeTo investigate the effects of delamination on free vibration characteristics of graphite‐epoxy composite pretwisted cylindrical shallow shells of various stacking sequences considering length of delamination as a parameter.Design/methodology/approachA multipoint constraint algorithm which leads to unsymmetric elastic stiffness matrix is incorporated into an eight noded isoparametric plate bending finite element to satisfy the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The study is focused upon long, intermediate and short cylindrical shells as defined by Aas‐Jakobsen's parameters and considers symmetric and unsymmetric composite laminates.FindingsThe non‐dimensional fundamental natural frequencies are obtained for angle ply (45/−45/45, 45/−45) and cross ply (0/90/0, 0/90) configurations corresponding to different crack lengths and twist angles. The study implies the importance of the symmetric laminate as well as the long shell.Research limitations/implicationsThe standard eigenvalue computations using QR iteration algorithm for the present analyses take enormous time and hence, an efficient eigen‐solver needs to be employed.Practical implicationsNew vibration modes are exhibited by the delaminated composite structures. The existence of invisible interlaminar cracking can be identified with the help of prior knowledge of natural frequencies for a delaminated composite pretwisted shell which can be idealized as a turbine blade with low aspect ratio.Originality/valueThis paper presents a numerical approach for natural frequency determination of composite pretwisted shallow shells having delamination without taking care of the effect of dynamic contact between delaminated layers. The non‐dimensional frequencies obtained could serve as reference solutions for future investigators.

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