Dipole hyperpolarizability of the spherically confined hydrogen atom under quantum plasmas

The dipole hyperpolarizability (γ) along with the dipole polarizability (α) of the spherically confined hydrogen atom under quantum plasmas are calculated quite accurately within the framework of the variation-perturbation method. The collective effect in a quantum plasma has been modeled by a pseudopotential in the form of exponential cosine screened Coulomb potential. Specifically, γ and α are extracted from the variational expression of two definitive functionals which respectively correspond to the second order and fourth order corrections to the ground state energy of the confined hydrogen atom subject to the perturbation induced by the dipole moment operator. The stationary values of these variational functionals are evaluated with respect to a non-linear variational parameter by using two basis sets. Convergence of the results are corroborated by increasing the number of terms in the basis sets. An inclusive study is carried out to explore the changes emerging in γ and α due to the variation of the spherical box as well as the quantum wave number.