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We investigate the electric dipole response of $^{34}$Na, a probable $p$-waveone-neutron halo nucleus, lying in the "island of inversion" and having adeformed structure. We use a semi-analytic approach to probe the dipoleresponse and further compare the results obtained from a post form finite-rangedistorted wave Born approximation theory of Coulomb breakup. The effects ofdeformation are figured out on the peak positions of the electric dipolestrength distribution which further constraint the one-neutron separationenergy of the deformed projectile and it leads to a two-dimensional scaling oftotal $B(E1)$ strength with parameters: separation energy and deformation.

Scaling with deformation in probable $p$-wave halo $^{34}$Na