In this theoretical communication we look towards understand the underlying phenomenology concerning the Elko spinors within VSR theory. The program to be accomplished here start when we define the eigenspinors of the charge conjugation operator as eigenstates of the helicity operator in the Cartesian coordinates system. This prescription is very useful in the sense of phenomenological point of view, so, we propose a set of Elko spinors ready to be computationally implemented. Regardless of, in order to show the application of given approach we impose to these spinors to be restrict to an axis, coincidentally the axis of locality (Ahluwalia-Khalilova and Grumiller in JCAP, 07:12 2005; Ahluwalia-Khalilova and Cheng-Yang Lee in Phys Rev D 83:065017, 2011) , and then, using the proposed prescription, we search for physical amounts and physical processes by analysing the Yukawa and the self-interaction in such framework.