Helium-3 relativistic wave function in light-front dynamics

TL;DR

This work develops a fully relativistic description of the $^3$He nucleus in explicitly covariant light-front dynamics (LFD), yielding a wave function with $32$ spin-isospin components each depending on five scalar variables. By constructing two covariant spin bases, $V_{ij}$ and $oldsymbol{ n}$-based $oldsymbol{}_n$, and solving a three-body bound-state equation with a one-boson-exchange kernel, the authors quantify relativistic effects via comparisons to the non-relativistic limit, revealing additional components and momentum-space structure arising from relativistic dynamics. The results show that relativistic corrections significantly alter isospin content and introduce orientation- and momentum-fraction dependencies that do not appear in NR calculations, while NR-like behavior is recovered in the low-momentum regime. This framework enables calculation of high-$Q^2$ observables such as $^3$He electromagnetic form factors and can be extended to hypernuclei and heavier nuclei, offering a path toward integrating nucleon LF wave functions with few-body and many-body nuclear structure.

Abstract

The relativistic wave function of $^3$He nucleus is calculated in the framework of Light-Front Dynamics. It is determined by 32 spin-isospin components, each of which depends on five scalar variables. For NN interaction, the one-boson exchange model is assumed, but without a potential approximation. The relativistic effects manifest themselves in deviation of the relativistic components from the non-relativistic input, in the appearance of the components absent in the non-relativistic limit, and in dependence of solutions on specific variables that don't exist in the non-relativistic wave function.

Figures (9)

• Figure 1: Three-body equation for the vertex function $\Gamma$.
• Figure 2: One boson exchange kernel.
• Figure 3: Logarithmic plots of dominant components (dashed lines: non-relativistic components, solid lines: relativistic components) as functions of $q$. The fixed arguments are $x_1=x_2=x_3=1/3$, $q_1 = q_2 = q_3 = q$, and $\langle \vec{q}_1, \vec{q}_2\rangle = \langle \vec{q}_1, \vec{q}_3\rangle = \langle \vec{q}_2, \vec{q}_3\rangle = 2\pi/3$. The component functions are in units of $\mathrm{GeV^{-3}}$.
• Figure 4: Plots of typical non-dominant components (dashed lines: non-relativistic components, solid lines: relativistic components) as functions of $q$. The fixed arguments are $x_1=x_2=x_3=1/3$, $q_1 = q_2 = q_3 = q$, and $\langle \vec{q}_1, \vec{q}_2\rangle = \langle \vec{q}_1, \vec{q}_3\rangle = \langle \vec{q}_2, \vec{q}_3\rangle = 2\pi/3$. The component functions are in units of $\mathrm{GeV^{-3}}$.
• Figure 5: Logarithmic plots of dominant components (dashed lines: non-relativistic components, solid lines: relativistic components) as functions of $q$. The fixed arguments are $x_1 = x_2 = x_3 = 1/3$, $\vec{q}_1 = (0, q, 0)$, $\vec{q}_2 = (q, 0, 0)$, $\vec{q}_3 = -\vec{q}_1 - \vec{q}_2$, and $\vec{n} = (0,0,1)$. All momenta are in units of GeV. The wave functions are in units of $\mathrm{GeV^{-3}}$.