Two Rotating Particles Interacting via Two-Body Gaussian Potential and Harmonically Confined in Two Spatial Dimensions

期刊论文
发表日期：

2026年6月10日

查看全文

Md Hamid,
M. A. H. Ahsan

摘要

We investigate a system of two particles harmonically confined in a 2D plane interacting via a two-body Gaussian potential and subjected to an externally impressed rotation about an axis perpendicular to the plane of the motion. Separating the free motion of the center of mass from the relative motion, we use perturbation theory to obtain the eigenenergy for the relative motion of the pair, in a given relative angular momentum state l. We numerically demonstrate that for the Gaussian interaction potential with interaction strength $g_{2}$ $g_{2}$ and interaction range $\sigma $ $σ$ , the ground-state energy converges within a subspace of finite number of basis functions. We obtain energies for the ground, the first, and the second excited states in the interaction strength regime $-4\le g_{2}\le 4$ $- 4 \leq g_{2} \leq 4$ , for various values of the interaction range $\sigma $ $σ$ , for the relative angular momenta $l=0$ $l = 0$ and $l=1$ $l = 1$ . For angular momentum $l=0$ $l = 0$ and attractive interaction with $g_{2}<0$ $g_{2} < 0$ , the ground-state energy becomes negative, thus forming a bound state. As the interaction strength $g_{2}$ $g_{2}$ takes further negative values below $-2$ $- 2$ , the ground-state energy diverges to $-\infty $ $- \infty$ , thus forming a tightly-bound pair of particles. In contrast, for the angular momentum $l=1$ $l = 1$ , there is no such divergence in the ground-state energy, instead, the ground, the first, and the second excited state energies coincide with the corresponding non-interacting values, independent of the value of the interaction strength in the regime $-4\le g_{2}\le +4$ $- 4 \leq g_{2} \leq + 4$ . For angular momentum $l=0 \text{ or } 1$ $l = 0 or 1$ and repulsive interaction with $g_{2}>0$ $g_{2} > 0$ , the ground-state energy increases with an increase in the interaction strength as well as the interaction range. For the ground-state of the pair, the inter-dependence of the average kinetic energy $\langle Ke \rangle $ $⟨ K e ⟩$ , the average harmonic-potential $\langle V_{ho} \rangle $ $⟨ V_{ho} ⟩$ and the average interaction energy $\langle V_{int} \rangle $ $⟨ V_{int} ⟩$ are analyzed with interaction strength $g_{2}=1$ $g_{2} = 1$ and interaction range in the regime $0.1\le \sigma \le 0.9$ $0.1 \leq σ \leq 0.9$ , for relative angular momentum $l=0$ $l = 0$ and $l=1$ $l = 1$ .