The resonance state of $\Delta$ baryon existing in four isospin ($I=\frac{3}{2}$) states, has been studied using Hypercentral Constituent Quark Model (hCQM) with a simple linear potential with added first order correction. The calculated data range for 1S-5S, 1P-5P, 1D-4D and 1F-2F with possible spin-parity assignments of all the states. The magnetic moments have also been obtained for all four configuration. The $N\pi$ decay channel width has been calculated for few states. The linear nature of the data has been verified through Regge trajectories.

中文翻译：

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$\Delta$重子的光谱特性

$\Delta$ 重子的共振态存在于四种同位旋 ($I=\frac{3}{2}$) 状态中，已使用超中心本构夸克模型 (hCQM) 进行了研究，该模型具有简单的线性势和添加一阶校正. 1S-5S、1P-5P、1D-4D 和 1F-2F 的计算数据范围以及所有状态的可能自旋奇偶分配。还获得了所有四种配置的磁矩。已针对少数状态计算了 $N\pi$ 衰减通道宽度。数据的线性特性已通过 Regge 轨迹得到验证。