Exact Solutions of a Spatially Dependent Mass Dirac Equation for Coulomb Field plus Tensor Interaction via Laplace Transformation Method

Table 1

The bound state energy eigenvalues of the Coulomb potential under the pseudo-spin symmetry limit for several values of 𝑛 and 𝜅 for 𝑚₀=5.0fm⁻¹,ℏ=𝑐=1, 𝑞=1,𝑇=(0,1,2,5), and 𝐶_𝑝𝑠=−1.

𝑙̃	𝑛,𝜅<0	(𝑙,𝑗=𝑙+1/2)	𝑚1	𝐸𝑛,𝜅<0
				𝑇=0	𝑇=1	𝑇=2	𝑇=5
1	1, −2	1𝑝3/2	0.0	−4.86154	−4.75676	−4.47059	−4.86154
			0.2	−4.80508	−4.66644	−4.36211	−4.80508
			0.4	−4.74207	−4.57172	−4.26086	−4.74207
			0.5	−4.70859	−4.52376	−4.21286	−4.70859
2	1, −3	1𝑑5/2	0.0	−4.91089	−4.86154	−4.75676	−4.75676
			0.2	−4.87335	−4.80508	−4.66644	−4.66644
			0.4	−4.83043	−4.74207	−4.57172	−4.57172
			0.5	−4.80716	−4.70859	−4.52376	−4.52376
3	1, −4	1𝑓7/2	0.0	−4.93793	−4.91089	−4.86154	−4.47059
			0.2	−4.91138	−4.87335	−4.80508	−4.36211
			0.4	−4.88067	−4.83043	−4.74207	−4.26086
			0.5	−4.86385	−4.80716	−4.70859	−4.21286
4	1, −5	1𝑔9/2	0.0	−4.95431	−4.93793	−4.91089	−4.47059
			0.2	−4.93461	−4.91138	−4.87335	−4.36211
			0.4	−4.91166	−4.88067	−4.83043	−4.26086
			0.5	−4.89903	−4.86385	−4.80716	−4.21286
1	2, −2	2𝑝3/2	0.0	−4.91089	−4.86154	−4.75676	−4.91089
			0.2	−4.87402	−4.80794	−4.69083	−4.87402
			0.4	−4.83243	−4.75015	−4.62526	−4.83243
			0.5	−4.81014	−4.72024	−4.59287	−4.81014
2	2, −3	2𝑑5/2	0.0	−4.93793	−4.91089	−4.86154	−4.86154
			0.2	−4.9116	−4.87402	−4.80794	−4.80794
			0.4	−4.88134	−4.83243	−4.75015	−4.75015
			0.5	−4.86487	−4.81014	−4.72024	−4.72024
3	2, −4	2𝑓7/2	0.0	−4.95431	−4.93793	−4.91089	−4.75676
			0.2	−4.93469	−4.9116	−4.87402	−4.69083
			0.4	−4.91194	−4.88134	−4.83243	−4.62526
			0.5	−4.89945	−4.86487	−4.81014	−4.59287
4	2, −5	2𝑔9/2	0.0	−4.96498	−4.95431	−4.93793	−4.75676
			0.2	−4.94984	−4.93469	−4.91160	−4.69083
			0.4	−4.93218	−4.91194	−4.88134	−4.62526
			0.5	−4.92244	−4.89945	−4.86487	−4.59287