Table 2.

Comparison of our calculated logarithmic half-lives $lo{g}_{10}$T$_{1/2}^{}$(column 7) of proton emitters (column 1) with the experimental values (column 6) and other theoretical predictions (columns 8-27)^{20,26–29,36,38,41,42,44–46,51,53,54,79,84–87}. Experimental Q$_p^{}$, land half-life values are taken from NUBASE2020⁶⁹and AME2020⁸⁸. $\beta$ values computed using RMF theory. Other theories including UDLP(universal decay law for proton decay); GLDM and ELDM (generalized and effective liquid drop models); DDDM (deformed density-dependent model); RMF+BCS (Relativistic mean field theory combined with BCS method); PCM+UFM (preformed cluster model modified into a unified fission model); DDM3Y (density dependent M3Y interaction); JLM (Jeukenne, Lejeune and Mahaux interaction); CPPM (Coulomb and proximity potential model) and CPPMDN (CPPM for the deformed nuclei) have been used for comparison. $\#$values are the estimated from Trends in Neighboring Nuclei (TNN) in NUBASE2020⁶⁹.

Proton	$Q_p$	l	${\beta }_p$	${\beta }_d$	$lo{g}_{10}$T$_{1/2}^{}$ (sec.)
Emitter	(MeV)				Exp.	Present	Sreeja	Delion	UDLP	Zhang	Chen	Budaca	Yusofvand	CPPMDN	DDDM	RMF+BCS	PCM+UFM	DDM3Y	GLDM	JLM	Medeiros	Ni	Dehghani	ELDM	CPPM	Gamow-Like
					69.	Formula	44	41	20	45	46	51	79	38	36	84	27	26	29	28	42	54	53	85	86	87
Ground to Ground Transition
$_{}^{109}$I	0.83±0.004	2	0.16	0.12	-3.99±0.002	-4.14	-3.86	-4.99	-3.61	-	-3.51	-3.95	-3.44	-3.18	-4.42	-4.43	-	-	-	-	-3.98	-3.82	-3.88	-3.91	-4.28	-
$_{}^{112}$Cs	0.82±0.004	2	0.20	0.15	-3.30$_{-0.097}^{+0.079}$	-3.95	-3.08	-4.29	-2.93	-	-2.84	-3.24	-2.67	-2.35	-3.64	-3.33	-	-	-	-	-3.28	-3.00	-3.10	-3.13	-3.57	-
$_{}^{113}$Cs	0.98±0.002	2	0.22	0.15	-4.78$_{-0.019}^{+0.018}$	-4.48	-5.03	-5.75	-4.81	-	-4.80	-5.22	-4.92	-4.51	-5.21	-5.43	-	-	-	-	-4.87	-4.95	-5.06	-5.30	-5.55	-
$_{}^{130}$Eu	1.03±0.200	2	0.38	0.38	-3.05$_{-0.169}^{+0.189}$	-4.05	-3.09	-3.94	-3.32	-	-3.12	-2.74	-3.27	-2.66	-3.39	-3.82	-	-	-	-	-2.82	-2.59	-2.65	-3.49	-3.76	-
$_{}^{135}$Tb	1.19±0.007	3	0.36	0.37	-3.03$_{-0.116}^{+0.131}$	-4.25	-3.50	-4.77	-3.74	-	-3.38	-3.21	-	-3.55	-3.75	-3.81	-	-	-	-	-2.77	-3.00	-3.22	-3.91	-3.98	-
$_{}^{141}$Ho	1.19±0.007	3	0.33	0.21	-2.39$_{-0.121}^{+0.095}$	-4.00	-2.94	-4.09	-3.19	-	-2.81	-2.57	-	-2.88	-2.89	-1.73	-	-	-	-	-2.20	-2.86	-3.09	-3.34	-3.40	-
$_{}^{144}$Tm	1.73±0.016	5	0.24	0.21	-5.57$_{-0.001}^{+0.002}$	-4.76	-5.39	-	-4.66	-	-5.22	-	-5.35	-6.12	-5.20	-5.72	-5.14	-5.17	-	-	-	-	-4.79	-5.14	-4.97	-
$_{}^{145}$Tm	1.75±0.007	5	0.33	0.20	-5.41±0.027	-4.84	-5.57	-9.50	-4.83	-5.41	-5.40	-4.92	-5.52	-6.32	-5.20	-5.72	-5.14	-5.17	-5.66	-5.10	-5.24	-5.33	-5.09	-5.42	-5.16	-
$_{}^{155}$Ta	1.45±0.015	5	0.03	0.06	-2.54$_{-0.165}^{+0.225}$	-3.71	-2.32	-8.86	-2.25	-2.30	-2.40	-2.21	-2.48	-3.24	-2.31	-2.45	-4.65	-4.65	-2.41	-4.57	-4.57	-4.59	-2.57	-2.32	-2.27	-
$_{}^{159}$Re	1.82±0.020	5	0.05	0.09	$_{}^{\#}$ -4.68$_{-0.092}^{+0.076}$	-4.30	-4.46	-	-	-4.59	-4.49	-4.39	-	-5.42	-4.40	-4.67	-	-	-4.64	-	-4.31	-	-4.64	-4.64	-4.43	-
$_{}^{160}$Re	1.28±0.007	2	0.11	0.10	-3.05$_{-0.048}^{+0.079}$	-3.42	-2.35	-3.84	-2.91	-3.15	-2.45	-3.05	-2.88	-1.99	-3.17	-3.14	-3.00	-3.11	-3.11	-2.87	-3.48	-3.16	-3.08	-2.92	-3.09	-3.48
$_{}^{161}$Re	1.21±0.005	0	0.13	0.11	-3.43±0.010	-3.39	-3.18	-3.43	-2.84	-3.38	-3.28	-3.05	-2.96	-1.57	-3.44	-3.35	-3.46	-3.23	-3.32	-3.29	-3.43	-	-2.99	-2.95	-3.15	-3.64
$_{}^{164}$Ir	1.84±0.009	5	0.11	0.11	$_{}^{\#}$ -3.96$_{-0.139}^{+0.190}$	-4.27	-4.14	-7.77	-4.08	-4.15	-4.25	-	-3.93	-5.17	-4.04	-4.24	-3.92	-4.19	-4.21	-3.86	-	-3.93	-4.46	-4.38	-4.21	-
$_{}^{170}$Au	1.49±0.012	2	0.04	0.12	-3.49$_{-0.060}^{+0.075}$	-3.56	-3.11	-	-3.82	-	-3.25	-4.03	-3.86	-2.95	-	-	-	-	-	-	-3.08	-	-4.04	-3.93	-3.98	-
$_{}^{171}$Au	1.47±0.010	0	-0.01	0.12	-4.65$_{-0.151}^{+0.185}$	-3.51	-4.39	-4.77	-4.26	-4.92	-4.46	-4.54	-4.18	-3.13	-4.93	-4.88	-5.02	-4.79	-4.87	-4.86	-3.74	-4.40	-4.47	-4.53	-4.57	-3.22
$_{}^{176}$Tl	1.28±0.018	0	0.01	-0.09	-2.21$_{-0.012}^{+0.025}$	-2.62	-2.35	-	-2.07	-	-2.36	-2.25	-2.18	-0.59	-	-	-	-	-		-2.72	-	-2.16	-1.91	-2.13	-
$_{}^{177}$Tl	1.18±0.019	0	0.00	-0.12	-1.17±0.121	-2.19	-1.33	-1.05	-0.92	-1.12	-1.26	-4.33	-1.15	0.71	-0.91	-1.05	-1.36	-0.99	-1.05	-1.20	-1.14	-0.74	-0.96	-0.61	-0.86	-5.00
$_{}^{185}$Bi	1.62±0.080	0	-0.17	-0.06	$_{}^{\#}$ -4.23$_{-0.349}^{+0.191}$	-3.66	-	-	-4.72	-	-	-4.23	-	-	-	-	-	-	-3.39	-5.36	-	-4.47	-	-	-	-
Isomer to Ground Transition
$_{}^{141}$Ho$_{}^m$	1.26±0.007	0	0.33	0.21	-5.18$_{-0.197}^{+0.196}$	-4.38	-5.58	-5.18	-5.22	-5.58	-5.78	-4.86	-5.30	-4.44	-5.83	-4.88	-	-	-	-	-4.51	-5.19	-5.79	-	-5.77	-5.87
$_{}^{147}$Tm$_{}^m$	1.14±0.006	2	-0.19	-0.16	-3.44±0.048	-3.51	-2.54	-4.28	-2.82	3.43	0.68	-3.04	-2.72	-1.99	-3.37	-3.43	-3.39	-3.20	-3.44	-3.27	-3.77	-3.63	-3.32	-	0.61	0.87
$_{}^{150}$Lu$_{}^m$	1.32±0.033	2	-0.17	-0.16	-4.52$_{-0.005}^{+0.007}$	-3.81	-3.71	-5.34	-4.03	-4.76	-3.63	-4.27	-4.05	-3.33	-4.71	-4.81	-4.38	-4.56	-4.76	-4.24	-4.96	-4.77	-4.20	-	-4.73	-4.37
$_{}^{151}$Lu$_{}^m$	1.33±0.002	2	-0.14	-0.15	-4.80±0.027	-3.83	-3.84	-5.61	-4.27	-4.92	-3.90	-	-4.35	-3.61	-4.86	-4.96	-4.88	-4.72	-4.91	-4.73	-4.96	-4.91	-4.55	-	-4.58	-4.66
$_{}^{159}$Re$_{}^m$	1.83±0.020	5	0.05	0.09	-4.70±0.087	-4.33	-4.55	-	-4.32	-4.55	-4.59	-	-4.38	-5.52	-4.49	-4.71	-0.60	-0.46	-	-	-	-	-4.43		-4.74	-4.52
$_{}^{164}$Ir$_{}^m$	1.85±0.009	5	0.11	0.11	-3.96±0.190	-4.41	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-3.77	-	-	-	-	-
$_{}^{165}$Ir$_{}^m$	1.73±0.007	5	0.10	0.12	-3.4±0.087	-4.08	-3.42	-	-3.41	-3.39	-3.55	-3.43	-3.20	-4.42	-3.29	-3.48	-3.51	-3.43	-3.46	-3.44	-3.46	-	-3.41	-4.17	-3.69	-3.50
$_{}^{170}$Au$_{}^m$	1.77±0.012	5	0.04	0.12	-2.98$_{-0.028}^{+0.035}$	-3.95	-3.17	-	-3.32	-3.17	-3.33	-3.31	-2.91	-4.24	-2.33	-2.63	-3.01	-2.20	-	-	-2.77	-	-3.01	-	-3.44	-3.31
$_{}^{171}$Au$_{}^m$	1.72±0.010	5	-0.01	0.12	-2.65±0.013	-3.71	-2.81	-6.41	-3.00	-2.60	-2.99	-2.99	-2.56	-3.87	-2.33	-2.63	-3.03	-2.20	-2.61	-2.96	-2.46	-2.61	-2.64	-	-3.14	-2.97
$_{}^{177}$Tl$_{}^m$	1.99±0.019	5	0.00	-0.12	-3.35±0.076	-3.80	-4.05	-7.01	-4.30	-3.45	-3.64	-	-3.74	-5.28	-3.28	-3.47	-4.49	-4.38	-3.47	-4.46	-3.60	-3.84	-3.68	-	-3.31	-3.03
$_{}^{185}$Bi$_{}^m$	1.62±0.080	0	-0.17	-0.06	-4.23$_{-0.105}^{+0.201}$	-3.66	-4.61	-	-	-4.61	-4.73	-	-4.47	-3.60	-4.13	-3.38	-5.44	-5.18	-	-	-4.36	-	-4.02	-4.89	-5.02	-4.97