The folding potential description of ⁹C + ²⁰⁸Pb elastic scattering at 227 MeV

Figures & data

Figure 1. Panels (a) and (b) show the nuclear matter density distributions of ⁹C as logarithmic and linear scales, respectively.

Figure 2. The variation of real folded potential depths by using different density forms of different NN interactions for ⁹C + ²⁰⁸Pb system at 227 MeV.

Figure 3. The real folded potentials by using RMF density form and different NN interactions for ⁹C + ²⁰⁸Pb system at 227 MeV.

Figure 4. The normalized real folded potentials by using different-NN interactions form and different ⁹C densities for ⁹C + ²⁰⁸Pb system at 227 MeV in FM-1 scenario.

Figure 5. The elastic-scattering differential cross sections in comparison with the experimental data of the ⁹C+ ²⁰⁸Pb reaction at 227 MeV [11] by using different combination of densities and NN interactions within DFP of scenario FM-1.Labels indicated on the figures.

Figure 6. The elastic-scattering differential cross sections in comparison with the experimental data of the ⁹C+ ²⁰⁸Pb reaction at 227 MeV [11] by using different combination of densities and NN interactions within DFP of scenario FM-2. Labels indicated on the figures

Table 1. Best-fit parameters of the double folded potentials (DFPs) using the two scenarios; FM-1 and FM-2 for ⁹C + ²⁰⁸Pb scattering data at 227 MeV.

Density	Interaction	Model Scenario	NR	W /NI (MeV)	R (fm)	a (fm)	JR (MeV fm^3)	JI (MeV.fm^3)	σR (mb)	χ^2
G1-2pF	M3Y	FM-1	1.05	23.01	1.404	0.240	406.40	73.48	3140	0.35
		FM-2	1.20	1.49	–	–	464.33	574.67	3233	1.24
	KH1	FM-1	1.03	22.28	1.405	0.226	375.84	71.27	3120	0.34
		FM-2	1.10	1.33	–	–	403.44	488.36	3237	1.38
	S1Y	FM-1	0.96	13.82	1.447	0.187	215.58	48.13	3181	0.36
		FM-2	1.21	1.20	–	–	271.46	269.19	3038	1.51
	CDM3Y6	FM-1	0.81	13.84	1.440	0.138	256.73	47.53	3106	0.34
		FM-2	0.79	0.60	–	–	249.42	190.04	2959	1.76
GO	M3Y	FM-1	0.82	61.62	1.369	0.202	318.94	182.15	3041	0.34
		FM-2	0.75	0.78	–	–	290.19	301.09	3263	2.40
	KH1	FM-1	0.83	54.18	1.384	0.172	304.96	165.34	3037	0.36
		FM-2	0.72	0.73	–	–	264.05	268.03	3270	2.69
	S1Y	FM-1	0.95	29.46	1.394	0.215	212.88	91.86	3082	0.35
		FM-2	1.02	1.07	–	–	228.77	239.00	3244	2.26
	CDM3Y6	FM-1	0.58	28.24	1.406	0.170	205.32	90.25	3069	0.35
		FM-2	0.55	0.59	–	–	195.46	209.39	3262	2.34
RMF	M3Y	FM-1	0.78	70.78	1.365	0.215	302.98	207.33	3062	0.33
		FM-2	0.80	0.78	–	–	309.51	302.42	3259	2.63
	KH1	FM-1	0.75	75.21	1.362	0.202	281.92	219.08	3031	0.34
		FM-2	0.70	0.72	–	–	256.71	265.06	3251	2.34
	S1Y	FM-1	0.91	42.27	1.390	0.214	203.91	130.85	3107	0.35
		FM-2	1.00	1.08	–	–	224.32	242.03	3237	2.01
	CDM3Y6	FM-1	0.78	41.33	1.386	0.140	273.34	126.67	2971	0.42
		FM-2	0.55	0.59	–	–	192.17	205.08	3250	2.18

Figure 7. Modulus of the scattering matrix $|S_L|$ to the calculated real folded potential by using RMF density and S1Y-NN interaction within DFP of scenarios; FM-1 and FM-2 versus the orbital angular momentum (L).

Table 2. Values of some characteristic quantities accompanied by the best-fit parameters of the selected bold case in Table 1.

Interaction/density	Model Scenario	R${}_{\frac{1}{2}}$ (fm)	L${}_{\frac{1}{2}}$ ($\hslash$)	W / V${}_{(R\frac{1}{2})}$
S1Y/ RMF	FM-1	11.45	91.26	1.9
	FM-2	11.14	93.68	1.1

Figure 8. Radial sensitivity of elastic-scattering differential cross sections to the calculated real folded potential by using RMF density and S1Y-NN interaction within DFP of scenario FM-1.

Figure 9. The elastic scattering calculated with different values of real folded potential renormalization factor (N_R) by using RMF density and S1Y-NN interaction added to WS imaginary potential within the folding model (FM-1) compared with experimental data as linear and logarithmic scales.

Figure 10. The elastic scattering was calculated with different values of imaginary potential depth (W_o) added to real folded potential by using RMF density and S1Y-NN interaction within folding model (FM-1) compared with experimental data as linear and logarithmic scales.

Yang YY, Liu X, Pang DY, et al. Elastic scattering of the proton drip line nuclei 7Be 8B, and 9C on a lead target at energies around three times the Coulomb barriers. Phys Rev C. 2018;98:044608.

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