Inner Crust

Tables and data concerning the inner crust, taken from multiple sources, for example [PkecakZC+24].

Bulk Neutron Properties

Quantities extracted from simulations for each density of the inner crust \(\bar\rho\): \(\rho_{Bn}\) – bulk density of neutrons, \(\Delta_n\) – pairing energy of neutrons, \(k_{\mathrm{F}}\) – wave vector calculated for bulk density of neutrons, \(\epsilon_{\mathrm{F}}\) – Fermi energy, \(\epsilon_{\mathrm{F}}^*\) – Fermi energy calculated with respect to effective mass, \(N\) – number of neutrons, \(\xi\) – coherence length, \(R\) – radius of impurity, \(M_{\mathrm{eff}}\) – effective mass of impurity.

\(\\bar\\rho\) [fm -3]	\(\\rho_{Bn}\) [fm -3]	\(\\Delta_n\) [MeV]	\(k_{\\mathrm{F}}\) [fm -1]	\(\\epsilon_{\\mathrm{F}}\) [MeV]	\(\\epsilon_{\\mathrm{F}}^*\) [MeV]	\(N\)	\(\\xi\) [fm]	R [fm]	\(M_{\\mathrm{eff}}\) [ \(m_n\)]
0.0023	0.0016	0.826	0.363	2.723	2.694	376.6	5.79	5.32	150.75 \(\pm\) 1.8
0.0058	0.0045	1.236	0.512	5.436	5.301	934.4	5.47	5.21	139.30 \(\pm\) 1.0
0.0104	0.0084	1.483	0.628	8.165	7.840	1696.8	5.58	5.64	164.70 \(\pm\) 3.1
0.0148	0.0120	1.562	0.707	10.37	9.839	2385.3	5.98	5.79	155.25 \(\pm\) 2.9
0.0187	0.0152	1.557	0.766	12.15	11.421	3032.5	6.49	6.21	174.45 \(\pm\) 4.1
0.0237	0.0193	1.621	0.829	14.24	13.248	3789.3	6.75	5.28	168.55 \(\pm\) 6.3
0.0267	0.0217	1.566	0.863	15.42	14.268	4258.0	7.27	5.55	168.80 \(\pm\) 7.1
0.0300	0.0244	1.514	0.898	16.70	15.368	4847.1	7.82	7.46	171.85 \(\pm\) 8.3
0.0338	0.0276	1.467	0.935	18.10	16.558	5430.9	8.40	7.27	166.15 \(\pm\) 8.3
0.0428	0.0351	1.327	1.013	21.28	19.260	6925.0	10.1	8.71	150.50 \(\pm\) 8.8
0.0510	0.0422	1.097	1.077	24.05	21.618	8070.6	13.0	9.03	150.60 \(\pm\) 8.8

Effective Masses

Effective masses for dynamical, static, and hydro approaches for zirconium clusters in the inner crust. For the static case, one can think about \(M_{\mathrm{eff}}^s\) semi-classically as the number of protons plus bound neutrons. However, due to the neutron medium, this is not the proper picture.

\(\\bar\\rho\) [fm -3]	\(\\rho_{Bn}\) [fm -3]	\(M_{\\mathrm{eff}}^d\) [ \(m_n\)]	\(M_{\\mathrm{eff}}^s\) [ \(m_n\)]	\(M_{\\mathrm{eff}}^h\) [ \(m_n\)]
0.0023	0.0016	150.75	145.02	55.98
0.0058	0.0045	139.30	144.50	57.46
0.0104	0.0084	164.70	172.34	62.29
0.0148	0.0120	155.25	172.56	59.58
0.0187	0.0152	174.45	197.12	63.93
0.0237	0.0193	168.55	190.26	58.17
0.0267	0.0217	168.80	195.16	56.31
0.0300	0.0244	171.85	215.65	55.52
0.0338	0.0276	166.15	216.84	53.57
0.0428	0.0351	150.50	229.78	42.70
0.0510	0.0422	150.60	161.96	34.32

Collisions Initial State

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The system description is not accurate. Please correct it!

Two nuclei in an elongated box. The Coulomb interaction is present, and the ultrarelativistic electrons are treated as a uniform gas. Schematic:

+-----------+
| o |   | o |
+-----------+

The nuclei are two zirconium atoms, so in total there are \(Z=80\) protons. The units of energy \(E_{\mathrm{tot}}\), pairing \(\Delta\), and chemical potential \(\mu\) are in MeV. The densities are measured in fm ^-3.

\(\\bar\\rho\)	\(\\rho_{Bn}\)	\(\\mu_p\)	\(N\)	\(\\mu_n\)	\(\\Delta_n\)	\(\\Delta_p\)	\(E_{\\mathrm{tot}}\)
0.000	0.000101	-25.255	246.725	0.373642	0.192	0.0069	-5.420
0.002	0.001624	-25.828	623.797	1.937040	0.832	0.0494	-1.796
0.006	0.004533	-29.776	1370.09	3.555630	1.256	0.1061	0.659
0.010	0.008369	-37.631	2404.02	4.962623	1.478	0.1066	2.230
0.015	0.011945	-38.414	3322.71	5.862966	1.579	0.1193	3.153
0.019	0.015194	-42.382	4203.90	6.589333	1.599	0.1057	3.825
0.024	0.019125	-45.139	5209.08	7.239645	1.639	0.1057	4.463
0.027	0.021536	-45.138	5836.39	7.591119	1.591	0.1051	4.792
0.030	0.024601	-47.516	6636.53	8.032960	1.538	0.1031	5.174
0.034	0.027579	-49.270	7409.12	8.423588	1.512	0.1013	5.508
0.043	0.035360	-52.454	9401.53	9.212281	1.354	0.0907	6.241
0.051	0.041282	-55.162	10923.8	9.842774	1.106	0.0795	6.712