Neutrino energy loss by electron capture in magnetic field at the crusts of neutron stars

Based on the p-f shell model,the effect of strong magnetic field on neutrino energy loss rates by electron capture is investigated.The calculations show that the magnetic field has only a slight effect on the neutrino energy loss rates in the range of 108-1013 G on the surfaces of most neutron stars.But for some magnetars,the range of the magnetic field is 1013-1018 G,and the neutrino energy loss rates are greatly reduced,even by more than four orders of magnitude due to the strong magnetic field.     

Effect of strong magnetic field on electron capture of iron group nuclei in crusts of neutron stars

In this paper electron capture on iron group nuclei in crusts of neutron stars in a strong magnetic field is investigated. The results show that the magnetic fields have only a slight effect on electron capture rates in a range of 10$^{8}-10^{13}$G on surfaces of most neutron stars, whereas for some magnetars the magnetic fields range from 10$^{13}$ to 10$^{18}$~G. The electron capture rates of most iron group nuclei are greatly decreased, reduced by even four orders of magnitude due to the strong magnetic field.     

Effect of superstrong magnetic field on electron screening at the crusts of neutron stars

The influences of electron screening (ES) and electron energy correction (EEC) are investigated by superstrong magnetic field (SMF). We also discuss in detail the discrepant factor between our results and those of Fushiki, Gudmundsson and Pethick (FGP) in SMF. The results show that SMF has only a slight effect on ES when B < 109 T on the surfaces of most neutron stars. Whereas for some magnetars, SMF influence ES greatly when B > 109 T . For instance, due to SMF the ES potential may be increased about 23.6% and the EEC may be increased about 4 orders of magnitude at ρ/μe = 1.0 × 106 mol/cm3 and T9 = 1. On the other hand, the discrepant factor shows that our results are in good agreement with FGP’s when B < 109 T . But the difference will be increased with increasing SMF.     

Influence of strong magnetic field on β decay in the crusts of neutron stars

βdecay in the strong magnetic field of the crusts of neutron stars is analysed by an improved method. The reactions ⁶⁷ Ni(β^-)⁶⁷ Cu and ⁶² Mn\beta ^-62 Fe are investigated as examples. The results show that a weak magnetic field has little effect on βdecay but a strong magnetic field (B>10¹²G) increases β decay rates obviously. The conclusion derived may be crucial to the research of late evolution of neutron stars and nucleosynthesis in r-process.     

Neutrino energy loss by electron capture on strongly screened iron group nuclei

The influences on the neutrino energy loss rates in iron group nuclei at the same density are investigated in the presence of strong electron screening and in the absence of electron screening. The results show that at a temperature of $15\ti10^9$\,K, the neutrino energy loss rates which come from the electron capture process for most iron group nuclei decrease no more than 2 orders of magnitude but for the others (such as $^{53,55,56,57,58,59,60}$Co, $^{56,59}$Ni) they can decrease about 3 orders of magnitude due to strong electron screening (SES), whereas, at a temperature of $10^9K$ the neutrino energy loss rates of the most iron group nuclei can be diminished greatly due to the SES. For example, $^{61}$Fe, $^{60}$Fe, and $^{62}$Ni the neutrino energy loss rates decrease about 4, 15 and 16 orders of magnitude and for $^{57}$Cr, $^{58}$Cr, and $^{60}$Cr decrease about 18, 12, and 10 orders of magnitude respectively. According to our calculations the neutrino energy loss rates of nuclei $^{58}$Mn, $^{59}$Mn, $^{60}$Mn, and $^{62}$Mn may decrease about 13 orders of magnitude at a temperature of $10^9$\,K due to the SES.     

超强磁场对中子星外壳层核素56Fe,56Co,56Ni,56Mn和56Cr电子俘获过程中微子能量损失的影响

研究了超强磁场对中子星外壳层核素⁵⁶Fe,⁵⁶Co,⁵⁶Ni,⁵⁶Mn和⁵⁶Cr电子俘获过程中微子能量损失的影响.结果表明,就大部分中子星表面的磁场B<10¹³G,超强磁场对中微子能量损失率的影响很小.对于一些磁场范围为10¹³—10¹⁵G的超磁星,超强磁场可使中微子能量损失率大大降低,甚至超过5个数量级.     

Gaussian modification of neutrino energy loss on strongly screening nuclides 55Co and 56Ni by electron capture in stellar interior

Gaussian modifications of the neutrino energy loss (NEL) by electron capture on the strongly screening nuclides 55Co and 56Ni are investigated. The results show that in strong electron screening (SES),the NEL rates decrease without modifying the Gamow-Teller (G-T) resonance transition. For instance, the NEL rates of 55Co and 56Ni decrease more than two and three orders of magnitude for ρ7 = 5.86, T9≤ 5,Ye = 0.47, △ = 6.3, respectively. In contrast, due to Gaussian modification, the NEL rates increase about two orders of magnitude in SES. Due to SES, the maximum values of the C-factor (in %) on NEL of 55Co, 56Ni are of the order of 99.80%, 99.56% at ρ7 = 5.86 Ye = 0.47 and 99.60%, 99.65% at ρ7 = 106 Ye = 0.43, respectively.     

Microscopic calculation of the magnetic field of neutron stars

Based on the Dirac equation describing an electron moving in a uniform and cylindrically symmetric magnetic field which may be the result of the self-consistent mean field of the electrons themselves in a neutron star, we have obtained the eigen solutions and the orbital magnetic moments of electrons in which each eigen orbital can be calculated. From the eigen energy spectrum we find that the lowest energy level is the highly degenerate orbitals with the quantum numbers pZ=0, n=0, and m≥0. At the ground state, the electrons fill the lowest eigen states to form many Landau magnetic cells and each cell is a circular disk with the radius λfree and the thickness λe, where λfree is the electron mean free path determined by Coulomb cross section and electron density and λe is the electron Compton wavelength. The magnetic moment of each cell and the number of cells in the neutron star are calculated, from which the total magnetic moment and magnetic field of the neutron star can be calculated. The results are compared with the observational data and the agreement is reasonable.     

Microscopic calculation of the magnetic field of neutron stars

Based on the Dirac equation describing an electron moving in a uniform and cylindrically symmetric magnetic field which may be the result of the self-consistent mean field of the electrons themselves in a neutron star, we have obtained the eigen solutions and the orbital magnetic moments of electrons in which each eigen orbital can be calculated. From the eigen energy spectrum we find that the lowest energy level is the highly degenerate orbitals with the quantum numbers pz = 0, n = 0, and m ≥0. At the ground state, the electrons fill the lowest eigen states to form many Landau magnetic cells and each cell is a circular disk with the radius λfree and the thickness λe, where λfree is the electron mean free path determined by Coulomb cross section and electron density and λe is the electron Compton wavelength. The magnetic moment of each cell and the number of cells in the neutron star are calculated, from which the total magnetic moment and magnetic field of the neutron star can be calculated. The results are compared with the observational data and the agreement is reasonable.     

Gaussian modification of neutrino energy loss on strongly screening nuclides ~（55）Co and ~（56）Ni by electron capture in stellar interior

Gaussian modifications of the neutrino energy loss (NEL) by electron capture on the strongly screening nuclides ⁵⁵Co and ⁵⁶Ni are investigated. The results show that in strong electron screening (SES), the NEL rates decrease without modifying the Gamow-Teller (G-T) resonance transition. For instance, the NEL rates of ⁵⁵Co and ⁵⁶Ni decrease more than two and three orders of magnitude for ρ₇=5.86, T₉≤5, Y_e=0.47, Δ=6.3, respectively. In contrast, due to Gaussian modification, the NEL rates increase about two orders of magnitude in SES. Due to SES, the maximum values of the C-factor (in %) on NEL of ⁵⁵Co, ⁵⁶Ni are of the order of 99.80%, 99.56% at ρ₇=5.86 Y_e=0.47 and 99.60%, 99.65% at ρ₇=106 Y_e=0.43, respectively.     

Effects of the symmetry energy slope on the axial oscillations of neutron stars

The impact of symmetry energy slope L on the axial w-mode oscillations is explored, where the range of the con- strained slope L of symmetry energy at saturation density is adopted from 25 MeV to 115 MeV while keeping the equation of state （EOS） of symmetric nuclear matter fixed. Based on the range of the symmetry energy slope, a constraint on the frequency and damping time of the wi-mode of the neutron star is given. It is found that there is a perfect linear relation between the frequency and the stellar mass for a fixed slope L, and the softer symmetry energy corresponds to a higher frequency. Moreover, it is confirmed that both the frequencies and damping times have a perfect universal scaling behavior for the EOSs with different symmetry energy slopes at saturation density.     

Rotational energy conversion and thermal evolution of neutron stars

Pulsars are rapidly spinning, strongly magnetized neutron stars. Their electromagnetic dipole radiation is usually assumed to be at the expense of the rotational energy. In this work, we consider a new channel through which rotational energy could be radiated away directly via neutrinos. With this new energy conversion channel, we can improve the chemical heating mechanism that originates in the deviation from β equilibrium due to spin-down compression. The improved chemical and thermal evolution equations with different magnetic field strengths are solved numerically. The results show that the new energy conversion channel could raise the surface temperature of neutron stars, especially for weak field stars at later stages of their evolution. Moreover, our results indicate that the new energy conversion channel induced by the non-equilibrium reaction processes should be taken into account in the study of thermal evolution.     

Constraint on nuclear symmetry energy imposed by f-mode oscillation of neutron stars

Due to improvements in the sensitivity of gravitational wave (GW) detectors, the detection of GWs originating from the fundamental quasi-normal mode (f-mode) of neutron stars has become possible. The future detection of GWs originating from the f-mode of neutron stars will provide a potential way to improve our understanding of the nature of nuclear matter inside neutron stars. In this work, we investigate the constraint imposed by the f-mode oscillation of neutron stars on the symmetry energy of nuclear matter using Bayesian analysis and parametric EOS. It is shown that if the frequency of the f-mode of a neutron star of known mass is observed precisely, the symmetry energy at twice the saturation density (E_sym(2ρ₀)) of nuclear matter can be constrained within a relatively narrow range. For example, when all the following parameters are within the given intervals: 220 ≤ K₀ ≤ 260 MeV, 28 ≤ E_sym(ρ₀) ≤ 36 MeV, 30 ≤ L ≤ 90 MeV, −800 ≤ J₀ ≤ 400 MeV, − 400 ≤ K_sym ≤ 100 MeV, −200 ≤ J_sym ≤ 800 MeV, E_sym(2ρ₀) will be constrained to within ${48.8}_{-5.5}^{+6.6}$ MeV if the f-mode frequency of a canonical neutron star (1.4 M_⊙) is observed to be 1.720 kHz with a 1% relative error. Furthermore, if only f-mode frequency detection is available, i.e. there is no stellar mass measurement, a precisely detected f-mode frequency can also impose an accurate constraint on the symmetry energy. For example, given the same parameter space and the same assumed observed f-mode frequency mentioned above, and assuming that the stellar mass is in the range of 1.2–2.0 M_⊙, E_sym(2ρ₀) will be constrained to within ${49.5}_{-6.8}^{+8.1}\,\mathrm{MeV}$. In addition, it is shown that a higher slope of 69 ≤ L ≤ 143 MeV will give a higher posterior distribution of E_sym(2ρ₀), ${53.8}_{-6.4}^{+7.0}\,\mathrm{MeV}$.     

Effect of strong magnetic field on chemical potential and electron capture in magnetar

The chemical potential of electrons in a strong magnetic field is investigated. It is shown that the magnetic field has only a slight effect on electron chemical potential when B 〈 10^11 T, but electron chemical potential will decrease greatly when B 〉 10^11 T. The effects of a strong magnetic field on electron capture rates for ^60Fe are discussed, and the result shows that the electron capture sharply decreases because of the strong magnetic field.     

Relativistic theory of inverse beta-decay of polarized neutron in strong magnetic field

The relativistic theory of the inverse beta-decay of polarized neutron,ν _e +n → > p +e ^-, in strong magnetic field is developed. For the proton wave function we use the exact solution of the Dirac equation in the magnetic filed that enables us to account exactly for effects of the proton momentum quantization in the magnetic field and also for the proton recoil motion. The effect of nucleons anomalous magnetic moments in strong magnetic fields is also discussed. We examine the cross-section for different energies and directions of propagation of the initial neutrino accounting for neutron polarization. It is shown that in the super-strong magnetic field the totally polarized neutron matter is transparent for neutrinos propagating antiparallel to the direction of polarization. The developed relativistic approach can be used for calculations of cross-sections of the other URCA processes in strong magnetic fields.     

Effects of the density dependence of the symmetry energy on neutron stars

In this paper,we include the density dependence behavior of the symmetry energy in the improved quark mass density dependent （IQMDD） model.Under the mean field approximation,this model is applied to investigate neutron star matter and neutron stars successfully.Effects of the density dependence of the symmetry energy on neutron stars are described.     

Effects of the density dependence of the symmetry energy on neutron stars

In this paper,we include the density dependence behavior of the symmetry energy in the improved quark mass density dependent (IQMDD) model.Under the mean field approximation,this model is applied to investigate neutron star matter and neutron stars successfully.Effects of the density dependence of the symmetry energy on neutron stars are described.     

强磁场中修正URCA过程的中微子产能率

基于n-p-e模型并考虑修正URCA过程中的质子分支,研究了强磁场对中子星核心区域修正URCA过程中微子产能率的影响.结果表明,强磁场使修正URCA过程的中微子产能率产生明显振荡;与中子分支相比,强磁场对质子分支中微子产能率的影响偏弱,但是它将提高总的中微子产能率.所得结论将有助于进一步研究中子星的冷却机理. 关键词： 中子星 强磁场 修正的URCA过程     

极化中子照相磁场量化技术方案比较与分析

极化中子照相技术通过分析极化中子束的自旋相移对样品磁场进行成像,目前已发展出多种成像技术方案,其中能量选择法和自旋回波法极化中子成像技术从不同的原理出发,解决了极化中子照相中磁场量化的周期解问题,同时避免装置极化效率等参数的影响,可以实现较高的量化精度.本文对两种极化中子照相技术方案进行研究,通过对单色器能量分辨率和装置极化效率等关键参数的分析和模拟,确定在研究堆上开展相关实验的可行性,并初步明确其量化能力和适用范围.相关结果可为极化中子照相的实验数据处理技术研究及装置设计提供参考.     

Structure of Rotating Neutron Stars in Uniform Strong Magnetic Field

Properties and deformations of the rotating neutron stars in uniform strong magnetic field are calculated. The magnetic field will soften the equation of state of the neutron star matters and make an obvious effect on the structure of the rotating neutron star. If the magnetic field is superstrong （B=10^17 T）, the mass, radius, and the deformation will become smaller effectively.