$\beta $-decay properties of some astrophysically important Sc isotopes

Farooq, Fakeha; Nabi, Jameel-Un; Shehzadi, R.

doi:10.1007/s10509-021-03990-y

Cited by 1 publication

(1 citation statement)

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“…类的致密天体 [1,2] ，其表面磁场超过电子的临界磁场 B cr (B cr =4.41×10 13 G)，在这样强的磁场下，电子朗道能级被强烈地量子化 [3,4] 。磁星的典型特征之一是 X 射线波段和软 γ 射线波段有着超过爱丁顿光度的短期爆发；部分磁星会发射出中等或巨型闪耀，后者在不到 0.5s 内能释放出高达 10 46 erg 的能量。软 γ 射线重复暴和反常 X 射线脉冲星被认为是磁星候选者。磁星耀发和爆发被解释为由剧烈磁重联或壳层的破裂造成的，在宁静状态下 X 射线辐射归因于超强磁场的衰减 [3][4][5][6][7] 电子费米能是致密星物态方程中的一个非常重要的物理量。近年来，国内外不少作者 [8][9][10][11][12][13][14] 对致密星环境下的物态方程、中微子辐射和相对论电子进行关注和研究。其中，刘晶晶等人 [15][16][17][18][19] 对包括修正的 Urca 过程、β 衰变、电子俘获以及中微子吸收等进行长期的研究，并取得了丰硕的成果。高志福等人 [20] 通过引入了超强磁场下的 Dirac- 函数，给出超强磁场下简并的相对论电子压强 P e 的一个特解：…”

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Modified pressure of relativistic electrons in a superhigh magnetic field

Dong¹,

Gao²,

Yang³

et al. 2023

Acta Phys. Sin.

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Magnetars are a kind of pulsars powered by magnetic field energy. The study of magnetars is an important hotspot in the field of pulsars. In this paper, based on the work of Zhu Cui et al. (2016), we reinvestigate the Landau-level stability of electrons in a superhigh magnetic field (SMF), B>> Bcr (Bcr =4.414×1013G is the quantum critical magnetic field) and their influences on the pressure of electrons in magnetars. Firstly, we briefly review the pressure of electrons in neutron stars (NSs) with a weak-magnetic field limit (B<< Bcr). By introducing the electron Landau level stability coefficient gn and the Dirac -δ function, then we deduce a modified formula for pressure of degenerate and relativistic electrons in a SMF with an application range of ρ ≥107g cm-3and Bcr<<B<1017G. By modifying the phase space of relativistic electrons, a SMF can enhance the electron number density ne, and decrease the maximum of electron Landau level number νmax, which results in a redistribution of electrons. As B increases, more and more electrons will occupy higher Landau levels, the electron Landau level stability coefficient gν will decrease with the increase in Landau energy-level number ν. By modifying the phase space of relativistic electrons, the electron number density ne increases with the MF strength, leading to an increase in the electron pressure Pe. Utilizing this modified expression of electron pressure, we discuss the phenomenon of Fermion spin polarization and electron magnetization in SMFs, and the modification of the equation of state by the SMFs. We calculate the baryon number density, magnetization pressure, and pressure differences parallel to and perpendicular to the magnetic field under the relativistic mean field model and find that the pressure anisotropy due to the strong magnetic field is very small and can be ignored under the present model. We have compared our results with other similar works, and found that there are similarities and differences between our work and other similar work. The similarities include: (1) the abnormal magnetic moment of electrons and the interaction between them are ignored; (2) The electron pressure is related to magnetic field intensity B, electron number density ne and electron Fermi energy EF(e) and the latter two are complex functions containing B. (3) Given ne and EF(e), Pe increases with B; (4) As B increases, the pressure-density curve fitted by other similar work will have irregular protrusions or fluctuations, which is caused by the transformation of electron energy state from partial filling to complete filling at the ν -level or the transition of electrons from the ν to the (ν+1)-level. This phenomenon is believed to be related to the behavior of electrons near the Fermi surface in a strong magnetic field, which essentially reflects the Landau level instability. Finally, we look forward to the prospects of the future research. The results provide a reference for future studies on the equation of state and emission mechanism of high-B pulsars, magnetars and strongly magnetized white dwarfs.

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