双电荷交换声子态
Double charge-exchange phonon states
摘要：
本文研究了丰中子核中的双电荷交换声子态，特别是双同位旋算符$\sum_{i,j=1}^At_-(i) t_-(j)$和自旋-同位旋算符$\sum_{i,j=1}^Aσ(i) t_-(i)σ(j) t_-(j)$诱导的双同量异位素模拟态和双Gamow-Teller激发.我们采用四次换位子关系来计算平均能量$E_{\rm DIAS} - 2E_{\rm IAS}$和$E_{\rm DGTR}-E_{\rm DIAS} - 2(E_{\rm GTR}-E_{\rm IAS})$，采用传统的双换位子关系来计算平均能量$E_{\rm GTR}-E_{\rm IAS}$和$E_{\rm IAS}$ .我们发现四次修正子引起的修正遵循近似定律：$E_{\rm DIAS} - 2E_{\rm IAS}\approx \frac{3}{2} A^{-1/3}$ MeV和$E_{\rm DGTR}-E_{\rm DIAS} - 2(E_{\rm GTR}-E_{\rm IAS})\approx 16 A^{-1}$ MeV。前者主要受直接库仑效应的影响，但由于库仑交换在一定程度上抵消了核力对同位旋对称性破缺的贡献，而后者则对强相互作用的自旋通道和自旋-同位旋通道的强度差异敏感。
英文摘要：
We study double charge-exchange phonon states in neutron-rich nuclei, in particular the double isobaric analog states and the double Gamow-Teller excitations, induced by the double isospin operator $\sum_{i,j=1}^At_-(i) t_-(j)$ and spin-isospin operator $\sum_{i,j=1}^Aσ(i) t_-(i)σ(j) t_-(j)$, respectively. We employ quartic commutator relations to evaluate the average energies $E_{\rm DIAS} - 2E_{\rm IAS}$ and $E_{\rm DGTR}-E_{\rm DIAS} - 2(E_{\rm GTR}-E_{\rm IAS})$, and conventional double commutator relations to evaluate the average energies of $E_{\rm GTR}-E_{\rm IAS}$ and $E_{\rm IAS}$. We have found that the corrections due to quartic commutators follow the approximate laws: $E_{\rm DIAS} - 2E_{\rm IAS}\approx \frac{3}{2} A^{-1/3}$ MeV and $E_{\rm DGTR}-E_{\rm DIAS} - 2(E_{\rm GTR}-E_{\rm IAS})\approx 16 A^{-1}$ MeV. While the former is dominated by direct Coulomb effects, since Coulomb exchange cancels out to some extent with isospin symmetry breaking contributions originated form the nuclear strong force, the latter is sensitive to the difference in strength between the spin and spin-isospin chanels of the strong interaction.
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