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Constraints for the vector-isoscalar channel
Validity of the CE for the vector-isoscalar density,
Eq. (30) for
and
, imposes through
Eq. (48) at second order the following constraints on
the coupling constants of the functional,
![$\displaystyle C_{00,1101}^{1101,t}$](img203.png) |
![$\textstyle =$](img6.png) |
![$\displaystyle -\frac{1}{\sqrt{3}}C_{00,2011}^{0011,t},$](img204.png) |
(59) |
![$\displaystyle C_{00,1110}^{1110,t}$](img189.png) |
![$\textstyle =$](img6.png) |
![$\displaystyle -\frac{1}{\sqrt{3}}C_{00,2000}^{0000,t},$](img205.png) |
(60) |
![$\displaystyle C_{00,1111}^{1111,t}$](img191.png) |
![$\textstyle =$](img6.png) |
![$\displaystyle -C_{00,2000}^{0000,t},$](img206.png) |
(61) |
![$\displaystyle C_{00,1112}^{1112,t}$](img193.png) |
![$\textstyle =$](img6.png) |
![$\displaystyle -\sqrt{\frac{5}{3}}C_{00,2000}^{0000,t},$](img207.png) |
(62) |
![$\displaystyle C_{20,0011}^{0011,t}$](img208.png) |
![$\textstyle =$](img6.png) |
![$\displaystyle C_{22,0011}^{0011,t} = 0,$](img209.png) |
(63) |
![$\displaystyle C_{11,1111}^{0000,t}$](img195.png) |
![$\textstyle =$](img6.png) |
![$\displaystyle C_{11,0011}^{1101,t} = 0 ,$](img196.png) |
(64) |
![$\displaystyle C_{00,2211}^{0011,t}$](img210.png) |
![$\textstyle =$](img6.png) |
![$\displaystyle 0 ,$](img211.png) |
(65) |
whereas the two coupling constants
are left
unrestricted. We note here that the constraints now connect scalar
and vector coupling constants. Altogether, at second order, for the
vector-isoscalar channel of the CE we have 6 free and 8 dependent
coupling constants. Apart from that, 10
second-order coupling constants must vanish, which includes the
surface ones in Eq. (63), spin-orbit ones of the
Eq. (64), and tensor ones in Eq. (65).
For the fourth and sixth orders, analogous constraints are
presented in Appendix B.
Next: Constraints for the vector-isovector
Up: Continuity equations in the
Previous: Constraints for the scalar-isovector
Jacek Dobaczewski
2011-11-11