Segregated solutions for a critical Choquard system with a small interspecies repulsive force

We consider the following elliptic system aligned -Δ uᵢ=(|x|-μ*|uᵢ|4-μ /2)|uᵢ|2-μ /2uᵢ+∑ j=1\, j =i²β uᵢuⱼ² in \, \, R⁴, i=1,2. aligned - Δ u i = ( | x | - μ ∗ | u i | 4 - μ 2 ) | u i | 2 - μ 2 u i + ∑ j = 1 j ≠ i 2 β u i u j 2 in R 4 , i = 1 , 2 . If β <0, |β | β < 0 , | β | is small enough we build solutions such that the first component looks like the radial positive solution of the single equation, while the second one blows-up at the k vertices of a regular polygon.