Legal Question in Wills and Trusts in Louisiana

In a normal, no will situation, the surviving spouse owns 50% of all community property, which would include the house if purchased during the marriage. The 4 children, and any other he may have had by other women, would divide the other 50% equally, EXCEPT that 50% is burdened by the usufruct in favor of the surviving spouse. So the children could not force a sale or a buyout since the surviving spouse has the right of ownership of 1/2 and has the exclusive use of the other half.