Criticality in the configuration-mixed interacting boson model : (1) $U(5)-\hat{Q}(\chi)\cdot\hat{Q}(\chi)$ mixing
The case of U(5)--$\hat{Q}(\chi)\cdot\hat{Q}(\chi)$ mixing in the configuration-mixed Interacting Boson Model is studied in its mean-field approximation. Phase diagrams with analytical and numerical solutions are constructed and discussed. Indications for first-order and second-order shape phase transitions can be obtained from binding energies and from critical exponents, respectively.