Comparison of IBM-2 Calculations with X(5) Critical Point Symmetry for Low-Lying States in 144-154Nd

Abstract

Abstract-The X(5) would take place when moving continously from the pure U(5) symmetry to the SU(3) symmetry and it implies a definite relations among the level energies and among the E2 transition strengths. It was recently shown that a signature of phase transition is observed in the chain of Sm, Mo and Nd isotopes, where 152 Sm, 104 Mo and 150 Nd display the predicted features of the X(5) symmetry and mark therefore the critical point. However, more detailed studies and experiments are needed to get ideas about this signature. Without entering into detail we have firstly compared the results obtained in our previous study [15] of [144][145][146][147][148][149][150][151][152][153][154] Nd with that of the limits in X(5) symmetry and then given a clear descripton about the validity of the Hamiltonian parameters used in the study. At the end, we have concluded that some of Nd isotopes display X(5) symmetry features.

Structural evolution in 146–158 Nd isotopes using IBM-2 Hamiltonian

“…This figure suggests that [152][153][154][155][156][157][158] Nd is inore deformed than [146][147][148] Nd, It also shows that for [152][153][154][155][156][157][158] Nd the (𝐸 4 1 + /𝐸 2 1 + ) ratios are far from the U(5) limit; for [146][147][148] Nd the ratios reach the O(6) limit, 2.5, while [152][153][154][155][156][157][158] Nd the ratios arise to reach the SU(3), rotational limit, 3.3, in contrast the ratios for 150 Nd were very closely follow the X(5), limit (critical point symmetry), 2.91. [26], [27] Figure (3) shows the theoretical limits plotted for three schematic nuclei: vib., 500 keV; 𝛾-unstable, 300 keV; and rotor, 100 keV, with respect to isotope's E-GOS curve. We can note that the [146][147][148] Nd isotopes curves follow the 𝛾 -unstable (O ( 6)) limit, but [152][153][154][155][156][157][158] Nd isotopes curves follow the axially deformed rotor (SU (3)) limit, in contrast for 150 Nd isotope was not far from SU (3) limit, and it classified as X (5) limit, these results enhance what was inferred from the use of energy ratio classification.…”