Electromagnetic properties of100Mo: Experimental results and theoretical description of quadrupole degrees of freedom

Abstract

The Coulomb excitation experiment to study electromagnetic properties of the heaviest stable Mo isotope, 100 Mo, was performed using a 76 MeV 32 S beam from the Warsaw cyclotron U-200P. Magnitudes and relative signs of 26 E1, E2, E3, and M1 matrix elements coupling nine low-lying states in 100 Mo were determined using the least-squares code GOSIA. Diagonal matrix elements (related to the spectroscopic quadrupole moments) of the 2 + 1 , 2 + 2 , and 2 + 3 states as well as the 4 + 1 state were extracted. The resulting set of reduced E2 matrix elements was complete and precise enough to obtain, using the quadrupole sum rules approach, quadrupole deformation parameters of 100 Mo in its two lowest 0 + states: ground and excited. The overall deformation of the 0 + 1 and 0 + 2 states in 100 Mo is of similar magnitude, in both cases larger compared to what was found for the neighboring isotopes 96 Mo and 98 Mo. At the same time, the asymetry parameters obtained for both states strongly differ, indicating a triaxial shape of the 100 Mo nucleus in the ground state and a prolate shape in the excited 0 + state. Low-energy quadrupole excitations of the 100 Mo nucleus were studied in the frame of the general quadrupole collective Bohr Hamiltonian model (GBH). The potential energy and inertial functions were calculated using the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) method starting from two possible variants of the Skyrme effective interaction: SIII and Sly4. The overall quadrupole deformation parameters resulting from the GBH calculations with the SLy4 variant of the Skyrme interaction are slightly closer to the experimentally obtained values than those obtained using SIII.

Low-energy Coulomb excitation of Sr96,98 beams

“…10. These results were obtained in safe Coulomb excitation experiments of 100 Mo [42] and 94,96 Kr [4] or determined in the present work. The results for the first 2 + states in all nuclei are consistently low.…”

“…The obtained transitional quadrupole moment of the prolate state, Q spins [42]. An inverse trend is observed for 102 Mo, interpreted as a rotational-to-vibrational transition at high spin.…”

Systematic study of nuclear matrix elements in neutrinoless double-βdecay with a beyond-mean-field covariant density functional theory

“…If the ground state of 96 Zr was taken as the pure spherical configuration, the NME becomes 5.64 (PC-PK1) and 3.94 (D1S), respectively. We note that the consideration of higher-order deformation in nuclear wave functions, such as octupole deformation in 150 Sm-Nd [58,59], and triaxiality in 76 Ge-Se [52,53] and 100 Mo-Ru [60], is expected to hinder the corresponding NMEs further in the DFT calculation. Table III lists the upper limits of the effective neutrino mass m ββ based on the present calculated NMEs for the nuclei whose lower limits of the half-life T 0ν 1/2 for the 0νββ-decay have been recently measured [9,10,[61][62][63][64].…”

Shape Coexistence in the Neutron-Deficient Even-EvenHg182−188Isotopes Studied via Coulomb Excitation

“…These results can be analyzed in terms of the quadrupole deformation parameters, Q and δ, which are universal variables of quadrupole collective models within the General Bohr Hamiltonian (GBH) [27]. Using the quadrupole sum rules approach [28][29][30][31] the quadrupole invariants, hQ 2 i and hQ 3 cosð3δÞi, can then be obtained. Invariants describe the charge distribution of a nucleus in a given nuclear state.…”

“…3: the sum of squared E2 matrix elements (SSM) related to hQ 2 i and the sum of triple products of E2 matrix elements (STM) related to hQ 3 cosð3δÞi. The quadrupole invariants can be further related to the GBH collective model variables [31], β (overall deformation parameter) and γ (nonaxiality parameter). It can be concluded that the ground states of the even-even mercury isotopes are weakly deformed with a β value close to 0.15 and are consistent with an oblatelike deformation [hcosð3δÞi ≃ −1], while the excited 0 þ states are more deformed.…”