Lifetime measurement of neutron-rich even-even molybdenum isotopes

Abstract

Background: In the neutron-rich A ≈ 100 mass region, rapid shape changes as a function of nucleon number as well as coexistence of prolate, oblate, and triaxial shapes are predicted by various theoretical models. Lifetime measurements of excited levels in the molybdenum isotopes allow the determination of transitional quadrupole moments, which in turn provides structural information regarding the predicted shape change. Purpose: The present paper reports on the experimental setup, the method that allowed one to measure the lifetimes of excited states in even-even molybdenum isotopes from mass A = 100 up to mass A = 108, and the results that were obtained. Method:The isotopes of interest were populated by secondary knock-out reaction of neutron-rich nuclei separated and identified by the GSI fragment separator at relativistic beam energies and detected by the sensitive PreSPEC-AGATA experimental setup. The latter included the Lund-York-Cologne calorimeter for identification, tracking, and velocity measurement of ejectiles, and AGATA, an array of position sensitive segmented HPGe detectors, used to determine the interaction positions of the γ ray enabling a precise Doppler correction. The lifetimes were determined with a relativistic version of the Doppler-shift-attenuation method using the systematic shift of the energy after Doppler correction of a γ -ray transition with a known energy. This relativistic Doppler-shiftattenuation method allowed the determination of mean lifetimes from 2 to 250 ps. Results: Even-even molybdenum isotopes from mass A = 100 to A = 108 were studied. The decays of the low-lying states in the ground-state band were observed. In particular, two mean lifetimes were measured for the first time: τ = 29.7 Conclusions:The reduced transition strengths B(E2), calculated from lifetimes measured in this experiment, compared to beyond-mean-field calculations, indicate a gradual shape transition in the chain of molybdenum isotopes when going from A = 100 to A = 108 with a maximum reached at N = 64. The transition probabilities decrease for 108 Mo which may be related to its well-pronounced triaxial shape indicated by the calculations.

New insights into triaxiality and shape coexistence from odd-mass Rh109

“…In this region, near-spherical and highly quadrupoledeformed shapes are observed to closely compete for the lowest energy configuration resulting in wide shape variations between neighboring isotopes. As a result, these isotopes provide a sensitive test for modern nuclear models rooted in density functional theory (DFT) [19][20][21][22][23][24][25] or even large-scale Monte Carlo Shell Model (MCSM) calculations [26][27][28] that are both capable of predicting nuclear properties out to extreme neutron-to-proton ratios. Indeed, the rapidly varying nuclear structure in this region has recently been attributed to large-scale reconfiguration of single-particle orbitals near the Fermi surface, known as Type II shell evolution [26][27][28], however such calculations have so far been limited by the high computational demands required to adequately model the A ∼ 100 region and its large valence space.…”

“…Indeed, the rapidly varying nuclear structure in this region has recently been attributed to large-scale reconfiguration of single-particle orbitals near the Fermi surface, known as Type II shell evolution [26][27][28], however such calculations have so far been limited by the high computational demands required to adequately model the A ∼ 100 region and its large valence space. Self-Consistent Mean Field (SCMF) DFT calculations, with their global applicability, have also demonstrated promising results in reproducing experimental trends [17,[19][20][21][22][23][24][25]29] and, thus, provide another good option for studying the shape variations in this region.…”

“…In spite of the theoretical challenges, within the past few years alone, there has been a multitude of experimen-tal efforts directed towards the A ∼ 100 region of nuclides [17,19,20,22,[27][28][29][30][31][32][33][34][35][36]. Many of the recent experiments have been focused on the sudden increase in deformation for N >60 in isotope chains with Z<40 and how sudden or gradual the isotopic trends are in order to map out the low-Z boundary for which shape coexistence remains prevalent in the low-energy structure [19,20,[28][29][30][31]37].…”

“…Many of the recent experiments have been focused on the sudden increase in deformation for N >60 in isotope chains with Z<40 and how sudden or gradual the isotopic trends are in order to map out the low-Z boundary for which shape coexistence remains prevalent in the low-energy structure [19,20,[28][29][30][31]37]. Other studies have focused on measuring the collectivity beyond N = 60 showing that the maximum in deformation seems to occur at N = 64, just ahead of the midshell point [7,22,35,38].…”

“…Many studies indicate that in Mo and Ru isotopes, the coexisting shapes tend to merge to form relatively rigid, triaxially-deformed ground states [22,25,36,43,48,49] or, in the least, potential energy surfaces that are γ-soft [21,23,[50][51][52]. The rigidity of triaxial deformation in nuclei remains an open question, but the general consensus is that triaxiality occurs in isotopes that are transitional between two regions where widely different shapes are favored: either between prolate and oblate regions, or between spherical and substantially (quadrupole) deformed regions [14,21,24].…”