Narrow Results

The shell evolution of even–even drip line argon isotopes ${}^{46\text{–}54}\mathrm{\text{Ar}}$ has been investigated via the shell model calculations using SDPF-U and SDPF-NR two-body effective interactions in two different shell model spaces $\pi (sd)-\nu (fp)$ and $\pi (sd)-\nu (f_{7/2}p)$. In this work, the energy of first $2^{+}$, reduced transition probability $B(E2)$, excitation energy levels as well as how the proton shells evolve with $N$ have been studied. Excellent agreements were obtained for the first $2^{+}$ level along the investigated isotopes within $\pi (sd)-\nu (fp)$ and $\pi (sd)-\nu (f_{7/2}p)$ model spaces.

Lifetime measurement of the first excited 2⁺ state in ¹⁸C was performed using an upgraded recoil shadow method to determine the electric quadrupole transition. The measured mean lifetime is 18.9 ± 0.9 (stat) ± 4.4 (syst) ps, which corresponds to a value of 4.3 ± 0.2 ± 1.0 e²fm⁴, or about 1.5 Weisskopf units. The mean lifetime of the first 2⁺ state in ¹⁶C was remeasured to be about 18 ps, about four times shorter than the value reported previously. By incorporating the γ-ray angular distribution measured in this work into the previous measurement, this discrepancy has been explained. The observed transition strengths in ^16,18C are hindered compared to the empirical transition strengths, indicating that the anomalous hindered E2 strength observed in ¹⁶C persists in ¹⁸C.

We have performed shell model calculations for neutron deficient even ^102-108Sn and odd ^103-107Sn isotopes in sdg_7/2h_11/2 model space using two different interactions. The first set of interaction is due to Brown et al. and second is due to Hoska et al. The calculations have been performed using doubly magic ¹⁰⁰Sn as core and valence neutrons are distributed over the single particle orbits 1g_7/2, 2d_5/2, 2d_3/2, 3s_1/2 and 1h_11/2. In more recent experimental work for ¹⁰¹Sn [I. G. Darby et al., Phys. Rev. Lett.105 (2010) 162502], the g.s. is predicted as 5/2⁺ with excited 7/2⁺ at 172 keV. We have also performed another two set of calculations by taking difference in single particle energies of 2d_5/2 and 1g_7/2 orbitals by 172 keV. The present state-of-the-art shell model calculations predict fair agreement with the experimental data. These calculations serve as a test of nuclear shell model in the region far from stability for unstable Sn isotopes near the doubly magic ¹⁰⁰Sn core.

The shapes and low-energy spectra of ${}^{176-194}$Pt isotopes are discussed by a nonrelativistic Skyrme–Hartree–Fock (SHF) approach plus a density-dependent pairing in the BCS approximation. Two different Skyrme parameters SLy5 and SGII are used to perform constrained triaxial mean-field calculations of energy surface. The calculations beyond mean field are introduced by a projection of mean-field intrinsic wave functions onto good angular momentum. Theoretical calculations exhibit the evolution of shapes from triaxial in light Pt isotopes to $\gamma$ soft for medium Pt isotopes, and finally oblate shapes in heavy isotopes. In particular, the calculated excitation spectra are in good agreement with available data and the trend of experimental $B(E2)$ is reproduced. The mean-field calculations indicate a stable shape evolution with SLy5 and SGII interactions, respectively. In the present SHF approach, the lighter nuclei Pt isotopes present a slightly triaxial shapes.

The well known, one-parameter Davydov–Filippov model (DFM) or its variants have been used often to study the inter band $\gamma$-g B(E2) ratios for the triaxially deformed nuclei. Here, its application for the axially deformed nuclei with $\gamma$ less than $20^{\circ }$ is illustrated, which has not received attention so far. Instead of the usual practice of studying the gamma-ground B(E2) ratios, we focus on the absolute B(E2) values in DFM. It offers a wholly new role of the $\gamma$-variable in explaining the spectral features of the axially deformed nuclei. Further, it illustrates the intimate relationship of the $\gamma$ variable and the quadrupole deformation variable $\beta$. Additionally, a unified view of the various differing patterns of the variation of the $\gamma$-g B(E2) ratios versus $\gamma$ is presented.

Recently, from the study of the absolute $B(E2)$ values for the ($\gamma$–$g$) $E$2 transitions, the different roles of the triaxiality parameter $\gamma =(0^{\circ }\text{–}20^{\circ })$ and $\gamma =(20^{\circ }\text{–}30^{\circ })$ parts were pointed out. Here, the use of the triaxial rotor model expressions for the $B(E$2)s in producing the bell-shaped curve of $B(E2,2_{\gamma }-0_1^{+})$ is illustrated. The variation of certain ($\gamma$–$g$) $B(E2)$ ratios versus $\gamma$ for the states $2_{\gamma }$ and $3_{\gamma }$ are illustrated, reflecting the two regions of $\gamma$. The inter relation of the $\gamma$ and $\beta$ variables is illustrated for the Os isotopes.

In this paper, the interacting boson model (IBM-1) with intrinsic coherent state is used to study the O(6) shapes in Se isotopes. The Hamiltonian is written in the annihilation and creation form with one and two body terms. For each nucleus, a fitting procedure is adopted to get the best model parameters by fitting selected experimental energy levels, B(E2), B(M1) transition rates and mixing ratio with the calculated ones. The O(6) IBM potential energy surfaces (PESs) are analyzed.

We use a new scheme to describe the X(5) nuclei, in which the SU(3) quadrupole-quadrupole interaction is replaced by the SO(6) cubic [Q₍₀₎ × Q₍₀₎ × Q₍₀₎]⁰ interaction. Some energy ratios and B(E2) ratios of X(5) nuclei are studied in this work. The results of this new scheme are compared with the corresponding experimental data and those of the traditional U(5)-SU(3) description. It is shown that the results from this new scheme are better than those of the traditional description.