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<jats:title>Abstract</jats:title> <jats:p>We examined the low-lying quadrupole states in Sn isotopes in the framework of fully self-consistent Hartree-Fock+BCS plus QRPA. We focus on the effect of the density-dependence of pairing interaction on the properties of the low-lying quadrupole state. The SLy5 Skyrme interaction with surface, mixed, and volume pairings is employed in the calculations, respectively. We find that the excitation energies and the corresponding reduced electric transition probabilities of the first 2<jats:sup>+</jats:sup> state are different, given by the three pairing interactions. The properties of the quasiparticle state, two-quasiparticle excitation energy, reduced transition amplitude, and transition densities in <jats:sup>112</jats:sup>Sn are analyzed in detail. Two different mechanisms, the static and dynamical effects, of the pairing correlation are also discussed. The results show that the surface, mixed, and volume pairings indeed affect the properties of the first 2<jats:sup>+</jats:sup> state in the Sn isotopes. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The inelastic scattering cross section for muons, <jats:inline-formula> <jats:tex-math><?CDATA $ \mu^- $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094102_M1.jpg" xlink:type="simple" /> </jats:inline-formula>, with energies <jats:inline-formula> <jats:tex-math><?CDATA $ E $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094102_M2.jpg" xlink:type="simple" /> </jats:inline-formula> = 9–100 eV from the <jats:inline-formula> <jats:tex-math><?CDATA $ ^{229} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094102_M3.jpg" xlink:type="simple" /> </jats:inline-formula>Th nuclei is calculated in the framework of the second order of the perturbation theory for quantum electrodynamics. The dominant contribution to the excitation of the low energy isomer <jats:inline-formula> <jats:tex-math><?CDATA $ ^{229m} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094102_M4.jpg" xlink:type="simple" /> </jats:inline-formula>Th <jats:inline-formula> <jats:tex-math><?CDATA $ (3/2^+,8.19\pm0.12 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094102_M5.jpg" xlink:type="simple" /> </jats:inline-formula> eV) originates from the <jats:inline-formula> <jats:tex-math><?CDATA $ E2 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094102_M6.jpg" xlink:type="simple" /> </jats:inline-formula> multipole. The excitation cross section reaches the value of <jats:inline-formula> <jats:tex-math><?CDATA $ 10^{-21} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094102_M7.jpg" xlink:type="simple" /> </jats:inline-formula> cm <jats:inline-formula> <jats:tex-math><?CDATA $ ^2 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094102_M8.jpg" xlink:type="simple" /> </jats:inline-formula> in the range <jats:inline-formula> <jats:tex-math><?CDATA $ E\approx $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094102_M9.jpg" xlink:type="simple" /> </jats:inline-formula>10 eV. This value is four to five orders of magnitude larger than the electron excitation cross section and is sufficient for the efficient excitation of <jats:inline-formula> <jats:tex-math><?CDATA $ ^{229m} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094102_M10.jpg" xlink:type="simple" /> </jats:inline-formula>Th on the muon beam at the next generation of muon colliders. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>Systematic calculations of low-lying energy levels, <jats:inline-formula> <jats:tex-math><?CDATA $B(E2)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094103_M1.jpg" xlink:type="simple" /> </jats:inline-formula> transitions, and <jats:italic>g</jats:italic> factors of even-even tellurium isotopes with mass numbers from 128 to 140 are performed via the nucleon-pair approximation (NPA) of the shell model with phenomenological multipole-multipole interactions. An optimal agreement is obtained between the calculated results and experimental data. The yrast band structures of nuclei below and above the <jats:inline-formula> <jats:tex-math><?CDATA $N=82$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094103_M2.jpg" xlink:type="simple" /> </jats:inline-formula> shell closure are compared and discussed. In particular, the evolutionary differences of <jats:inline-formula> <jats:tex-math><?CDATA $B(E2;2_1^{+}\rightarrow 0_1^{+})$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094103_M3.jpg" xlink:type="simple" /> </jats:inline-formula> values and <jats:inline-formula> <jats:tex-math><?CDATA $g(2_1^{+})$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094103_M4.jpg" xlink:type="simple" /> </jats:inline-formula> factors, with respect to the symmetry of <jats:inline-formula> <jats:tex-math><?CDATA $N=82$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094103_M5.jpg" xlink:type="simple" /> </jats:inline-formula>, are attributed to the dominant contribution differences in neutron and proton excitations, respectively. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The complexity of threshold phenomena is exemplified on a prominent and long-known case - the structure in the <jats:inline-formula> <jats:tex-math><?CDATA $\Lambda p$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094104_M1.jpg" xlink:type="simple" /> </jats:inline-formula> cross section (invariant mass spectrum) at the opening of the <jats:inline-formula> <jats:tex-math><?CDATA $\Sigma N$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094104_M2.jpg" xlink:type="simple" /> </jats:inline-formula> channel. The mass splitting between the <jats:inline-formula> <jats:tex-math><?CDATA $\Sigma$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094104_M3.jpg" xlink:type="simple" /> </jats:inline-formula> baryons together with the angular momentum coupling in the <jats:inline-formula> <jats:tex-math><?CDATA $^3S_1$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094104_M4.jpg" xlink:type="simple" /> </jats:inline-formula>- <jats:inline-formula> <jats:tex-math><?CDATA $^3D_1$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094104_M5.jpg" xlink:type="simple" /> </jats:inline-formula> partial wave imply that, in principle, up to six channels are involved. Utilizing hyperon-nucleon potentials that provide an excellent description of the available low-energy <jats:inline-formula> <jats:tex-math><?CDATA $\Lambda p$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094104_M6.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $\Sigma N$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094104_M7.jpg" xlink:type="simple" /> </jats:inline-formula> scattering data, the shape of the resulting <jats:inline-formula> <jats:tex-math><?CDATA $\Lambda p$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094104_M8.jpg" xlink:type="simple" /> </jats:inline-formula> cross section is discussed and the poles near the <jats:inline-formula> <jats:tex-math><?CDATA $\Sigma N$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094104_M9.jpg" xlink:type="simple" /> </jats:inline-formula> threshold are determined. Evidence for a strangeness <jats:inline-formula> <jats:tex-math><?CDATA $S=-1$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094104_M10.jpg" xlink:type="simple" /> </jats:inline-formula> dibaryon is provided, in the form of a (unstable) <jats:inline-formula> <jats:tex-math><?CDATA $\Sigma N$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094104_M11.jpg" xlink:type="simple" /> </jats:inline-formula> bound state in the vicinity of the <jats:inline-formula> <jats:tex-math><?CDATA $\Sigma N$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094104_M12.jpg" xlink:type="simple" /> </jats:inline-formula> threshold. Predictions for level shifts and widths of <jats:inline-formula> <jats:tex-math><?CDATA $\Sigma^-p$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094104_M13.jpg" xlink:type="simple" /> </jats:inline-formula> atomic states are given. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>In this study, we investigated the entrance channel effect on the evaporation residue cross section of a superheavy element <jats:sup>296</jats:sup>119. Using 29 projectile-target combinations, we investigated the role of the entrance channel on the 3<jats:italic>n</jats:italic> and 4<jats:italic>n</jats:italic> evaporation channels in hot combinations. This effect can be evaluated based on the entrance channel asymmetry and Q value of complete fusion. We calculated the variation of the maximum evaporation residue cross sections ( <jats:inline-formula> <jats:tex-math><?CDATA $\sigma_{3n}^{\rm max}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094105_M1.jpg" xlink:type="simple" /> </jats:inline-formula>and <jats:inline-formula> <jats:tex-math><?CDATA $\sigma_{4n}^{\rm max}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094105_M2.jpg" xlink:type="simple" /> </jats:inline-formula>) with <jats:inline-formula> <jats:tex-math><?CDATA $|Q|$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094105_M3.jpg" xlink:type="simple" /> </jats:inline-formula> for the reactions <jats:inline-formula> <jats:tex-math><?CDATA $^{49-47}{\rm{Ti}}+^{247-249}{\rm{Bk}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094105_M4.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $^{60-57}{\rm{Fe}}+^{236-239}{\rm{Np}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094105_M5.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $^{44-42}{\rm{Ca}}+^{252-254}{\rm{Es}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094105_M6.jpg" xlink:type="simple" /> </jats:inline-formula>, and <jats:inline-formula> <jats:tex-math><?CDATA $^{55,54,52}{\rm{Mn}}+^{241,242,244}{\rm{Pu}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094105_M7.jpg" xlink:type="simple" /> </jats:inline-formula>. With an increase in <jats:inline-formula> <jats:tex-math><?CDATA $|Q|$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094105_M8.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $\sigma_{3n}^{\rm max}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094105_M9.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $\sigma_{4n}^{\rm max}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094105_M10.jpg" xlink:type="simple" /> </jats:inline-formula> increase. In addition, we studied the role of asymmetry and mean fissility parameters in the synthesis of the superheavy element. The obtained results in this study can be utilized in future studies. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The semimagic nucleus <jats:sup>90</jats:sup>Zr, with <jats:italic>Z</jats:italic> = 40 and <jats:italic>N</jats:italic> = 50, is investigated in terms of large scale shell model calculations. A logical agreement is obtained between the available experimental data and predicted values. The calculated results indicate that the low-lying states are primarily dominated by the proton excitations from the <jats:italic>fp</jats:italic> orbitals across the <jats:italic>Z</jats:italic> = 38 or 40 subshell into the high-<jats:italic>j</jats:italic> <jats:inline-formula> <jats:tex-math><?CDATA $1g_{9/2}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094106_M1.jpg" xlink:type="simple" /> </jats:inline-formula> orbital. For the higher-spin states of <jats:sup>90</jats:sup>Zr, the breaking of the <jats:italic>N</jats:italic> = 50 core plays a crucial role, and the contribution of different orbitals to each state are discussed in this article. The evolution from neutron core excitations to proton excitations is systematically studied along the neighboring <jats:italic>N</jats:italic> = 50 isotones. Furthermore, the strong <jats:inline-formula> <jats:tex-math><?CDATA $\Delta I$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094106_M2.jpg" xlink:type="simple" /> </jats:inline-formula> = 1 sequence demonstrates an abrupt backbend attributed to the alignment of the valence nucleons in <jats:italic>fp</jats:italic> proton orbitals and is proposed to have a <jats:inline-formula> <jats:tex-math><?CDATA $\pi(fp)^{-2}(1g_{9/2})^{2} \otimes $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094106_M3.jpg" xlink:type="simple" /> </jats:inline-formula> <jats:inline-formula> <jats:tex-math><?CDATA $ \nu(1g_{9/2})^{-1}(2d_{5/2}/1g_{7/2})^{1}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094106_M3-1.jpg" xlink:type="simple" /> </jats:inline-formula> configuration before the backbend, based on the shell model calculations. The properties of this sequence before the backbend indicate a general agreement with the fingerprints of magnetic rotation; hence, the sequence with the <jats:inline-formula> <jats:tex-math><?CDATA $\pi(fp)^{-2}(1g_{9/2})^{2} \otimes \nu(1g_{9/2})^{-1}(2d_{5/2}/1g_{7/2})^{1}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_9_094106_M4.jpg" xlink:type="simple" /> </jats:inline-formula> configuration is suggested as a magnetic rotational band arising from shears mechanism. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>We study the gauge invariant cosmological perturbations up to the second order. We demonstrate that there are infinite families of gauge invariant variables at both the first and second orders. The conversion formulae among different families are verified to be described by a finite number of bases that are gauge invariant. For the second order cosmological perturbations induced by the first order scalar perturbations, we explicitly represent their equations of motion in terms of the gauge invariant Newtonian, synchronous and hybrid variables, respectively.</jats:p>