The contribution of the first forbidden transitions to the nuclear β~--decay half-life

β-decay half-life is a key quantity for nuclear structure and nucleosynthesis studies.There exist large uncertainties in the contributions of allowed and forbidden transitions to the total β-decay life,which limits the resolution of the predicted β-decay half-life.We systematically study the contribution of the first forbidden(FF) transitions to the β~--decay half-life,and quantify it with a formula based on simple physics considerations.We also propose a new formula for calculation of the β~--decay half-life that includes the FF contribution.It is shown that the inclusion of the contribution of FF transitions significantly improves the precision of calculations of the β~--decay half-life.By fitting of the RQRPA results for neutron-rich Z=47,57 isotopes and N=80,94 isotones,the formula for the contribution of the FF transitions gives similar results as the RQRPA calculations.However,because of limited experimental data for the branching ratios of unstable nuclei,the fit parameters are not fully constrained.Therefore,the proposed formula for the β~--decay half-life is more suitable for calculations of half-lives than of the FF contributions.The formula could be used to predict the β~--decay half-life in nuclear structure studies as well as nucleosynthesis calculations in stars.     

Gound State Properties of Nuclei in ^295118 α-Decay Chain

The properties of nuclei belonging to the α-decay chain of superheavy element ^295118 have been studied in the framework of axially deformed relativistic mean field （RMF） theory with the parameter set of NL-Z2 in the blocked BCS approximation. Some ground state properties such as binding energies, deformations, and α-decay energies Qα have been obtained and agree well with those from finite-range droplet model （FRDM）. The single-particle spectra of nuclei in ^295118 α-decay chain show that the shell gaps present obviously nucleon number dependence. The root-mean-square （rms） radii of proton, neutron and matter distributions change slowly from ^283112 to ^295118 but dramatically from ^279110 to ^283112, which may be due to the subshell closure at Z = 110 in ^279110. The α-decay half-lives in 295118 decay chain are evaluated by employing the cluster model and the generalized liquid drop model （GLDM）, and the overall agreement is found when they are compared with the known experimental data. The α-decay lifetimes obtained from the cluster model are slightly larger than those of GLDM ones. Finally, we predict the α-decay half-lives of Z=118, 116, 114, 112 isotopes using the cluster model and GLDM, which also indicate these two models can corroborate each other in studies on superheavy nuclei. The results from GLDM are always lower than those obtained from the cluster model.     

Magnetic Field Effect on β^＋ Decay in the Crusts of Accreting Neutron Stars

Based on shell model of nuclei, the influence of a high magnetic field on β^＋ decay in the crusts of accreting neutron stars is analyzed. The magnetic field effect on 54 Mn is discussed. The results show that a weak magnetic field makes little effect on β^＋ decay but a strong magnetic field （B 〉 10^11 G） improves β^＋ decay rates obviously. The conclusion derived will benefit to develop further research on nuclear astrophysics in the future.     

Density Dependence of the Beta Decay Width in Astronuclear Matter

By combining the four-fermion interaction theory and the linear σ-ω model, we propose an approach to describethe density dependence of the fi-decay width (the half-life time of the decay) in infinite and charge-neutral nuclearmatter. We find that the half-life time of the β-decay decreases rapidly with the increase of the nuclear matterdensity.     

New levels and transitions in ^72Ge following thedecay of ^72Ga

The decay of ^72Ga has been investigated by means of γ-ray spectroscopy. The 72Ga nuclei were produced through the ^71Ga(n, γ)^72Ga reaction. The Compton-suppressed spectrometer and high-purity Ge detectors have been used singly and in coincidence, separately, to study γ-rays in the β-decay of ^72Ga to ^72Ge. Ninety-three events of γ-rays were reported, of which 7 were observed for the first time. A decay scheme of ^72Ga including 4 new levels is proposed which accommodates 87 of these transitions. Spins and parities for new levels are proposed from calculated logft values, modes on the observed decay, and some nuclear reaction experimental results.     

Alpha-decay branching ratios to high-lying excited-states of the ^242Cm → ^238Pu → ^234U → ^230Th → ^226Rn decay chain

We present a systematic calculation on the α-decay branching ratios to excited-states of an even-even α-decay chain ^242Cm → ^238Pu → ^234U → ^230Th → ^226Rn by the improved barrier penetration approach. The changes of the parities between the parent nuclei and the daughter nuclei are properly taken into account. The theoretical values are compared with the available experimental data and the deviation between them is within a factor of 5 in most cases.     

Properties of the β-Delayed Proton Decay of 147Er

The β-delayed proton decay of 147Er is studied experimentally using the 58 Ni＋92Mo reaction at a beam energy of 383 MeV. Based on a He-jet apparatus coupled with a tape transport system, the β-delayed proton radioactivities both from the vδl/2 ground state and the vh11/2 isomer in 147 Er are identified by proton-7 coincidence measurements. By analyzing the time distribution of the 4＋ → 2＋-γ transition in the grand-daughter nucleus 146Dy, a half-life of 1.6 ± 0.2s is determined for the Vh11/2 isomer in 147 Er. The half-life for the ground state of 147Er is estimated to be 3.2±1.2 s.     

Asymptotic Normalization Coefficient of ^27P → ^26Si ＋ p and Radius of ^27P Halo

The asymptotic normalization coefficient of the virtual decay ^27P → ^26Si ＋ p is extracted to be 1840 ± 240 fm^-1 from the peripheral ^26Mg（d,p）^27Mg reaction using charge symmetry of mirror pair, for the first time. It is then used to derive the rms radius of the valence proton in the ground state of ^27P. We obtain the rms radius （γ^2〉^1/2 = 4.57 ± 0.36 fm, significantly larger than the matter radius of ^27P. The probability of the valence proton outside the matter radius of ^27P is found to be 73%. The present work supports the conclusion that the ^27p ground state has a proton halo structure.     

Unusual Threshold Anomaly in the ^6Li＋^208Pb System

The angular distributions of elastic scattering for the ^6Li ＋^208Pb system have been measured at several energies around the Coulomb barrier. The parameters of optical potential are extracted by means of a phenomenological optical model analysis. It is found that the real and imaginal potentials show a pronounced energy dependence. The behaviour of the potential at the nearly especially sub-barrier energies in the ^6Li＋^208Pb system is quite different from the results of some previous reports observed in other systems, such as ^19F＋^208Pb and ^16O＋^208Pb. This unusual threshold phenomenon indicates that breakup channel is strongly coupled with the elastic channel and has obvious effects on optical potential.     

Exploring the uncertainties in theoretical predictions of nuclear β-decay half-lives

Nuclear β-decay half-lives are predicted based on an empirical formula and the mass predictions from various nuclear models.It is found that the empirical formula can reproduce the nuclearβ-decay half-lives well,especially for short-lived nuclei with T_1/2<1s.The theoretical half-life uncertainties fromβ-decay energies and the parameters of the empirical formula are further investigated.It is found that the uncertainties of the half-lives are relatively large for heavy nuclei and nuclei near the neutron-drip line.For nuclei on the r-process path,the uncertainties for those with N=126 are about one order of magnitude,which are much larger than the uncertainties for those with N=50 and 82.However,theoretical uncertainties from the parameters of the empirical formula are relatively small for the nuclei on the r-process path,which indicates that the empirical formula is very suitable for predicting theβ-decay half-lives in r-process simulations.     

Systematical law of β+-decay half-lives of nuclei far from β-stable line

Experimental data of nuclear β⁺-decay half-lives are systematically analyzed and investigated. We present an exponential law between the half-life of β⁺-decay with the same forbiddenness and the nucleon number (Z,N) of parent nucleus far from the β-stable line. A formula with four parameters is proposed to describe the β⁺-decay half-lives of nuclei far from stability. Experimental β⁺-decay half-lives of the first and second forbidden transitions are well reproduced by this simple formula. The physics of the exponential law is related to the statistical properties of β⁺-decay far from β-stable line.     

Benford＇s Law and β-Decay Half-Lives

The experimental values of 2059 β-decay half-lives are systematically analyzed and investigated. We have found that they are in satisfactory agreement with Benford＇s law, which states that the frequency of occurrence of each figure, 1-9, as the first significant digit in a surprisingly large number of different data sets follows a logarithmic distribution favoring the smaller ones. Benford＇s logarithmic distribution of β-deeay half-lives can be explained in terms of Neweomb＇s justification of Benford＇s law and empirical exponential law of β-decay half-lives. Moreover, we test the calculated values of 6721 β-decay half-lives with the aid of Benford＇s law. This indicates that Benford＇s law is useful for theoretical physicists to test their methods for calculating β-decay half-lives.     

Green and red up-conversion emissions and thermometric application of Er^3＋-doped silicate glass

The green and red up-conversion emissions centred at about 534, 549 and 663 nm of wavelength, corresponding respectively to the ^2H11/2 → ^4I15/2, ^4S3/2 → ^4I15/2 and ^4F9/2 → ^4I15/2 transitions of Er^3＋ ions, have been observed for the Er^3＋-doped silicate glass excited by a 978 nm semiconductor laser beam. Excitation power dependent behaviour of the up-conversion emission intensity indicates that a two-photon absorption up-conversion process is responsible for the green and red up-conversion emissions. The temperature dependence of the green up-conversion emissions is also studied in a temperature range of 296-673 K, which shows that Er^3＋-doped silicate glass can be used as a sensor in high-temperature measurement.     

Competition between α-decay and β-decay for heavy and superheavy nuclei

In this work, the β-stable region for Z 90 is proposed based on a successful binding energy formula.The calculated β-stable nuclei in the β-stable region are in good agreement with the ones obtained by Mo¨ller et al. The half-lives of the nuclei close to the β-stable region are calculated and the competition between α-decay andβ-decay is systematically investigated. The calculated half-lives and the suggested decay modes are well in line with the experimental results. The decay modes are mostly β--decay above the β-stable region. Especially for Z 111,all the decay modes are β--decay. Regarding the nuclei above the β-stable region, α-decay and β--decay(α+β-)can occur simultaneously when Z 112. This is a very interesting phenomenon. The competition between α-decay and β-decay is very complex and drastic below the β-stable region. The predictions for half-lives and decay modes of the nuclei with Z =107–110 are presented in detail.     

Effects of Target Deformation on the Synthesis of Superheavy Nucleus 283^112

We investigate the effects of target deformation on the synthesis of superheavy nucleus 283^112 in the framework of the extra-push model. Our results show that the cross sections of the 3n evaporation residue in the 48^Ca 238^U reaction for the case of β2=0.275 are several times larger than those of β2=0. Meanwhile, the peak position of ER excitation function in the case of the deformed target is shifted to lower energy as compared to that of the spherical target.     

Large Decay Rate Variation of ^7Be in Pd and Au

Platinum and gold have the similar crystal structure but different electronic affinities, as well as different effective electron densities near the implanted ions. Both the differences favour larger decay rate of ^7 Be in Pd than that in Au. We measured the variation of the decay rate of ^7Be implanted in Pd and Au host materials. We have found that the decay rate of ^7 Be in Pd is larger than that in Au by 0.8%.     

Ion source effect on the bond length of ^4HeH^＋

The bond length of ^4HeH^＋ resulting from collision-induced destruction is measured at 1.4420 MeV using the Coulomb Explosion Technique. The measured bond length of ^4HeH^＋ is 0.094±0.003nm. The bond length of ^4HeH^＋ obtained with our radio frequency （RF） ion source is larger than that obtained with a duoplasmatron ion source at Argonne National Laboratory （ANL）, but the bond lengths of H^＋2 and H^＋3obtained separately by ANL and by us with the two different ion sources are consistent with each other, which implies that there exists an ion source effect on the bond length of ^4HeH^＋. The main reason why the 4^4HeH^＋ bond lengths obtained by the two different ion sources are different is also discussed.     

Isotope Dependence of Superheavy Nucleus Formation Cross Section

The dynamical process in the superheavy nucleus synthesis is studied on the basis of the two-dimensional Smoluchowski equation. Special attention is paid to the isotope dependence of the cross section for the superheavy nucleus formation by means of making a comparison among the reaction systems of ^54Re＋204pb, ^56Re ＋206Pb, and ^58Fe＋^208Pb. It is found by this comparison that the formation cross section is very sensitive to the conditional saddle-point height and the neutron separation energy of the compound nucleus. Reaction systems with lower height of conditional saddle-point and smaller neutron separation energy are more favourable for the synthesis of the superheavy nucleus.     

Temperature dependence of the photoluminescence of MnS/ZnS core–shell quantum dots

The temperature dependence of the photoluminescence（PL） from Mn S/Zn S core–shell quantum dots is investigated in a temperature range of 8 K–300 K. The orange emission from the ^4T1→^6A1transition of Mn^2＋ions and the blue emission related to the trapped surface state are observed in the Mn S/Zn S core–shell quantum dots. As the temperature increases, the orange emission is shifted toward a shorter wavelength while the blue emission is shifted towards the longer wavelength. Both the orange and blue emissions reduce their intensities with the increase of temperature but the blue emission is quenched faster. The temperature-dependent luminescence intensities of the two emissions are well explained by the thermal quenching theory.     

Characterization of the BaBiO3-doped BaTiO3 positive temperature coefficient of a resistivity ceramic using impedance spectroscopy with Tc=155℃

BaBiO 3-doped BaTiO3(BB-BT) ceramic,as a candidate for lead-free positive temperature coefficient of resistivity (PTCR) materials with a higher Curie temperature,has been synthesized in air by a conventional sintering technique. The temperature dependence of resistivity shows that the phase transition of the PTC thermistor ceramic occurs at the Curie temperature,Tc=155℃,which is higher than that of BaTiO3(≤130℃). Analysis of ac impedance data using complex impedance spectroscopy gives the alternate current (AC) resistance of the PTCR ceramic. By additional use of the complex electric modulus formalism to analyse the same data,the inhomogeneous nature of the ceramic may be unveiled. The impedance spectra reveal that the grain resistance of the BB-BT sample is slightly influenced by the increase of temperature,indicating that the increase in overall resistivity is entirely due to a grain-boundary effect. Based on the dependence of the extent to which the peaks of the imaginary part of electric modulus and impedance are matched on frequency,the conduction mechanism is also discussed for a BB-BT ceramic system.