Calculated half-lives and kinetic energies for spontaneous emission of heavy ions from nuclei

The most probable decays by spontaneous emission of heavy ions are listed for nuclides with Z = 47−106 and total half-lives > 1 μsec. Partial half-lives, branching ratios relative to α decay, kinetic energies, and Q values are estimated by using the analytical superasymmetric fission model, a semi-empirical formula for those α-decay lifetimes which have not been measured, and the new Wapstra-Audi mass tables. Numerous “stable” nuclides with Z > 40 are found to be metastable with respect to the new decay modes. The current experimental status is briefly reviewed.     

Beta-decay half-lives calculated on the gross theory

Beta-decay half-lives have been calculated by the use of the gross theory which was formulated by Takahashi, Yamada, and Koyama. Both allowed and first-forbidden transitions have been taken into account, and consideration also has been given to the possibility that all the transitions to the levels near the ground states may be highly forbidden. The Q-values used in the calculation have been taken from the mass formula of Myers and Swiatecki. The calculated half-lives are shown in the PLOTS together with the experimental data and the Q-values. The PLOTS cover all the isotopes between the proton-drip and neutron-drip lines with Z = 3 to Z = 100.     

Phenomenological formula for alpha-decay half-lives

A phenomenological formula is presented for the partial half-life from the Q value for α decay. It is constructed in a conventional way by considering the penetrability of a charged particle in a spherical Coulomb potential. Parameters in the formula are fixed because they are determined by physical constants except for the following three adjustable parameters: the product of the collision frequency of an α particle and the formation probability, N; the distance between the charge radius and the radius of an inner point of the Coulomb barrier, r ₀; and the odd-mass hindrance, h ₀. The values obtained for the three adjustable parameters are reasonable, in contrast with those of conventional models such as the Viola–Seaborg formula. The root-mean-square deviations from experimental partial half-lives for even–even, odd-A, and odd–odd nuclei are 0.344, 0.740, and 0.940 (in log₁₀), respectively. The obtained formula gives half-lives that are two or three times longer than those obtained using the Viola–Seaborg formula in the superheavy nuclear mass region.     

Nuclear half-lives for α-radioactivity of elements with 100 ? Z ? 130

Theoretical estimates for the half-lives of about 1700 isotopes of heavy elements with 100 ? Z ? 130 are tabulated using theoretical Q-values. The quantum mechanical tunneling probabilities are calculated within a WKB framework using microscopic nuclear potentials. The microscopic nucleus-nucleus potentials are obtained by folding the densities of interacting nuclei with a density-dependent M3Y effective nucleon-nucleon interaction. The α-decay half-lives calculated in this formalism using the experimental Q-values were found to be in good agreement over a wide range of experimental data spanning about 20 orders of magnitude. The theoretical Q-values used for the present calculations are extracted from three different mass estimates viz. Myers-Swiatecki, Muntian-Hofmann-Patyk-Sobiczewski, and Koura-Tachibana-Uno-Yamada.     

A mass table for 50 ≤ Z ≤ 118, 130 ≤ A ≤ 311 derived from nuclear energy systematics

The atomic masses for unknown heavy nuclides with Z = 50 – 118 and A = 130 – 311 have been derived from extrapolation of experimental nuclear energy systematics. Alpha-decay-energy systematics served as the primary basis for these extrapolations, while beta-decay and two-neutron separation-energy systematics were used as secondary bases. The 1971 Atomic Mass Evaluation of Wapstra and Gove provided the experimental input. Tabulations present atomic mass defects, alpha-decay Q-values, proton and neutron separation energies, and negatron-decay energies for each species.     

Systematics studies of (n, α) reaction cross sections at 14.5 MeV neutrons energy

A new semi-empirical formula for the calculation of the (n, α) cross-section at 14.5 MeV neutron energy is obtained. It is based on the pre-equilibrium exciton and evaporation models and uses the Droplet model of Myers and Swiatecki to express the reaction energy Q(n, α). The systematics behavior of the different terms of the Droplet model involved in Q(n, α) was checked individually before choosing the pertinent terms and setting up the formula. Fitting this formula to the existing cross-section data, the adjustable parameters have been determined and the systematics of the (n, α) reaction have been studied. The predictions of this formula are compared with those of the existing formulae and with the experimental data. The formula with five parameters is found to give a better fit to the data than the previous comparable formulae.     

CHARGE STATE DISTRIBUTIONS OF SWIFT HEAVY IONS BEHIND VARIOUS SOLID TARGETS (36 ≤Zp≤ 92, 18 MeV/u ≤E≤ 44 MeV/u)

Noting the lack of and the increasing need for information concerning heavy ion stripping in the intermediate velocity regime, we have studied a large number of ion-target systems experimentally. We present experimental charge state distributions obtained at the GANIL accelerator for several projectiles (36 ≤Z_p≤ 92) with energies ranging from 18 MeV/u to 44 MeV/u, emerging from various target foils (4 ≤Z_t≤ 79) of natural isotopic composition. The target thicknesses (from 1 μg/cm²up to several mg/cm²) are chosen to cover the pre- and post-charge-state equilibrium regimes. Charge state fractions, mean charge state, charge distribution width, and emerging ion energy are tabulated for each of the 107 projectile–target element–target thickness combinations. We also present an improvement of the semi-empirical formulae proposed by Baron et al. to predict the mean charge states and the distribution widths at equilibrium. These formulae are compared with the available experimental data.     

Dirac-Fock-Slater calculations for the elements Z = 100, fermium,to Z = 173

Listed here for the elements Z = 100, fermium, to Z = 173 are energy eigenvalues and total energies found from relativistic Dirac-Fock-Slater calculations. The effect of high ionization on the energy eigenvalues is presented for two examples. The use of these tables in connection with the energy levels of superheavy elements and molecular orbital (MO) x-ray transitions in superheavy quasiatoms, is discussed. In addition, a brief comparison between the results of the Dirac-Fock-Slater and Dirac-Fock calculations is given.     

Improved Formula for (<Emphasis Type="Italic">n</Emphasis>,<Superscript>3</Superscript>He) Fusion Reactions Cross Sections Using Optical Model

Non-elastic cross-sections have been calculated by using optical model for (n, ³He) reactions at 14–15 MeV energy. The new empirical formula including optical model non-elastic effects by fitting two parameters for the (n, ³He) reaction cross-sections have been suggested. The excitation function character and reaction Q-values depending on the asymmetry term effect for the (n, ³He) reaction have been investigated. The obtained cross-section formula with new coefficients has been compared with the experimental data and the other fitting formulae existed in the literature and discussed. It has seen that the fit of new formula in this paper is greatly improved with the experimental data.     

Determination of mass attenuation coefficients, effective atomic and electron numbers, mean free paths and kermas for PbO, barite and some boron ores

The total mass attenuation coefficients, μ_m, for PbO, barite, colemanite, tincal and ulexite were determined at 80.1, 302.9, 356.0, 661.7 and 1250.0 keV photon energies by using NaI (Tl) scintillation detector. Effective atomic number, Z_eff, effective electron number, N_eff, total atomic cross-section, σ_t, total electronic cross-section, σ_e, mean free path, mfp, and kerma relative to air were determined experimentally and theoretically. The theoretical mass attenuation coefficients were estimated using mixture rule. The calculated values were compared with the experimental values for all samples.     

Effective atomic and electron numbers of some steels at different energies

The effective atomic numbers (Z_eff) and effective electron density (N_e) for three different steels have been determined via the mass attenuation coefficients (μ/ρ). The mass attenuation coefficients have been calculated at the photon energy range of 1 keV–1 GeV and measured at the photon energies of 662, 1173 and 1332 keV. The measurement has been performed using a gamma spectrometer that contains a NaI(Tl) detector connected to Multi-Channel-Analyzer (MCA). The measured results of effective atomic numbers (Z_eff) and effective electron density (N_e) were found to be in good agreement with the calculations.     

Transition probability,B(E2)↑, from the ground to the first-excited 2+ state of even-even nuclides

Adopted values for the reduced electric quadrupole transition probability, B(E2)↑, from the ground state to the first-excited 2⁺ state of even-even nuclides are given in Table I. Values of τ, the mean life of the 2⁺ state, E, the energy, and β₂, the quadrupole deformation parameter, are also listed there. The ratio of β₂ to the value expected from the single-particle model presented. The intrinsic quadrupole moment, Q₀, is deduced from the B(E2)↑ value. The product E × B(E2)↑ is expressed as a percentage of the energy-weighted total and isoscalar E2 sum-rule strengths.Table II presents the data on which Table I is based, namely the experimental results for B(E2)↑ values with quoted uncertainties. Information is also given on the quantity measured and the method employed. The literature has been covered to January 1986.     

Transition probabilities for the alkali isoelectronic sequences Li I,Na I,K I,Rb I,Cs I,Fr I

Dipole transition probabilities, oscillator strengths, lifetimes (mean lives), and branching ratios derived from a numerical Coulomb approximation are presented for experimentally identified (and some extrapolated) states n ≤ 12, l ≤ 4 for each of the following members of the alkali sequences (Z_net is the net charge of the corresponding ion): Li I

$\text{Z}{}_{\mathrm{<mtext>net</mtext>}}$

=1–15,17–24 Na I

$\text{Z}{}_{\mathrm{<mtext>net</mtext>}}$

=1–24 K L

$\text{Z}{}_{\mathrm{<mtext>net</mtext>}}$

=1–7 Rb I

$\text{Z}{}_{\mathrm{<mtext>net</mtext>}}$

=1–6 Cs I

$\text{Z}{}_{\mathrm{<mtext>net</mtext>}}$

=1–5 Fr I

$\text{Z}{}_{\mathrm{<mtext>net</mtext>}}$

=2,4 The results are presented in transition diagrams and in tables giving energy-level values and transition wavelengths as well. An appendix on hydrogen results for 5 ≤ n ≤ 12, 4 ≤ l ≤ 11 is included to represent the high-angular-momentum states of all members of the alkali isoelectronic sequences.     

Semi-empirical systematics of (n,p) cross sections for 14.5 MeV neutrons

A new semi-empirical formula with five parameters has been derived to systematise the (n,p) cross section data of 14 MeV neutrons. It is based on the evaporation model and uses the Droplet model of Myers and Swiatecki to express the Q(n,p). The behaviour of the different terms of the Droplet model involved in Q(n,p) was checked individually before choosing the pertinent terms and setting up the formula. This relation leads to the lowest value of χ² compared with the existing formulas, when used to correlate the experimental σ(n,p) data for 161 nuclei with 39⩽A⩽209.     

Total stopping power formulae for high energy electrons and positrons

New simple empirical formulae for the total stopping power for electrons and positrons in matter have been derived from Wilson's theory. The formulae are valid for electrons and positrons in the energy region from 5 to 1000 MeV in absorbers of atomic number from Z = 1 to 92. Values of the total stopping power, obtained by the present approach are compared with the theoretical values recently reported by Berger and Seltzer, National Bureau of Standards, Report No. NBSIR 82-2550-A(1982). The presented formulae yield good approximate values of the total stopping power for electrons and positrons in matter within an accuracy of ± 10%.     

Steady-state radiative cooling rates for low-density,high-temperature plasmas

For 47 elements in the range 2 ≤ Z ≤ 92, steady-state radiative cooling rates, average charge states 〈Z〉, and mean-square charge states 〈Z²〉 have been calculated for low-density, high-temperature plasmas (n_e ? 10¹⁶electrons/cm³ and T = 0.002–100 keV). The average-ion model described in the Appendix was used. The 47 materials treated include many materials of interest in controlled fusion research. The results are presented in graphs and tables. The graphs show curves calculated from the model and least-squares polynomial fits to these curves. The tables present coefficients for the least-squares fits.     

Superallowed 0+ → 0+ and isospin-forbidden Jπ → Jπ fermi transitions

Experimental data on Q-values, β end-point energies, half-lives, and branching ratios pertaining to superallowed 0⁺ → 0⁺ β-transitions are complied and evaluated. Out of a total of eighteen $\text{J}$t values, seven are known to better than 0.3% accuracy. The weighted average of all values, $\text{J}$t = 3088.6 ± 2.1 sec, was employed to determine the effective vector coupling constant G′_v = (1.4115 ± 0.0005) × 10^?49 erg cm³. Experimental data on β-transitions between states of same spin but different isospin are also compiled and evaluated if they yield Fermi matrix elements. Information is obtained on isospin impurities of thirty-three nuclear states as deduced from β-decay experiments. The isospin impurities are extremely small, the largest being 0.05% reported for the ⁶⁴Ga ground state. The literature survey ended in April 1975.     

满壳层附近原子核α衰变性质的研究

利用有效液滴模型计算了Z=82和N=126及其附近原子核α衰变的半衰期,计算包含了基态→基态、基态→激发态、激发态→基态、激发态→激发态4种衰变模式,发现计算结果能很好地再现实验数据。这表明有效液滴模型可推广至满壳层附近奇异α衰变性质的研究,有助于人们利用该模型预言超重区的新幻数。另外,还对一些未知的原子核的半衰期进行了理论预言,供将来的实验参考。     

Measurement of hydrogen permeation due to atomic flux using permeation probe in the spherical tokamak QUEST

Particle retention and recycling in plasma fusion devices are generally associated with the diffusion of atomic hydrogen into the materials. The resulted permeation of atomic hydrogen is known as plasma driven permeation (PDP). This permeation may also be significant, even in the walls, which are not directly exposed to the plasma. Under similar conditions, the permeation flux (Γ_perm) of hydrogen through a 30 μm thick Ni membrane heated at 412-575 K has been measured in the spherical tokamak QUEST. Γ_perm is being measured during the scans of different operating parameters like RF power (P_RF), chamber pressure (P_chamber), discharge widths (τ_dis) and vertical magnetic field (B_Z). Simultaneously edge plasma density and spectral intensities of atomic (Balmer) lines and molecular (Fulcher) bands have been compared with the permeation measurements. A linear relationship has been established between the time integrated Γ_perm i.e. permeation fluence (Q_perm) and the time integrated H_α intensity i.e. H_α fluence (Q_α). Q_perm also shows a strong relationship with the edge plasma density and various spectral fluences. The obtained results are discussed for exploring the applicability of the permeation probes in measuring the atomic flux near the first walls.