Radiative strength functions in odd-A spherical nuclei

The radiative strength functions for the partial γ-transitions from neutron resonances to the ground and low-lying states of odd-A spherical nuclei are calculated within the quasiparticle-phonon nuclear model. The fragmentation of one-quasiparticle and quasiparticle-plus-phonon states is calculated. This allowed one to calculate γ-transitions between the one-quasi-particle components (valence transitions) and γ-transitions between the quasiparticle-plus-phonon and one-quasiparticle components of the wave functions. The energy dependence of the strength functions $\text{C}$(E1, η) and $\text{C}$(M1, η) is calculated near the neutron binding energy B_n for ⁵⁵Fe and ^{59, 61}Ni. The corresponding experimental data are described qualitatively. The contribution of the valence E1 transitions to the strength function is shown to be from 20% to 90%, and M1 transitions about 1%. The influence of the M1 giant resonance is important for M1 transition probabilities.     

Description of radiative strength functions in deformed nuclei

Radiative strength functions ofE1- andM1-transitions from ground states of doubly even deformed nuclei to states near the neutron binding energyB _n are calculated within the quasiparticle-phonon nuclear model. The wave functions of excited states include one- and two-phonon components. The calculations were made with the Pauli principle being or not included in the two-phonon components of the wave functions. It is shown that the radiativeE1- andM1-strength functions as well as the widths of giant dipole resonances in deformed nuclei are slightly influenced by the two-phonon components of the wave functions and they can be calculated in the RPA. Thek _E1- andk _M1-values are calculated for some deformed nuclei of the rare-earth and actinide region. The calculated values ofk _E1 are 1.5–2 times larger and the values ofk _M1 are somewhat less than the average values obtained in [14] from the analysis of available experimental data.     

Beta-delayed neutrons and high-energy gamma-rays from decay of137I

Beta-delayed neutrons and high-energyγ-rays following decay of¹³⁷I have been studied in order to characterizeβ-decay to and deexcitation of neutron-unbound levels in¹³⁷Xe. The totalγ-ray intensity observed accounts for at least 20% of theβ-intensity to levels aboveB _n . No evidence was found for neutron andγ-ray emission from the same levels. With the experimentalβ-strength function aboveB _n detailed tests were performed on the reproduction of the experimental neutron spectrum, the level density and Porter-Thomas fluctuations of the reducedβ-transition probabilities to highly excited states in¹³⁷Xe.     

Studies on the level structure of154Gd via the β-decay of154Eu nucleus

The excited states of¹⁵⁴Gd populated by theβ-decay of¹⁵⁴Eu (T _1/2=8.5y) have been studied. With a HPGe-NaI (T1) Compton suppression spectrometer and a HPGe-NaI(T1) coincidence circuitυ-ray singles spectra, coincidence spectra and theγ-γ directional correlational functions have been obtained. The deduced mixing ratios of multipolarities are presented. The energy levels and the relativeB(E2) values of the variousγ-transitions in¹⁵⁴Gd nucleus have been calculated both in the IBA model and it's extended version with boson surface delta interaction (BSDI).     

Excitons in monoclinic zinc diphosphide: Orthoexciton and polariton effects at n=1 resonance

Quantitative investigations of the hydrogen-like exciton B series in the absorption spectra of the β-ZnP₂ crystal for various wave vector directions and polarization states of radiation are conducted. It is shown that the B spectrum constitutes a single orthoexciton series with S-type envelope functions, and low-energy components in doublet lines belong to the S-type for lines in the series with n≥3. Polariton effects are clearly manifested at the B _n=1 exciton resonance, and Bouguer’s law is violated. The oscillator strength tensor components are determined for transitions to the exciton states of the B series, and the polariton parameters at the B _n=1 exciton resonance are calculated.     

Spin-orbit coupling and dissociation of CO2 molecules

Potential surfaces of the CO₂ molecule for the ground and excited ³ B ₂, ¹ B ₂ electronic states are calculated by quantum chemistry methods. The calculation of the spin-orbit coupling in the molecule shows a large the matrix element, which removes the prohibition for the dissociation-recombination process CO₂(X ¹Σ) + M ? CO(X ¹Σ) + O(³ P) + M. The barrier on the potential curve for ³ B ₂, the energy of which exceeds the limit of dissociation into components in the ground states, explains the data on the dissociation and recombination energies measured in experiments with shock tubes. The absorption cross section of CO₂ molecules in the UV spectral region measured at high temperatures allowed us to plot branches of potential curves near their minima for two upper singlet states assigned to the ¹ B ₂ and ¹ A ₂ symmetry.     

Semi-empirical analysis of magnetic moments of single-particle (or-hole) states around the 208Pb core

Magnetic moments of single-particle (or-hole) states around the ²⁰⁸Pb core were fitted by three state-independent parameters δg_l^(p), δg_l⁽ⁿ⁾ and α, where α is a parameter that is connected closely with δg_S and g_p. The analysis was performed under the assumptions that (i) the state-dependence of radial integral I((nl)²(n'l')²) involved in δg_s and g_p is calculated by the harmonic-oscillator potential, and (ii) δg_s is taken as being equal to ?4g_p, as expected from the δ-force type core polarization. An excellent fit was obtained when δg_l^(p) = 0.10(2), δg_l⁽ⁿ⁾ = ?0.05(1) and α = 1.2(1), which show that the main contributor to δg_s is the M1 core polarization and δg_l⁽ⁿ⁾ is certainly smaller than 0. B(M1)'s for allowed transitions calculated with the use of the same parameters as above are smaller than the observed B(M1)'s whereas α = 1.01(1) explains well the observed B(M1)'s.     

Effective charges for the unique first-forbidden β-transitions

The half-lives for the unique first-forbidden β-transitions in the vicinity of mass numbers A = 40 and A = 90 are obtained within the framework of the finite Fermi-system theory (FFST) using the nuclear wave functions calculated in the seniority scheme. The RMS deviation of the theoretical values of log fτ from the experimental ones is less than 0.1. This agreement with experiment enabled us to obtain the spin-isospin interaction constant g′₀ = 1.0 – 1.2 at C₀ = dn/d?_F = 300 MeV fm³ and the local charge e_qs = 0.8.     

Dipole resonances in the electroexcitation of the <Superscript>24</Superscript>Mg nucleus

The wave functions and form factors of E1 excited states of the deformed nucleus ²⁴Mg are obtained within the particle-core coupling version of the shell model by using spectroscopic data on direct nucleon-pickup reactions. A comparison of the calculated E1-strength distributions with experimental cross sections shows the validity of the theoretical approach used, which is based on connections between direct and resonance nuclear reactions.     

The Lorentz-Lorenz function of five gaseous and liquid saturated hydrocarbons

The refractive indices of compressed gaseous and liquid ethane, propane,n-butane,n-pentane, and liquidn-hexane were measured on up to seven isotherms at temperatures between 290 K and 500 K. Densities ranged from 0.2 g/cm³ to 0.7 g/cm³ at pressures up to 170 bar. The refractive index valuesn were combined with simultaneously measured density values ?, to compute the Lorentz-Lorenz function LL =(n ²-1)M/(n ²+2) ?=A _n+B_n(?/M), whereM is the molar mass andA _n andB _n are the first and second refractive index virial coefficients. Additionally, the functions LL/z (z=pV/nRT is the compressibility factor) of ethane, propane, andn-butane were computed to determine the second refractive index virial coefficientsB _n(T). The relative uncertainty of the measured LL functions is 0.1% in most cases. At constant temperature (LL?A _n)/A_n is ≦5·10^?3 for ethane, propane, andn-butane and ≦0.02 forn-pentane andn-hexane. The greatest deviations of the LL functions from theA _n value were measured at the temperatures near the critical points. TheA _n-values show a temperature dependence which increases with increasing molar mass (maximum value: ΔA _n/ΔT=0.0044 cm³/mol · K). The slopes of the LL-function become lower and the LL maxima become smaller with increasing distance of the temperature from the critical point. TheB _n values increase linearly with reciprocal temperature.     

Investigation of states in 30P via the 30Si(3He,t)30P reaction at 30 MeV

The ³⁰Si(³⁰He, t)³⁰P reaction has been measured for about 100 levels in ³⁰P with E_x < 8.8 MeV. Little selectivity in the population of states has been observed. For 75 levels angular distributions have been analysed using a “fingerprint method” by determining the L-value from a comparison in shape with transitions to states with known J^π. For possible mixed L-transitions a dominance of the higher L-value is observed for almost all cases. Coulomb displacement energy calculations utilizing shell-model wave functions have been used to identify T = 1 states.     

Systematics of neutron emission probabilities from delayed neutron precursors

A simple correlation based on the gross theory ofβ-decay is derived between the neutron emission probabilitiesP _n of delayed neutron precursors, theirβ-decay energies and the neutron binding energies of the daughter nuclei. The correlation is shown to be valid for delayed neutron precursors among the fission products. TheP _n-values of several expected but still unidentified neutron precursors are estimated together with their contributions to the delayed neutron groups in thermal-neutron induced fission of²³⁵U. Some aspects of theβ-strength function for transitions into highly excited states are discussed.     

Energy values for the H+2 ion in superstrong magnetic fields using the adiabatic approximation

Energy values, equilibrium internuclear separations, and zero-point energies of nuclear vibrations parallel to the magnetic field are calculated for the lowest states of the H⁺₂ ion in magnetic fields B?10⁶ T (characteristic of neutron stars) using numerical wave functions that are products of Landau states and arbitrary z-dependent functions, thus improving on previous estimates of variational or LCAO type, which have been obtained in the high-field regime.     

Beta-delayed neutron emission from93–100Rb to excited states in the residual Sr isotopes

Beta-delayed neutron emission from the precursors^93–100Rb to excited states in the residual nuclei^92–99Sr has been measured by means ofγ-ray and neutron spectroscopy. In general, considerable neutron feeding of excited final states is observed. The experimental branching ratios (P _n ⁱ ) are compared to predictions from statistical model calculations. It is demonstrated that the main parameter affecting theP _n ⁱ -values is the shape of theβ-strength function (S _β). For several Rb isotopes hindrance, respectively enhancement of neutron branches to specific final states is observed giving evidence for the persistence of intermediate structure of the neutron-emitting states. By the example of⁹⁸Rb it is shown that a few integralβ-delayed neutron properties may be sufficient to derive first estimates on the real shape ofS _β above the neutron binding energy. This result is of importance for exotic nuclei where detailed spectroscopic investigations are precluded.     

High spin states in205Pb and a precision test of the nuclear shell model for three nucleons

Using the²⁰⁴Hg(α, 3n) reaction withα-particles of about 40 MeV, we have proved by applying nowadays conventionalγ-ray spectroscopy in-beam technique, that there are two isomeric states in²⁰⁵Pb at the excitation energies 5,161.3 and 3,195.5 keV having the half-lives 71±3 and 217±5 ns, respectively. These isomeric states have spins and parities 33/2⁺ and 25/2^? and are mainly due to thei ₁₃ ^2/?3 andi ₁₃ ^2/?2 p ₁ ^2/?1 configurations, respectively. This conclusion is supported by the experimentalg-factors of these states being ?0.159±0.008 and ?0.0676±0.0011, respectively. It is furthermore shown that theE2 effective neutron charge is the same forE2 transitions from the 33/2⁺ state in²⁰⁵Pb and from the 12⁺ state in²⁰⁶Pb as required by the assumption that the²⁰⁸Pb core is responsible for the totalE2 strength of the neutron holes, and that these states are due to thei ₁₃ ^2/?3 andi ₁₃ ^2/?2 configurations. The calculatedB(E3) values ofE3 transitions from isomeric states in²⁰⁵Pb and²⁰⁶Pb agree reasonably well with the experimental values as expected from the assumption that theE3-strength should come from particle coupling to the octupole states of the²⁰⁸Pb core. The energies of the six most well established excited states in²⁰⁵Pb with angular momenta in the region 19/2–33/2 were calculated using empirical single-particle energies, empirical two-particle interactions and angular momentum algebra. The average deviation between experimental and calculated energies is ?3 keV and the root mean square deviation 6 keV as compared to the uncertainty ± 5 keV in the nuclear masses used in the calculation. For the orbits concerned the shell model is thus valid with an extremely high precision. The contribution of effective three-particle interaction in these orbits must consequently be less than about 5 keV.     

High-resolution (e,e') study of isovector M1 and M2 transitions in the oxygen isotopes: (I). 16O

The M1 and M2 transition strength distribution for ¹⁶O in the excitation energy range from 16 to 20 MeV has been measured in a high-resolution electron scattering experiment. The M1 strength is concentrated in three sharp states at E_x = 16.22, 17.14 and 18.79 MeV (± 0.01 MeV) with B(M1, k)↑ = 0.20 ± 0.02, 0.32 ± 0.03 and 0.13 ± 0.03 μ_N², respectively. An additional strength of 0.35 ± 0.09 μ_N², distributed over eight weakly excited states with excitation energies E_x = 17.4 to 18.0 MeV, brings the total measured M1 strength to B(M1, k)↑ = 1.0 ± 0.1 μ_N². The experimental M2 strength is distributed over states at E_x = 16.82, 17.78, 18.50 and 19.0 MeV (± 0.01 MeV) with B(M2, k)↑ = 19 ± 2, 13 ± 2, 59 ± 7 and 341 ± 51 μ_N² · fm², respectively. Electric transitions were also measured to states at E_x = 16.45 MeV (2⁺, E2), 17.30 MeV (1⁺, E1) and 18.20 MeV (2⁺, E2). Calculations were performed using the modified surface delta interaction in a 2p-2h shell model for the M1 transitions and the random phase approximation for the M2 transitions. The results show the sensitivity of the M1 strength as a measure of ground-state correlations and compare well with results from the ¹⁵N($\text{p}$, γ) reaction.     

Tentative level diagram of146Pm below 1.1 MeV

The level scheme of the doubly odd nucleus¹⁴⁶Pm was investigated by means of in-beam spectroscopy. The¹⁴⁶Nd(p, n) reaction in the 3.5–8 MeV proton energy interval on enriched targets has been used to populate the exited states of¹⁴⁶Pm. High resolutionγ-ray spectra using Ge(Li) and hyperpure Ge detectors and conversion electrons with a mini-orange spectrometer were measured. Withγ-exitation functions andnγ-coincidences usingnγ-discriminated NE231 neutron detectors transitions in¹⁴⁶Pm were identified,γγ-coincidences gave information aboutγ-cascades. With these data a level scheme of 38 levels below 1.1 MeV exitation energy has been deduced including 73 transitions. For 12 transitions experimental conversion coefficients have been evaluated, which agree with the expected values forM1/E2-transitions.     

The vertical spectrum of H2CO revisited: (SC)2-CI and CC calculations

The vertical electronic spectrum of formaldehyde has been studied by means of (SC)²-MR-SDCI and CCLR methods. Two basis sets of atomic natural orbitals (ANOs) complemented with a one-centre series of Rydberg orbitals were used. The first was taken from the CASPT2 study by Merchán, M., and Roos, B. O., 1995, Theoret. Chim. Acta, 92, 221, and may be described as C,O[4s3pld]/H[2slp] with a lslpld Rydberg series centred in the charge centroid of the ²B₂ state of the cation. The second was a larger basis set that may be described as C,O[6s5p3d2f]/H[4s3p2d] + 3s3p3d in the same centre. The (SC)² dressing may be applied efficiently to an MR-SDCI method and comparison with the dressed CAS-SDCI is satisfactory, in spite of the remarkable reduction in the CI space dimension. The consistency of the (SC)²-MR-SDCI results was tested also against the CCLR and CASPT2 results using the same basis sets and against the CCLR results using Dunning's aug- and daug-cc-pVQZ basis sets. The ³A₁(π → π *) state is correctly placed as the second excited triplet while the highly multi-configurational nature of the ¹A₁(π → π *) state is confirmed as well as its greatly mixed valence-Rydberg nature. This state is predicted as lying under the 10 eV level, on top of the (n_y → 3d) Rydberg states that are predicted in the 8.9–9.5eV region. The 5 ¹B₂(n^y → 4s) Rydberg state and the ¹B₂(σ_y → π*) also are predicted in this region. The triplet states also were calculated with the (SC)²-MR-SDCI method. The vertical ordering of the 2 ¹A₁(n_y → 3p_y) and 2 ¹B₂(n_y → 3p_z) states is discussed, as well as that of the ¹B₁(σ → π*) and the Rydberg ¹B₁(n_y → 3d_xy) states. This work shows the highly reliable values that may be reached applying the dressing method along with a large basis set. Such a procedure is made possible using an MR-SDCI selection of spaces instead of the CAS-SDCI that was used up to now in most (SC)² dressing applications.     

Highly excited spin-1 states in 88Sr by the (γ, γ) reaction

The resonant scattering of bremsstrahlung γ-rays by a SrCO₃ target has been studied for γ-ray energies of 5–11 MeV. Six γ-transitions of energies between 6–8 MeV, which indicate six resonant states in ⁸⁸Sr, were observed. The relative intensities of the resonantly scattered γ-rays at 125 and 150° were found to be compatible only with the assignment of spin 1 to the six states. Radiative widths of the resonant states were deduced. The possibility that these states are components of the giant M1 resonance in ⁸⁸Sr is discussed.