Energy levels of the nucleus248Bk

The ambiguities and contradictions in presently available experimental information on the energy levels of the doubly odd deformed nucleus²⁴⁸Bk are sought to be cleared through calculation of the band head energies of the two-particle states based on evaluation of the residualn-p interaction energy for a zero range interaction. The applicability of the Gallagher-Moszkowski rule for the relative ordering of the spin triplet and singlet states is critically examined. It is concluded that the 8^? state from the {7/2⁺[633]p; 9/2^?[734]n configuration is the long lived isomer and forms the ground state of this nucleus. The 1^? state of the same configuration is the short lived isomer and an excited state in accordance with the GM rule and so is the 6⁺ state of the {3/2^?[521]p; 9/2^?[734]n configuration. The expected location of 20 two particle states comprising 10 GM pairs is calculated and compared with the available experimental information.     

Energy levels of the nucleus 250Bk from residual interaction studies

The bandhead energies of twenty two-quasiparticle states expected to occur in the low-energy excitation spectrum of the doubly odd nucleus ²⁵⁰Bk are calculated using a zero-range residual interaction and the results are compared with the available experimental information. Configuration assignments to nine intrinsic states reported in earlier studies are confirmed. Our calculations support the excitation energy of 115 keV for the K^π = 3⁺ state and also the characterisation of the 317 keV 5⁺ state as the K^π = 5⁺ bandhead. In addition, we suggest acceptable two-particle configurations for the 175 keV 1⁺ state and the 216 keV 0⁺ state. The expected location of eight as yet unobserved two-quasiparticle states is predicted.     

Low-lying intrinsic energy levels in the nucleus170Ho

The band-head energies of the two-quasiparticle states expected in the doubly odd deformed nucleus¹⁷⁰Ho are calculated for a zero range residual interaction. The results are compared with the available experimental information. It is concluded that the ground state has the Nilsson configuration 6⁺{7/2^?[523↑] _p }+5/2[512↑] _n being the 2.76m isomer whereas the 43s isomer is the 1⁺ ∑=0 state arising from the same configuration and lies at about 100 keV excitation energy in agreement with the experiment. The first excited state in this nucleus is predicted to be the 4^?{3/2⁺[411↑] _p +5/2^?[521↑] _n } state close to the ground state with the corresponding 1^? ∑=0 member expected to appear well above the 1⁺ isomer.     

Study of low-lying states in151Eu via (n,n′γ) reaction

The levels of¹⁵¹Eu have been investigated in the (n,n′γ) reaction using nuclear reactor fast neutrons. The energies, intensities and angular distributions of theγ-rays have been measured with the Ge(Li) spectrometer. Four rotational bands with the following band heads and Nilsson configurations have been identified: ground state band, 5/2⁺ [402]; 21.5 keV, 7/2⁺[404]; 196.5 keV, 3/2⁺[411]; 260.5 keV, 5/2⁺[413]. The low spin states at 332.2 and 336.2 keV have been tentatively assigned to the l/2⁺[411] Nilsson orbital, but 522.8, 580.0 and 587.0 keV states to the 1/2⁺[420] Nilsson orbital. The negative parity levels at 353.7, 522.1 and probably 546.2 keV have been proposed basing on theh _11/2 proton state.     

States in 163Dy and 169Er populated in the (t,p) reaction

Angular distributions of protons from the ¹⁶¹Dy(t, p)¹⁶³Dy and ¹⁶⁷Er(t, p)¹⁶⁹Er reactions were studied, using 15 MeV and 17 MeV tritons from the McMaster University tandem Van de Graaff accelerator. The reaction products were analyzed with a magnetic spectrograph and detected with nuclear emulsions. Since the ¹⁶¹Dy target ground state is the $\text{5}\text{2}$⁺[642] orbital, a strong L = 0 transition was observed to the $\text{5}\text{2}$⁺[642] bandhead in ¹⁶³Dy, which was previously assigned at 251 keV. Also transitions to the $\text{7}\text{2}$, $\text{9}\text{2}$ and $\text{11}\text{2}$ band members were observed. Similarly, a strong L = 0 transition was observed to the $\text{7}\text{2}$⁺[633] bandhead at 244 keV in ¹⁶⁹Er, with the other band members only weakly populated. The angular distributions to the various members of these two bands can be described when higher-order reaction processes are taken into account. In ¹⁶³Dy, surprisingly strong L = 0 transitions were observed to levels at 1831 keV, 1937 keV and 2053 keV, with strengths of 23%, 30% and 37% of that for the $\text{5}\text{2}$⁺[642] bandhead. In ¹⁶⁹Er, the 905 keV level was populated with an L = 0 transition that had 31% of the strength observed for the strong L = 0 transition to the 244 keV level. The nature of these states is at present not understood.     

On the level scheme of the159Tm nucleus

Level in¹⁵⁹Tm have been excited in the¹⁵⁰Sm(¹⁴N,5n reaction. The yrast band 7/2^?[523] observed up to spin 45/2^? is built on a isomeric state at 166 keV (T _1/2=37±5ns). Connections between the 7/2^?[523] and 7/2⁺ [404] bands fix the band-head energies.     

Multi-quasiparticle isomers and rotational bands in 178W

The high spin structure of the nucleus ¹⁷⁸W has been studied following the ¹⁷⁰Er(¹³C,5n) reaction. Many previously unidentified rotational bands are seen based on high-K, 2-, 4-, 6- and 8-quasiparticle structures, some of which are isomeric. The excitation energies of the multi-quasiparticle bandheads are compared with BCS calculations, including residual interactions. The bands show substantial increases in moments-of-inertia with increasing quasiparticle number. These are examined in terms of pairing blocking. The effect of blocked pairing is also taken into account in the calculation of g-factors, which supports the configuration assignments. The K^π = 25⁺, 8-quasiparticle band forms the yrast line from its bandhead upwards. This bandhead is a 220 ns isomer whose decay is strongly hindered, compared to the decay of the four- and six-quasiparticle structures.     

Coulomb displacement energies of the T = 1, J = 0 states of A = 42 nuclei

Coulomb displacement energies of the T = 1, J = 0⁺ and 6₁⁺ states of A = 42 nuclei are analyzed with previously known charge dependent forces and effects, and with the available HartreeFock single-particle wave functions. From the study of the Coulomb displacement energies of the 6₁⁺ states, it is found that the present knowledge on the charge dependence, including a phenomenological charge symmetry breaking force previously introduced so as to help explain the Nolen-Schiffer anomaly, gives a sufficient and consistent explanation for both single-particle and twoparticle systems. From the study of the 0⁺ states, we found that the Coulomb displacement energies of the second 0₂⁺ states can be explained with a compensation between the smaller Coulomb energies of the second lowest two-particle state and larger ones of the deformed 4p-2h state.     

High-spin states in odd-odd 168Lu

High-spin states in the odd-odd ¹⁶⁸Lu nucleus, populated in the ¹⁵⁴Sm(¹⁹F,5n) reaction at a beam energy of 96 MeV, were investigated using in-beam γ-ray spectroscopy techniques. The BC neutron crossing in the yrast band, based on πg _7/2[404]7/2⁺⊗νi _13/2[642]5/2⁺ configuration, occurs at ħω= 0.31 MeV. The two side bands, based on πh _11/2[514]9/2⁻⊗νi _13/2[642]5/2⁺ and πh _9/2[541]1/2⁻⊗νi _13/2[642]5/2⁺ configurations, show anomalous signature-splitting and signature-inversion in the first one, to occur at ħω= 0.24 MeV. A moderately delayed BC-crossing is anticipated in the second one. Received: 15 June 1998 / Revised version: 11 January 1999     

Neutroneneinfangs-Gammaspektrum und Niveauschema von Erbium 167

The (n, γ)-spectrum of Er 167 was investigated by means of the Risø bent crystal spectrometer. The energies and intensities of 47 transitions were measured. 22 of them were fitted into a level scheme. The rotational bands of theK=7/2⁺[633],K=1/2^?[521], andK=5/2^?[512] states were found up to the spin valuesI=11/2⁺, 9/2^?, and 7/2^?. Gammavibrational states of these Nilsson orbitals were determined or proposed. The energy of theK=5/2^?[523] state was suggested. Branching ratios of gamma transitions were compared with theoretical predictions.     

Fragmentation of polyatomic ions produced by electron-loss collisions of butane and isobutane molecules with ions of kiloelectronvolt energy

Fragmentation accompanying the loss of electrons by butane and isobutane (C₄H₁₀) molecules in collisions with energy H⁺, He²⁺, and Ar⁶⁺ ions of kiloelectronvolt energies is studied. The electron density functional technique is applied to C _n H_2n+2 alkane molecules and their respective C _n H _2n+2 ⁺ ions to carry out quantum-chemical calculations of the atomic spacing, electron total energy for the initial configuration of the ionizing molecules and ions in the ground state, and atomic bond breaking energy necessary to produce different ion fragments. The fragmentation energy is correlated with the fragmentation probability. It is shown that the relative cross sections of ion fragmentation depend primarily on the related energy consumption. However, the process cross section is also strongly affected by the initial configuration of C₄H₁₀ isomer molecules, as well as by the amount of dangling and arising atomic bonds involved in the formation of each ion fragment.     

Self-consistency in the projected shell model

The projected shell model is a shell-model theory built up over a deformed BCS mean field. Ground state and excited bands in even-even nuclei are obtained through diagonalization of a pairing plus quadrupole Hamiltonian in an angular momentum projected 0-, 2-, and 4-quasiparticle basis. The residual quadrupole-quadrupole interaction strength is fixed self-consistently with the deformed mean field and the pairing constants are the same used in constructing the quasiparticle basis. Taking ¹⁶⁰Dy as an example, we calculate low-lying states and compare them with experimental data. We exhibit the effect of changing the residual interaction strengths on the spectra. It is clearly seen that there are many J^π = 0⁺, 1⁺, 4⁺ bandheads whose energies can only be reproduced using the self-consistent strengths. It is thus concluded that the projected shell model is a model with essentially no free parameters. The predicted energy of the 2⁺ bandhead lies however in nearly twice the experimental value.     

Interaction strength and shape difference for the h9/2 and h11/2 configurations in163Tm

The strongly shape driving πh_9/2[541]l/2^? configuration with α=+1/2 exhibits some anomalous, and so far unexplained, features concerning the crossing frequency, ?ω_c, the aligned angular momentum, i_x, and interaction strength, at the alignment of the first pair of i_13/2 quasineutrons in several odd-Z rare earth-nuclei. The h_9/2[541]1/2^? and h_11/2[523]7/2^? bands have been studied in the stably deformed rare-earth nucleus¹⁶³Tm to investigate these features. A difference in band crossing frequency of ～ 80 keV between the two bands is found. Rotational bands built on these two configurations have been found to cross in the spin range I=25/2–29/2 ?. Theγ-decay pattern between the two bands is established in the crossing region and analysed in terms of a moderate shape difference between them. A theoretical estimate of the size of the interaction strength between the two bands is presented and compared to the experimental value. The observed band structure in¹⁶³Tm is very similar to that of¹⁶⁷Lu which has 2 protons and 2 neutrons in addition. This observation is discussed in relation to the similarity of the yrast bands of the two even-even “core” nuclei¹⁶²Er and¹⁶⁶Yb, for which theγ-transition energies are identical within ～0.2 keV below the vi_13/2 crossing.     

Energy levels of a two-dimensional anharmonic oscillator: Hill determinant approach

The energy levels of the Schrödinger equation for the potentialx ²+y ²+λ[a _xxx⁴+2a _xyx² y ²+a _yyy⁴] are calculated using Hill determinant approach for several eigenstates and over a wide range of values of perturbation parameters. The obtained numerical results agree with those previously reported by other methods.     

Anomalous shift in crossing frequency for the proton 1/2[541] band in175Ta

High-spin states in¹⁷⁵Ta have been populated in the¹⁶⁰Gd (¹⁹F,4n)¹⁷⁵Ta reaction with beams provided by the HI-13 tandem accelerator at the Institute of Atomic Energy in Beijing. A level scheme was constructed from γ-γ coincidence experiments. Seven decay sequences built on 5/2⁺[402], 1/2^?[541], 7/2⁺[404] and 9/2^? [514] proton Nilsson configuration have been extended to higher spin. An anomalously large delay of the neutron AB crossing built on the h_9/2 proton Nilsson State 1/2^?[541] is discussed.     

Local-potential approximation for the Brueckner G matrix and problem of optimally choosing model subspace

The validity of the local-potential approximation, which was proposed previously for the singlet-pairing problem in semi-infinite nuclear matter, is investigated in the Bethe-Goldstone equation for the Brueckner G matrix. For this purpose, use is made of the method developed earlier for solving this equation for a planar slab of nuclear matter in the case of a separable form of NN interaction. The ¹ S ₀ singlet and the ³ S ₁+³ D ₁ triplet channel are considered. The complete two-particle Hilbert space is split into a model and the complementary subspace that are separated by an energy E ₀. The two-particle propagator is calculated precisely in the first subspace, and the local-potential approximation is used in the second subspace. With an eye to subsequently employing the G matrix to calculate the Landau-Migdal amplitude, the total two-particle energy is fixed at E=2μ, where μ is the chemical potential of the system under consideration. Specific numerical calculations are performed at μ=?8 MeV. The applicability of the local-potential approximation is investigated versus the cutoff energy E ₀. It is shown that, in either channel being considered, the accuracy of the local-potential approximation is rather high for E ₀≥10 MeV.     

Proton states in193Ir and195Ir populated via the (α) reaction

The nuclear structures of¹⁹³Ir and¹⁹⁵Ir have been studied using the¹⁹⁴Pt(t, α) and¹⁹⁶Pt(t, α) reactions. Levels up to ～2MeV in excitation energy were studied with a resolution of ～13keV (FWHM) and spectroscopic strengths were extracted. The low-lying states in¹⁹³Ir have been interpreted in terms of both the Nilsson and the rotation-vibration models including Coriolis, particle-vibration and rotation-vibrational couplings. The previously assigned 3/2⁺ [402], 11/2^? [505], 1/2⁺[400] and 1/2⁺[411] bands were populated and candidates for the 5/2⁺ [402] and 7/2⁺ [404] bandheads were observed. TheK ₀ +2 gamma vibration based on the ground state was populated because it is mixed with the 7/2⁺ [404] state. Surprisingly, there was no significant difference between the stripping and pick-up strengths for the low-lying states in¹⁹³Ir, suggesting that the equilibrium nuclear shape of¹⁹³Ir has large overlaps with the shapes of both¹⁹²Os and¹⁹⁴Pt. The nuclear level structure of¹⁹⁵Ir appears to be similar to those of the lighter iridium isotopes.     

New rotational bands in 174Ta

Three new bands in ¹⁷⁴Ta have been identified by using the ¹⁶⁰Gd(¹⁹F,5n) reaction at beam energies of 87 MeV and 96 MeV. Nilsson configurations are assigned to these bands. In the 9/2⁻[514]_p+5/2⁻[512]_n band, the AB neutron crossing occurs at a rotational frequency of 0.30 MeV. This is indicative of the disappearance of the evidence for a reduction in neutron pair correlations. Received: 30 March 1998     

Structure of the mirror nuclei21Ne and21Na

Theγ-decay of levels in²¹Ne up to 10 MeV excitation energy has been investigated byn — γ coincidence measurements initiated with the¹⁸O(α, nγ) reaction at 12, 13, 14.5 and 15.4 MeV bombarding energies. Spin(-parity) assignments of excited states are obtained by combining then — γ angular correlation measurements performed atE _α=11, 11.82 and 13.6 MeV with a consideration of lifetimes, neutron penetrabilities of the unbound states, and information from the mirror nucleus²¹Na. The resulting values of E_x[keV]?J ^π are as follows: 4525-5⁺, 4686-3⁺, 5431-7⁺, 5549-3⁺, 5819-7^?, 6175-7⁺, 6268-9⁺, 6550-9, 6639-9, 7006-7⁺, 7041-9, 7356-7 or 9, 7422-11^(?), 7648-7⁺, 7981-11 or (7⁺), 8154-9, 8240-11, 8664-9^? or 11 or 13^?, 9401-13^?, 9867-13^? or 15⁺, 9941-13^? or 15 or 17⁺. The assignment of mirror levels in²¹Ne —²¹Na has been extended to the 6175 keV level of²¹Ne. Excitation energies, electromagnetic properties, Gamow?Teller matrix elements and spectroscopic factors of positive parity states are compared with the results of shell-model calculations which employ a unifieds—d shell Hamiltonian and the unrestricted configuration space of the 0d _5/2 —1s _1/2—0d_3/2 shell. Collective properties contained in shell model wave functions are explored up to the termination of bands atJ=17/2 or 19/2. The spectrum of intruder states in²¹Ne is observed to begin with a 5628 keV,J ^π=7/2⁺ state. The 7422, 8664 and 9401 keV levels are assigned as members of previously established negative-parity rotational bands.     

Study of alkyl chain length dependent characteristics of imidazolium based ionic liquids [CnMIM]+[TFSA]− by Brillouin and dielectric loss spectroscopy

This study examined the acoustic phonon mode of ionic liquids consisting of 1-alkyl-3-methyl-imidazolium family (C_nMIM) cations with n values ranging from 2 to 10 and bis(trifluoromethylsulfonyl)amide (TFSA) anion in the temperature range from 300 K to 100 K. [C_nMIM]⁺[TFSA]^? showed depolarized (VH) components of Brillouin peaks at temperatures below the glass transition temperature when n is larger than 4. On the other hand, in the case of ionic liquids with different anions, such as [C₄MIM]⁺[BF₄]^?, [C₄MIM]⁺[PF₆]^? and [C₈MIM]⁺[BF₄]^?, the VH component of Brillouin peaks was not observed in the temperature range investigated. The dielectric loss spectra showed that the temperature dependence of alkyl chain domain relaxation of all ionic liquids followed the Arrhenius law and showed an increase in activation energy at the temperature where the VH component of Brillouin peak appeared. These results suggest that the observed depolarized component of Brillouin peak might originate from uniquely induced polarization in the 2nd domain composed of head groups of cations and anions.