Weak-coupling expansion of the low-lying energy values in the SU(2) gauge theory on a torus

Relying on analytic results obtained previously, we complete the one-loop computation of the low-lying energy values of the SU(2) gauge theory in an L × L × L periodic box. The expansions are then rewritten in terms of the universal parameter z = M(0⁺) · L (M(0⁺): energy gap in the J^p = 0⁺ sector). We find that the crossover from small-volume to large-volume behaviour is likely to take place at z ? 2. Furthermore, near the crossover, the lowest energy levels (above the ground state) in the 0⁺ sector and the 2⁺ sector are practically degenerate. In each of these sectors there is one more state at about 1.5 · M(0⁺). In the 0^? sector, on the other hand, the lowest energy value is greater than 3 · M(0⁺).     

α + 12C scattering at 110 MeV: Has exotic 7.65 MeV Hoyle’s state signatures “alpha-condensate” structure?

We present new measurements of the α + ¹²C elastic and inelastic (to the states 4.44, 7.65, and 9.64 MeV) scattering at E _lab = 110 MeV in the wide angular range from ～10° to 175°, which enable us to examine the condensate and cluster properties of the low-lying excited states in ¹²C. We present the diffraction-radius analysis of our data together with a considerable amount of the existing data. The magnitudes of the diffraction radii for the ground and the first excited (4.44 MeV) states are found to be equal, whereas they appear to be enhanced by ～0.6 fm both for 7.65 and 9.64 MeV states. This result shows that the radius of the Hoyle’s 0 ₂ ⁺ , 7.65 MeV state in ¹²C is by a factor of ～1.2–1.3 larger than that of the ground state. It is demonstrated that the direct transfer mechanism of ⁸Be dominates at the largest angles in all four reactions reported here. The configuration corresponding to the transfer of ⁸Be in its ground state (I ^π = 0⁺) with L = 0 turns out to be the most important for the 7.65 MeV state of ¹²C. Evidence of existence of some features of α-condensed structure of the Hoyle’s 0 ₂ ⁺ state in ¹²C was obtained: its enhanced radius and large contribution of α-particle configuration with L = 0.     

Application of the symplectic shell model to the L = 0+ states of 4He

The nature of the low-lying L = 0⁺ states of ⁴He is analyzed in the framework of the symplectic shell model. A generator coordinate method for microscopic calculations is used to diagonalize the Brink and Boecker force, B1, in the space defined by the 0ħω and 4ħω irreps of spatial symmetry [f] = [4] and the 2ħω irrep of symmetry [22]. A mixed Sp(3, R) calculation is also attempted. Results show that the first L^π = 0⁺ excited state is a vibrational excitation of the ground state.     

The valence states of NO+

Spectroscopic constants for the eight lowest electronic states of the NO⁺ ion are tabulated. These constants result from reanalysis of previously reported optical and photoelectron spectra and interpolation from corresponding states of the isoelectronic molecules CO and N₂. Similar spin-orbit perturbations of the A¹Π states of NO⁺ and CO are compared. An interpretation is given of previously reported emission from a beam of long-lived states of NO⁺. The intensities of ionizing transitions from NO X²Π (v = 0) observed in photoelectron spectra are compared with calculated Franck-Condon factors.     

High-spin states of 26Mg populated in the 12C(18O, α) reaction

The structure of ²⁶Mg has been investigated by means of the ¹²C(¹⁸O, α) reaction. Several previously unknown states were populated between excitation energies of 0 to 16 MeV. Excitation functions were measured for 126 states for bombarding energies between 43.2 and 45.9 MeV in 300 keV steps at a lab angle of 7°. The experimental energy averaged differential cross sections were compared with statistical model calculations and good agreement was obtained for the states whose spins and parities were previously established. The statistical model calculations were used to suggest the spins and parities for the rest of the states. In particular, candidates for 6⁺ and 8⁺ states were interpreted as members of three rotational bands in ²⁶Mg: the ground-state band, the K = 2⁺ band based on the 2.938 MeV 2⁺ state, and a K = 0⁺ band based on the 3.588 MeV 0⁺ state. Back bending of the yrast band is observed and it is suggested that it may be due to band crossing of the ground-state and first excited K = 0⁺ bands.     

Non-yrast states and shape co-existence in light Pt isotopes

Low-lying states in the even-even light platinum isotopes ¹⁷⁶Pt, ¹⁷⁸Pt, ¹⁸⁰Pt and ¹⁸²Pt have been populated using β⁺ /EC decay from parent gold nuclei, created in (HI,xn) reactions. State energies, spins and parities and γ-ray branching ratios were determined using γ-ray and electron spectroscopy. Whereas non-yrast states were observed in ¹⁷⁸Pt, ¹⁸⁰Pt and ¹⁸²Pt, none were seen in ¹⁷⁶Pt. The excitation energies of the observed states are analysed in terms of a band-mixing model, yielding the moments of inertia of the unperturbed bands. Branching ratios and ground-state-band quadrupole moments are calculated and compared with experimental values. The results indicate that the two lowest-lying 0⁺ states in each of the light Pt isotopes are formed from the mixing of two intrinsic states of different deformation, and other low-lying states can be described as admixtures of rotational states built on these intrinsic states, and on γ-vibrational states.     

Two-nucleon T = 0 transfer reactions in the 0p shell

The ¹⁶O(d, α)¹⁴N, ¹⁴N(d, α)¹²C and ¹²C(d, α)¹⁰B reactions at E_d = 40MeV and the ¹²C(α d)1¹⁴N at E_α = 55 MeV were investigated. A total of seventeen transitions are analysed in terms of one-step, zero-range DWBA calculations, using the two-particle coefficients of fractional parentage obtained from the Cohen-Kurath Op shell wave functions. For most transitions, fair agreement is obtained between experiment and calculation, possible exceptions being the transition to the E_x = 4.43 MeV, J^π = 2⁺ state in ¹²C and to the E_x = 2.15 MeV, J^π = 1⁺ state in ¹⁰B, for which the calculations predict too much L = 0 strength. Where possible, a comparison with previous (p, ³He) results is made. In ¹⁴N a state at E_x = 11.04 MeV was observed for which the values (J_π; T) = (3⁺; 0) are suggested. In ¹²C we found, in addition to the well known T = 0 states, two relatively sharp T = 0 states at E_x = 19.50 ± 0.10 and 20.55 ± 0.10 MeV. The shape and strength of the angular distribution for the transitions to these states can be approximately accounted for by the calculations, although no one-to-one correspondence between observed and predicted levels could be established.     

Two-particle,two-hole Jπ=0+ states in 40Ca

Excited J^π=0⁺ states in ⁴⁰Ca have been identified by the observation of L=0 angular distributions in the ³⁸Ar(τ, n) ⁴⁰Ca reaction. Strong transitions are observed to the ground state, the known 2p–2h at 9.38 (T=1) and 11.98 MeV (T=2), and to states at 8.28 and 10.65 MeV. The strongest excited-state transition is to the 8.28 MeV state, which we identify as the 2p–2h T=0 state. The J^π=0⁺ state at 7.30 MeV which has been suggested as the 2p–2h T=0 state is not observed.     

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.     

Investigation of the mechanism of inelastic alpha-particle scattering on 28Si nuclei by the method of angular αγ correlations at E α = 30.3 MeV

The angular dependence of the differential cross sections for alpha-particle scattering on ²⁸Si nuclei and double-differential cross sections for the reaction ²⁸Si(α, αγ)²⁸Si at E _α = 30.3 MeV is measured for the case of alpha-particle emission angle between 20° and 160° and the excitation of low-lying states of the ²⁸Si nucleus (0⁺, ground state; 2⁺ state at 1.78 MeV; 4⁺ state at 4.62 MeV; 0⁺ state at 4.96 MeV; and 3^? + 4⁺, 6.88 MeV + 6.89 MeV). The spin-tensor components of the density matrix for the 2⁺ state at 1.78 MeV and the 4⁺ state at 4.62 MeV in the ²⁸Si* nucleus are reconstructed in a modelindependent way. Seven rank-6 components are reconstructed for the 3^? state at 6.88 MeV. Orientation features of ²⁸Si* are determined. The experimental data in question are compared with the results of the calculations performed under the assumption of the collective-excitation mechanism and by the coupled-channel method.     

The (p,t) reactions on nuclei in the rare earth region

The (p, t) reactions on isotopic targets of ^{178, 180}Hf and all the stable isotopes of Yb and on natural targets of Gd, Dy, Er, Hf, Ta, W, Os and Au were studied at a beam energy of 19 MeV with an average resolution of 12 keV. A split-pole magnetic spectrometer was used to measure (p, t) Q-values and absolute differential cross sections. On the basis of angular distribution shapes definite 0⁺ and tentative 2⁺ assignments were made. Rotational bands were identified assuming an I(I+1) spacing. The (p, t) reaction populates excited 0⁺ states strongly in ¹⁷⁴Yb, ¹⁷⁶Hf, ¹⁶⁶Yb and several Gd, Dy and Er isotopes. The ¹⁷⁴Yb and ¹⁷⁶Hf 0⁺ states are discussed in terms of the pairing phase transition and in terms of Nilsson orbitals with unequal (p, t) reaction amplitudes. Members of gamma and octupole vibrational bands were observed in the even-N nuclei. The lowest L = 0 transfers to states in ^{169, 171}Yb were found to have less than 55% of the strength to ground states in adjacent even-N nuclei. A strong L = 0 transfer to a state at 1513 keV in ¹⁷¹Yb indicates the presence of a possible K = 0 core vibration coupled to the unpaired $\text{5}\text{2}$[512] neutron. The natural targets have furnished information on trends in cross sections for members of ground bands, gamma bandheads, 3^? octupole states, and strongly excited 0⁺ states.     

Two-proton pickup in the zirconium region using the (6Li, 8B) reaction

Spectra at θ_lab = 8° have been measured for the ^{92, 94, 96, 98, 100}Mo(⁶Li, ⁸B)^{90, 92, 94, 96, 98}Zr and ^{90, 92, 94}Zr(⁶Li, ⁸B)^{88, 90, 92}Sr two-proton pickup reactions at 90 MeV. The strongest transitions to levels in the Zr isotopes are the 0⁺ → 0⁺ transitions to the g.s. and first excited 0⁺ states. The salient feature of the five Zr spectra is the large increase in 0⁺₂ transition strength relative to that of the g.s. which is observed in the two heaviest isotopes, ^{96, 98}Zr. In ⁹⁰Zr, the 0⁺₂ transition is weak whereas it is the dominant transition in ⁹⁸Zr with twice the g.s. strength. These large variations in relative cross section, which are reproduced by DWBA calculations, are attributed to changing g.s. proton configurations in Zr. In the Sr spectra, which are distinctly different from the Zrspectra, the strongest transitions to excited states are to 2⁺ rather than 0⁺ states. The (⁶Li, ⁸B) reaction seems to be adequately described as a one-step cluster transfer of a T = 1, S = 0 proton pair. The suitability of this reaction for measurements of two-proton pickup is discussed.     

Spectroscopic properties of SbH

Relativistic configuration interaction calculations which include spin-orbit interaction are carried out for nine low-lying ω-ω states and four λ-s states. Spectroscopic properties of six bound ω-ω states are reported. These calculations not only enable assignment of the experimentally observed X₁, X₂, A₁, A₂, and B states but also predict the properties of other electronic states (0⁺(II), 0⁺(IV), 2, 2(II), 1(II), 0⁻) which are yet to be observed. The dissociation energy of SbH is predicted to be 2.7 ± 0.2 eV.     

Exotic clustering in 222,224,226Ra

We describe the J^π = 0⁺, 2⁺, 4⁺, … ground state bands of ^222,224,226Ra, using a model in which these bands are treated as a ¹⁴C cluster orbiting the appropriate Pb core. For each isotope, we obtain good agreement with the measured half-life for the ¹⁴C decay of the 0⁺ ground state, as well as with the excitation energies and in-band E2 decays of other states of the ground state band. We also propose extensions of the model to deal with the observed low-lying J^π = 1⁻, 3⁻, 5⁻, … bands, their in-band E2 decays, and the E1 and E3 transitions connecting to the ground state bands.     

Excited states of 176Hf

The properties of the excited levels of the even-even deformed nucleus ¹⁷⁶Hf are analyzed on the basis of available experimental data on ¹⁷⁶Ta decay. Thirty-nine new states are included in the energy-level scheme of the ¹⁷⁶Hf nucleus. The deexcitation of a number of known levels is supplemented with new transitions. New levels are included in three rotational bands, and the K _i =0 ₄ ⁺ band is identified. The 2470.95-keV level is considered as a two-phonon quadrupole-octupole state. A strong interplay of states belonging to different bands is indicated. The Coriolis interaction is calculated for pairs of K ^π = 0^? and 1^?, 0⁺ and 2⁺, and 2⁺ and 3⁺ bands. The interaction parameters are found. It is shown that the sets of positive-and negative-parity states are connected by El transitions characterized by large hindrance factors.     

The 48Ca(3He,t)48Sc reaction at 66 and 70 MeV: Reaction mechanism and Gamow-Teller strength

The ⁴⁸Ca(³He, t)⁴⁸Sc reaction has been studied at E_3He = 66 MeV and 70 MeV. Angular distributions are given from θ = 8° to 35°. The 0⁺–7⁺ multiplet in ⁴⁸Sc is strongly excited at these energies and the spectra are further characterized by some broad structures on a continuous background. Broad peaks at E_ex = 7.8, 10.6 and 13.3 MeV have an angular distribution similar to the low-lying 1⁺ state. The broad peaks are interpreted as envelopes of groups of 1⁺ states carrying a significant part of the Gamow-Teller strength. The strength distribution is consistent with a shell-model calculation. The reaction mechanism has been examined at 66 MeV. The cross section is calculated for the 0⁺–7⁺ multiplet in ⁴⁸Sc as a coherent sum of one-step and two-step processes. The two-step contribution is calculated in a full finite-range 2nd-order DWBA. The result is similar contributions from (³He, α, t) and (³He, d, t). The calculations account reasonably well for the data with the exception of the transition to 0⁺, IAS.     

Nonadiabatic couplings and charge transfer study in H + CS+ collision using time-dependent quantum dynamics

Experiments have reported the high stability of HCS⁺ ion and inhibit to decompose over the range of collision energies. In this study, the various energy transfer channels of atomic H collision with CS⁺ molecular ion has been performed by ab initio computations at the multireference configuration interaction/aug-cc-pVQZ level of theory. The ground and several low-lying excited electronic state potential energy surfaces in three different molecular orientations, namely, two collinear configurations with, (1) H approaching the S atom (γ = 0°), (2) H approaching the C atom (γ = 180°) and one perpendicular configuration, (3) H approaching the centre of mass of CS (γ = 90°) with the diatom fixed at the equilibrium bond length, have been obtained. Nonadiabatic effects with Landau–Zener coupling leading to avoided crossings are observed between the ground- and the first-excited states in γ = 90° orientation, and also between the first- and second-excited states in γ = 180° orientation. Quantum dynamics have been performed to study the charge transfer using time-dependent wave packet method on the diabatic potential energy surfaces. The probability of charge transfer is found to be highest with 42% in γ = 180°. The high charge transfer probability result in the formation of H⁺ + CS channel which ascertains the high stability of HCS⁺ ion.