States In 42Ca Research Articles

Nuclear shapes studied with low-energy Coulomb excitation

Coulomb excitation is one of the rare methods available to obtain information on static electromagnetic moments of short-lived excited nuclear states, including collective non-yrast levels. It is thus an ideal tool to study shape coexistence and shape evolution throughout the nuclear chart. Historically, these experiments were limited to stable isotopes, however the advent of new facilities, providing intense beams of short-lived radioactive species, has opened the possibility to apply this powerful technique to a much wider range of nuclei. Here, we present some recent complex Coulomb-excitation studies and use the example of superdeformed states in 42Ca to demonstrate the sensitivity of the method to second-order effects such as relative signs of electromagnetic matrix elements and quadrupole moments.

Cluster correlations in largely deformed states

The coexistence of various deformed states in 42Ca and α-38Ar correlations have been investigated using deformed-basis antisymmetrized molecular dynamics. Wavefunctions of the low-lying states are obtained via parity and angular momentum projections and the generator coordinate method (GCM). Basis wavefunctions of the GCM calculation are obtained via energy variation with constraints on the quadrupole deformation parameter β and the distance between α and 38Ar clusters. The rotational band built on the Jπ = 0+2 (1.84 MeV) state as well as the Jπ = 0+3 (3.30 MeV) state are both reproduced. The coexistence of two additional Kπ = 0+ rotational bands is predicted; one band is shown to be built on the Jπ = 0+3 state. Members of the ground-state band and the rotational band built on the Jπ = 0+3 state contain α-38Ar cluster structure components. The α-38Ar higher-nodal Jπ = 0+ state is also obtained, and the Jπ = 0+ state has large E0 transition strength from the ground state.

REFINEMENT OF THE Ca-42 LEVEL SCHEME. PRELIMINARY RESULTS FROM THE FIRST AGATA DEMONSTRATOR EXPERIMENT

The Coulomb excitation experiment to study electromagnetic properties of low-lying states in 42Ca with a focus on a presumably superdeformed band was performed at the Laboratori Nazionali di Legnaro in Italy using the \gamma -ray spectrometer AGATA Demonstrator coupled to the DANTE charged particle detector array. First results are presented, including the refinement of the 42Ca level scheme.

Shell model configurations in the [formula omitted] state in 46Ca from a g-factor measurement

The g factor of the first excited 21+ state in 46Ca has been remeasured with better accuracy than previously obtained, g(21+,Ca46)=−0.26(6). The experiment utilized the transient field technique combined with Coulomb excitation in inverse kinematics. This result was analyzed in terms of shell model plus deformed core calculations. The positive g factors of the 21+ states in 42Ca and 44Ca suggest that the 21+ state wave functions require significant particle–hole excitations of the Z=20, N=20 core. The new data for 46Ca show that (fp)ν6 configurations dominate near the shell closure at 48Ca and indicate that core excitation plays a lesser role than was hitherto believed.

Search for pairing-vibration states in multinuclon transfer reactions

Multinucleon transfer reactions in 40Ca+ 208Pb have been studied at several bombarding energies close to the Coulomb barrier. Light reaction products have been identified in mass and charge with a time-of-flight spectrometer. The energy spectra of the inclusive two neutron pick-up channel show a population in a narrow region of excitation energies which corresponds to the predicted energy of pairing-vibration state in 42Ca.

Longitudinal electroexcitation of the low-lying states in 42Ca and 44Ca

The form factors in electron scattering have been measured for 2 +, 3 − and 5 − states up to 7 MeV excitation in 42Ca and 44Ca. The range of the incident electron energy and scattering angles were 62.5–250 MeV at relatively forward angles, over the momentum transfer from 0.4–1.8 fm −. The reduced transition probabilities B(E l) for these states were determined using Tassie-type and shell-model-type transition densities. It is shown that the characteristics and the differences of the observed 2 + 1 and 2 + 2 form factors in 42Ca and 44Ca are explained by deformation effect and the coexistence model was well verified in 42Ca. The form factor of the 6.1 MeV transition in 42Ca may be interpreted as an isoscalar dipole transition by its E3-like q-dependence similar to those in the self-conjugate nucleus 40Ca, and the isoscalar E1 transition density is deduced.

The mean life of the second 0 + state in 42Ca

The mean life of the second excited state in 42Ca (1.84 MeV, O +) was measured by a direct electronic timing technique to be 558 ± 8 ps. This result compares with a previous measurement of 480 ± 30 ps which yields a high B(E2) value. The present result gives a B(E2; 0 2 + 1.84 MeV → 2 1 + 1.52 MeV) value of 484 e 2 · fm 4 or 55 single-particle units; the theoretical implications of this are discussed. The accurate mean life was extracted using a convoluted function to describe both the inherent time resolution of the experimental system and the exponential decay of the state of interest.

Wave functions of 0 + states in 42Ca

Ratios of cross sections in 41Ca(d,p) and 38Ar( 6Li,d) leading to 0 + states of 42Ca allow determination of the coefficients in wave functions of the type a(2p)+ b(4p−2h) + c(6p−4h), and an independent evaluation of the intrinsic amplitude for (sd) 2(fp) 2 and (fp) 4 α transfer.

High spin states in42Ca

High spin states in 42Ca have been excited with the 39K( alpha ,p)42Ca reaction at bombarding energies of 9.5 MeV and 16.0 MeV. Levels at 5491, 5744, 6145, 6409, 6554 and 7369 keV were shown to have Jpi of 6-, 7-, 7(-), 8-, 9- and 10-(8-) respectively. Lifetimes for the 5491, 5744 and 6145 keV levels were determined to be 85+or-20 fs, 600+or-140 fs and <100 fs respectively. Multipole mixing ratios were deduced.

Deformed negative parity states in42Ca

Negative parity states in 42Ca have been excited with the 39K( alpha ,p gamma )62Ca reaction at bombarding energies of 9.5 MeV and 11.5 MeV. The lifetimes of the known negative parity states at 3953(4-) keV. 4044(3-) keV and 4099(5-) keV were measured to be 4.7+or-0.3 ps, 240+or-70 fs and 580+or-145 fs respectively. Levels at 4353 keV and 4896 keV were shown to have Jpi of 4- and 5- with lifetimes of 760+or-100 fs and 80+or-30 fs respectively. Multipole mixing ratios were determined and several of the transitions were shown to have enhanced E2 strengths. The results are discussed in terms of the co-existence model of spherical and deformed states.

Lifetime measurements in42Ca (populated in28Si(16O,2p))

High spin states in 42Ca between 4.1 and 7.4 MeV excitation energy were populated in the reaction 28Si(16O,2p) at 36.5-50 MeV beam energy. Using the recoil distance Doppler shift method, their lifetimes and upper limits of their spins were determined. Neither strongly enhanced E2 transitions nor rotational-like behaviour of these states were observed.

Wave functions and particle transfer form factors of 42Ca and 18O

Wave functions and energies of 0 + states of 42Ca and 18O are calculated using an expansion in Sturm-Liouville functions. The method is an alternative to the inclusion of continuum wave functions in shell model calculations and represents a considerable simplification compared to this. The wave functions are used to calculate cross sections of two-particle transfer.

Lifetime of the 2755 keV 15/2− state in43Ca

Using the recoil distance Doppler shift method, we measured the lifetime of the 2755 keV 15/2− state in43Ca populated in the reaction28Si(180,2p n) to beΤ=39 ±5 ps. We also remeasured the lifetime of the 2751 keV 4+ state in42Ca excited in the reaction28Si(16O,2p) to beΤ=3.8±0.4ps. Effective charges derived fromE2 transition between (f7/2)v high-spin states are discussed.

Two particle wave functions in a Sturm-Liouville basis

Wave functions and energies of 0 + states of 42Ca are calculated by means of the Sturm-Liouville expansion, thus taking into account “continuum admixtures”. The wave functions are used in calculations of formfactors for two-particle transfer.

Quadrupole moments and coexistence in even calcium nuclei

The static electric quadrupole moments of the lowest 2 + states in 42Ca and 44Ca were measured to be −19±8 e · fm 2 and −14±7 e · fm 2 respectively. Values for B(E2; 0 1 + → 2 1 +) of 412±15 e 2 · fm 4 and 473±20 e 2 · fm 4 were measured for 42Ca and 44Ca respectively. The measured moments were considerably more negative than (fp)” shell model calculations predict. However, an excellent fit was obtained when the known E2 properties of the lowest seven levels of 42Ca were used to decompose these levels into (fp) 2 states plus a deformed band. The energy level structure, moments of inertia and intrinsic quadrupole moments of the deformed bands in 40Ca and 42Ca are nearly identical, implying that the lowest K = 0 + band in 40Ca is prolate in shape. Insufficient E2 data are available for a similar model fit to 44Ca. However, this model gives a plausible explanation of the known 44Ca properties.

Configurational mixing and the magnetic moment of [formula omitted]-Nucleons

It is shown that, after the corrections due to deformed components in the wave functions have been removed, the new measurement of the magnetic moment of the 6 + state in 42Ca together with the corresponding results from 41Ca, 41Sc as well as the β-decay results 41Sc → 41Ca, fit a picture in which the correction to the Schmidt magnetic moment of the f 7 2 nucleons is pure isovector and consists of a 10 percent reduction of the 〈 Σσ 2 τ 3〉 and δg l = 0.15 τ.

Estimate of the branching to the excited 0 + state in 42Ca in the β+-decay of 42Sc

The β +-branch of the decay of the 42Sc 0 + ground state to the 1.836 MeV 0 + state in 42Ca is estimated in a 1435 1098 simple Coulomb mixing model, which relates this branch to Coulomb displacement energies in 0 + isotriplets and off-diagonal Coulomb matrix elements. The estimates obtained are very small, ≈ 10 −4, which is consistent with current experimental data.

The (1f [formula omitted]) 2 multiplet in 42Ca

The states of 42Ca below 3.2 MeV excitation are studied by the 41Ca(d,p) 42Ca reaction at 12 MeV bombarding energy. The experimental spectroscopic factors are compared to predictions based on Gerace and Green's coexistence model.

Inelastic scattering of 50 MeV protons to the deformed states in 42Ca

The inelastic scattering of 49.75 MeV protons by 42Ca has been studied. Angular distribution for thirteen excited states up to an excitation energy of 5 MeV in 42Ca were obtained. Spin and parity assignments were made on the basis of a DWBA analysis with first-order collective form factors. The deformation parameters obtained from such an analysis were compared with other results. A microscopic-model calculation with 4p-2h deformed components in the nuclear wave functions was carried out and the results discussed in terms of the structure of 42Ca.

Branching in the β+ decay of the 42Sc ground state

The β + branch of the decay of the 42Sc 0 + ground state to the 1.83 MeV 0 + state in 42Ca is estimated to have an intensity of 0.06%. A preliminary measurement is reported showing Г 0 + 1 Г 0 + 1 < 1.2 × 10 −3