Low-lying Negative Parity States Research Articles

Description of the low-lying negative parity states in153Gd

To explain the properties of the recently observed negative parity states in the 89-neutron nucleus153Gd, the Nilsson model is extended to include the Coriolis couplings between the 3−/2 [521], 5−/2 [523], 3−/2 [532], 1−/2 [530], 1−/2 [510], 1−/2 [521] and 5−/2 [512] bands. The calculation reproduces rather well the experimental level energies, single neutron transfer cross sections and electromagnetic transition rates.

Structure of low-lying negative parity states ofB11andC11

The low-lying negative parity states of $^{11}\mathrm{B}$ and $^{11}\mathrm{C}$ are interpreted as arising from a ${p}_{\frac{3}{2}}$ hole coupled to the ground state and first excited state of $^{12}\mathrm{C}$. The coupling interaction has been expanded in a series of spherical tensor operators including dipole and quadrupole terms. The parameters of the interaction are found by fitting to the experimental energies, moments, and transition rates of $^{11}\mathrm{B}$. The calculated $\ensuremath{\beta}$ decay $log\mathrm{ft}$ value and most of the calculated static moments and transition rates are in excellent agreement with experiment. The exceptions are attributed to the limited basis used and to the fact that the free core and single particle operators are used; that is no effective operators are used. An improvement in energies and in one transition rate is obtained by treating $^{12}\mathrm{C}$ as a rotator and including a third core state. Possible improvements in the model are discussed.NUCLEAR STRUCTURE $^{11}\mathrm{B}$, $^{11}\mathrm{C}$. Calculated energies, moments, transition rates, $log\mathrm{ft}$, negative parity states.

The γdecay of low-lying states in44Sc (populated in44Ca(p,nγ),41K( α ,nγ) and28Si(18O,pn γ) reaction)

Levels in 44Sc have been studied using the reactions 44Ca(p,n gamma )44Sc, 41K( alpha ,n gamma )44Sc and 28Si(18O,pn gamma )44Sc. The level scheme up to 1.5 MeV has been established. Lifetimes have been measured using the Doppler shift attenuation method and the recoil distance method. gamma ray angular distributions were measured near threshold in the (p,n) reaction and these results together with the lifetimes and branching ratios allow spin assignments to be made for the most of the states. The low-lying negative parity states are interpreted as deformed bands, co-existing with the spherical positive parity states predicted by the shell model.

A proposed Kpi=0-band in44Sc

The lifetimes and spins of the low-lying negative parity states of 44Sc have been determined. The spin sequence 1-, 2-, 3-, 4- and possible 0- assigned to the 68, 235, 425. 631 and 146 keV states, together with the measured transition strengths, suggest that these states are members of a kpi =0- band based upon a d3/2 hole configuration.

Spectroscopic Investigation of Even-Even Neutron-Deficient Gd Isotopes

Properties of levels in $^{146}\mathrm{Gd}$, $^{148}\mathrm{Gd}$, and $^{150}\mathrm{Gd}$ have been investigated both by observing the electron-capture decay of $^{148}\mathrm{Tb}$ and $^{150}\mathrm{Tb}$ as well as the $\ensuremath{\gamma}$ transitions following the ($\ensuremath{\alpha}, \mathrm{xn}$) reactions on $^{144}\mathrm{Sm}$ and $^{148}\mathrm{Sm}$ targets. Decay schemes were constructed or confirmed. The angular distributions of the $\ensuremath{\gamma}$ lines with respect to the beam direction enabled spin assignments for most states. Searches for isomerism revealed lifetimes of ${T}_{\frac{1}{2}}=17.3\ifmmode\pm\else\textpm\fi{}2.0$ nsec and ${T}_{\frac{1}{2}}=9.1\ifmmode\pm\else\textpm\fi{}2.0$ nsec, respectively, for the ${8}^{+}$ 2689-keV level in $^{148}\mathrm{Gd}$ and the ${6}^{+}$ 2981-keV state in $^{146}\mathrm{Gd}$ and indicate a particle character for these states. An upper limit of 5 nsec was derived for the half-lives of any level reached in $^{150}\mathrm{Gd}$. The decay schemes of $^{148}\mathrm{Gd}$ and $^{150}\mathrm{Gd}$ are similar to those of the neighboring neutron-deficient nuclei, e.g. $^{148}\mathrm{Sm}$ and $^{146}\mathrm{Nd}$. The low-lying negative-parity states observed may represent a collective sequence based on a ${3}^{\ensuremath{-}}$ state.

Deformed states in46Sc

The lifetimes of the low-lying negative parity states in 46Sc have been measured using the Doppler shift attenuation method. The E2 transition strengths determined from these lifetimes are enhanced and confirm a suggestion that the 142.5 (1-), 289.5 (2-), 584.8 (3-) and 1124.4 (4-) keV states of 46Sc form a rotational band based upon the (f72/)7 (d32/)-1 configuration.

Coulomb displacement energies and the structure of the low-lying negative-parity states in 2s-1d shell nuclei

Negative-parity states in A = 13–33 nuclei are described as two-component wave functions, one containing a hole in the 1p shell, the other a particle in the 1f–2p shell. The large difference in Coulomb displacement energy (CDE) for both components has been used to determine the relative intensities by fitting the experimental CDE. For the lowest-lying states these intensities are compared to experimental ones derived from spectroscopic factors for pick-up reactions. Strong binding-energy effects seem to play an important role for these states.

States ofRb86: TheSr88(d,α)Rb86Reaction

The $^{88}\mathrm{Sr}(d,\ensuremath{\alpha})^{86}\mathrm{Rb}$ reaction has been studied with 17.00-MeV deuterons. Energy resolution of 11 keV was obtained using an Enge split-pole spectrograph. Accurate excitation energies (\ifmmode\pm\else\textpm\fi{}0.15%) were measured for more than 35 states up to an excitation energy of 3.3 MeV in the residual nucleus. Differential cross sections were obtained for most of the $^{86}\mathrm{Rb}$ states for $12.5\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}\ensuremath{\theta}\ensuremath{\le}65\ifmmode^\circ\else\textdegree\fi{}$, and compared with distorted-wave calculations. The deduced $L$-transfer values allowed the assignment of a narrow range of ${J}^{\ensuremath{\pi}}$ values to 25 of these states. Several unique spin assignments were possible. Microscopic-model calculations were performed for several of the low-lying negative parity states in $^{86}\mathrm{Rb}$, using simple two-component wave functions empirically derived from $^{87}\mathrm{Rb}(d,t)$ spectroscopic factors. The predictions agreed reasonably well with the experimental ($d,\ensuremath{\alpha}$) data for both the relative magnitudes and the shapes of the angular distributions, except for the ${J}^{\ensuremath{\pi}}={2}^{\ensuremath{-}}$ ground state.

Core-excitation calculations in75As

The nuclear properties of the low-lying negative parity states in75As are discussed in terms of the excited-core model. The core and particle parameters were determined by a simultaneous fitting of the available data into a least square iteration program.

Collective Correlations in the Giant Dipole Continuum ofC12

A continuum shell-model calculation based on the collective correlation model has been made for the giant resonance of $^{12}\mathrm{C}$ using the eigenchannel reaction theory. The low-lying negative-parity states of $^{11}\mathrm{C}$ and $^{11}\mathrm{B}$ have been taken into account by corehole coupling. Partial, total, and integrated photoabsorption cross sections are calculated for the region of the giant dipole resonance.

Nuclear Structure ofNa23: TheNe22(He3,d)Reaction

Using the $^{22}\mathrm{Ne}(^{3}\mathrm{He},d)^{23}\mathrm{Na}$ reaction at a bombarding energy of 15 MeV, excitation energies and angular distributions have been obtained for 96 levels below ${E}_{x}=10.2$ MeV in $^{23}\mathrm{Na}$. Data were recorded in 3.75\ifmmode^\circ\else\textdegree\fi{} steps in a multiangle spectrograph. Angular distributions were compared with distorted-wave Born-approximation predictions; values of transferred angular momentum and spectroscopic strength were extracted for 42 levels, including the three lowest $T=\frac{3}{2}$ states. An empirical forward-angle $J$ dependence has been used to distinguish between ${J}_{f}^{\ensuremath{\pi}}={\frac{3}{2}}^{+}$ and ${\frac{5}{2}}^{+}$ for ${l}_{P}=2$ transfers. The summed ${l}_{P}=0$ and ${l}_{P}=2$ spectroscopic strengths agree with theoretical expectations. The results of the present investigation are combined with previous information and discussed in terms of the rotational model. The low-lying negative-parity states are examined in terms of their particle or hole character. The results for both positive- and negative-parity states suggest significant deviations from the predictions of a simple rotational model, even with band mixing.

Low-lying negative-parity states in the vibrational nuclei

Properties of the negative-parity quintuplet of states I π = 1 −−5 − are calculated. The states can be interpreted as one-quadrupole + one-octupole phonon states. A simplified version of the time-dependent Hartree-Fock method is used to obtain parameters of the collective Hamiltonian. The equation of motion is then solved in a truncated space of harmonic phonon wave functions. The numerical calculations are made for nuclei with 140 ≦ A ≦ 148. The resulting spectra show the effect of gradual increase of anharmonic corrections when the corresponding quadrupole and octupole phonons become more collective.

Particle-core coupling in the lead region

Abstract Several nuclei in the neighbourhood of 208Pb have been studied in terms of the core-particle coupling model. The present studies include the high-lying negative-parity states in 209Pb and positive-parity states in 209Bi, the levels of 207Bi, the low-lying negative-parity states of 205Pb and the high-lying positive-parity states of 205Pb. The results are compared with the results of single-nucleon and double-nucleon transfer reactions.

Proton pick-up from 19F, 20Ne and 22Ne

Energy spectra and angular distributions of the 3He particles from the (d, 3He) reactions on 19F, 20Ne and 22Ne have been measured at an incident energy of 52 MeV. Excitation energies up to 15 MeV ( 18O), 7 MeV ( 19F) and 9 MeV ( 21F) and pick-up from seven different shell-model orbits have been observed. Several previously unknown negative parity states have been found in 18O. A ( 3 2 , 1 2 ) − level at 4.56 MeV was found in 19F, while the known J = 3 2 level at 3.91 MeV was not observed which suggests a positive parity assignment. The hole state spectrum of 21F resembles closely that of 19F. The spectroscopic factors are compared to the predictions from a simple rotational model and from various effective shell-model calculations. All models describe the positive parity transitions leading to 19, 21F reasonably well, but those leading to 18O are only understood by the inclusion of excited core contributions of 4p-2h character in 18O. The low-lying negative parity states, containing essentially the 1p 1 2 hole strengths, are also nicely described by the weak coupling calculations. Higher excited negative parity states show deviations which are discussed in terms of 2p particle-1p hole admixtures.

Levels in 47Ca and 41Ca populated in thermal neutron capture

Gamma radiation from the 46Ca(n, γ) 47Ca and 40Ca(n, γ) 41Ca reactions was measured with Ge(Li) detectors. The 47Ca γ-rays observed can be placed in a decay scheme with levels at 2013.62±0.20, 2875.27±0.25, 4057.9±0.3, 4809.2±0.3 and 5503.4±0.3 keV. The neutron binding energy of 47Ca is 7276.0±0.5 keV. The primary γ-ray intensities populating intermediate 1 2 − and 3 2 − states are found to be strongly correlated with l n = 1 transitions in 46Ca (d, p) 47Ca studies, which is consistent with the common unique parent assumption and suggests a direct process (channel capture) in the (n, γ) reaction. The decay of the low-lying negative parity states is consistent with their shell-model interpretation as 2 p 1 2 and 2 p 3 2 one-particle two-hole excitations in the 41Ca inert core. Energies of the previous established levels in 48Ca are 1942.69±0.14, 2009.88±0.24, 2462.15±0.17, 2669.82±0.18, 3400.08±0.26, 3613.42±0.17, 3944.20±0.25, 4603.7±0.7 and 4752.6±0.2 keV. The neutron binding energy of 41Ca is 8363.1±0.5 keV.

Level schemes and properties of the odd-mass Sb isotopes

Level schemes of 117, 119, 121Sb are calculated in a unified-model approach with surface vibrations coupled to the proton single-particle motion. The addition of octupole vibrations is necessary to explain low-lying negative parity states. Reaction data are calculated.

A nuclear structure study of 19F levels from the 18O( 3He, d) 19F reaction

Angular distributions have been measured for twenty deuteron groups from the 18O( 3He, d) 19F reaction at 11.0MeV 3He energy. The spectroscopic information obtained on even- l transitions is compared with recent shell-model intermediate coupling calculations as well as rotational particle coupling calculations. Good agreement between experiment and both models is observed for most of the strongly excited positive parity states. It is suggested that the lowest T = 3 2 state in 19F lies at 7.56 ± 0.03 MeV and that the 1 2 + level at 6.25 ± 0.03 MeV be identified with the Nilsson proton orbit 11. The l = 1 transitions to the low-lying negative parity states are analysed in terms of core excitation configurations in the 18O ground state and in 19F.

Structure of 51Ti

We reproduce the gross experimental features of the low-lying negative parity states in 51Ti basing the structure on single n, 2p-1h n and core plus n states. Most calculations do not consider the latter modes as distinct alternatives.

Transition rates in phonon-particle coupled nuclei

The low-lying non-normal parity states of 41Ca and 39K (positive-parity and negative-parity spectra respectively) are treated as a particle (hole) coupled to the low-lying negative-parity states of 40Ca (often called vibrational states). These spectra are calculated by the technique of Sherwood and Goswami 1), in which the RPA is extended from a closed shell to a closed shell plus a particle or hole. The calculated spectra are compared with experimental results. It is observed that the diagonalization of the energy matrix leads to roughly twice the number of physical states. It is shown that the doubling of the number of physical states does not lead to a breakdown of the theory, and a way to distinguish the physical states from the non-physical states is indicated. A method for calculating transition rates in the phonon-particle coupling is developed and is applied to the known electromagnetic transitions in 39K. In the calculated spectra, it is found that two vibrations are usually important, namely, the lowest J = 3 − and 5 − states of 40Ca. It is noted that the concept of a particle coupled to a vibration is ambiguous. The non-orthogonality is handled correctly in this microscopic theory and is quite important in calculating transition rates. The phonon-particle coupling model predicts that the non-normal parity states in 41Ca and 39K lie much lower in energy and are in much better agreement with experiment than according to conventional p-h calculation (TDA). The experimental levels (in MeV) and their calculated transition rates (in Weisskopf units) are 2.82 (2.5, 9), 3.02 (15 × 10 −4, 13 × 10 −4), 3.60 (16, 23), 3.94 (17, 16). The 4p-3h states were not included. Free charges rather than effective charges were used in the calculation of the transition rates.

Mixing of rotational bands in 160Dy

Low-lying negative-parity states in 160Dy have been interpreted as members of two strongly mixed rotational bands. The mixing amplitudes in the wave functions for the various states are calculated from the level energies. All the observed transition probabilities can be shown to be consistent with this interpretation.