Natural Parity States Research Articles

Search for high spin collective states inC*12→3α

Sequential decay modes for the four-body final-state reaction, $^{12}\mathrm{C}$${+}^{12}$C\ensuremath{\rightarrow}3\ensuremath{\alpha}${+}^{12}$C, are reported at a bombarding energy of 7.5 MeV/u. Position and energy measurement of all three alpha particles allows the kinematic reconstruction of the relative energies of all decay particle combinations. Several known natural parity states are observed from the alpha-particle decay of $^{16}\mathrm{O}^{\mathrm{*}}$ and $^{12}\mathrm{C}^{\mathrm{*}}$, and in addition unnatural parity states of $^{12}\mathrm{C}$ never before observed in inelastic heavy-ion scattering are seen. The branching fraction for the alpha-particle decay of the 14.08 MeV ${4}^{+}$ state of $^{12}\mathrm{C}$ to the $^{8}\mathrm{Be}^{\mathrm{*}}$, ${2}^{+}$ state is measured to be 0.83\ifmmode\pm\else\textpm\fi{}0.04. Monte Carlo calculations for the effective solid angle for detection of each process are presented. No evidence is found for any spontaneous three alpha-particle decay of $^{12}\mathrm{C}$ excited states and no previously unknown states are reported.

Signatures for isoscalar spin transitions excited in ( [formula omitted], [formula omitted]') reactions

Three different signatures for isoscalar spin transitions in nuclei have been tested in the 12C( d , d ') 12C reaction at 400 MeV. These signatures have values of close to zero for the natural parity states, and values ranging from 0.22 to 0.50 for the ΔS=1, ΔT=0, 12.7 MeV state.

Natural-parity states in superdeformed bands and pseudo SU(3) symmetry at extreme conditions.

The structure of recently discovered identical superdeformed bands in $^{151}\mathrm{Tb}$ and $^{152}\mathrm{Dy}$, and in $^{150}\mathrm{Gd}$ and $^{151}\mathrm{Tb}$ are discussed in terms of the strong-coupling approach. Based on the experimental evidence that the superdeformed core of $^{152}\mathrm{Dy}$ is extremely insensitive to the polarization effects induced by the odd particle, the bands are shown to exhibit the presence of the pseudo SU(3) symmetry at extreme conditions of large elongations and high spins.

A SIGNATURE FOR ISOSCALAR-SPIN TRANSITIONS IN ([d,d) SCATTERING

Three different signatures for isoscalar spin transitions in nuclei have been tested in the 12C(d,d)12C reaction at 400 MeV. These signatures have values close to zero for the natural parity states, and ranging from 0.22 to 0.50 for the ΔS=1 ΔT=0, 12.7 MeV state.

180 degrees electron scattering from 14C.

Inelastic electron scattering cross sections for $^{14}\mathrm{C}$ have been measured at a scattering angle of 180\ifmmode^\circ\else\textdegree\fi{}, with incident beam energies ranging from 81.9 to 268.9 MeV. Transverse form factors were measured for transitions to low-lying natural-parity states, to unnatural-parity ``stretched'' ${J}^{\ensuremath{\pi}}$${=4}^{\mathrm{\ensuremath{-}}}$ states, and to the ${J}^{\ensuremath{\pi}}$${=2}^{\mathrm{\ensuremath{-}}}$ analog to the $^{14}\mathrm{B}$ ground state. Cross sections for ${4}^{\mathrm{\ensuremath{-}}}$ states at 11.7 and 17.3 MeV are combined with pion scattering data to determine the isoscalar and isovector transition amplitudes. Form factors for other states are compared to shell-model calculations. From the excitation energy of the newly discovered ${J}^{\ensuremath{\pi}}$T${=2}^{\mathrm{\ensuremath{-}}}$2 state at 22.1 MeV, the $^{14}\mathrm{\ensuremath{-}}^{14}$B Coulomb energy difference is determined to be 2.25\ifmmode\pm\else\textpm\fi{}0.10 MeV.

Energy dependence of neutron-proton matrix element ratios derived from 25-800 MeV energy proton scattering.

New data are presented on elastic and inelastic proton scattering by $^{58}\mathrm{Ni}$ at 333 and 498 MeV and $^{208}\mathrm{Pb}$ at 318 MeV. We have analyzed these data using phenomenological distorting potentials and potentials generated by folding neutron and proton densities with a free nucleon-nucleon t matrix or with a medium modified nucleon-nucleon interaction. Making use of electromagnetic matrix elements, or charge transition densities, we have calculated neutron-proton transition matrix element ratios in the vibrating potential--vibrating density model (``collective form factors''), or with a scaling model in which the neutron transition densities are taken as proportional to the proton densities. In addition, we have calculated, neutron-proton matrix element ratios from earlier (p,p') results at 25--800 MeV for $^{40}\mathrm{Ca}$, $^{58}\mathrm{Ni}$, and $^{208}\mathrm{Pb}$. We conclude that, although there are some irregularities, the derived neutron/proton matrix element ratios for natural parity states show a tendency to decrease in magnitude with decreasing proton energy in the range 500--100 MeV. A quantitatively similar effect is seen in the ratio of experimental to theoretical cross sections, where the latter are calculated using transition densities adjusted to fit electron or 800 MeV proton scattering. We attribute these results to a failure of the impulse approximation and the vibrating potential model in this energy region.

Collective excitation of 172Yb from inelastic alpha scattering at 36 MeV.

The collective excitation of the natural parity states in $^{172}\mathrm{Yb}$ has been studied with 36 MeV \ensuremath{\alpha} particles. An analysis of the ground-state band data through ${I}^{\ensuremath{\pi}}$${=6}^{+}$ gave deformation parameters ${\ensuremath{\beta}}_{2}$=+0.21\ifmmode\pm\else\textpm\fi{}0.01, ${\ensuremath{\beta}}_{4}$=-0.028\ifmmode\pm\else\textpm\fi{}0.004, and ${\ensuremath{\beta}}_{6}$=0\ifmmode\pm\else\textpm\fi{}0.002. Two ${K}^{\ensuremath{\pi}}$${=2}^{+}$ bands, with band heads at 1465 and 1608 keV, and the \ensuremath{\beta} vibrational ${K}^{\ensuremath{\pi}}$${=0}^{+}$ band with a ${2}^{+}$ state at 1118 keV are excited weakly. Other ${2}^{+}$ states at 2184, 2255, 2367, 2465, 2580, 2650, 2738, 2836, 2890, and 2955 keV are seen, and their isoscalar strengths are found for the first time. The B(E2) strengths found are roughly in agreement with interacting boson model predictions close to the SU(3) limit. At 1263 keV, the ${4}^{+}$ state of the ${K}^{\ensuremath{\pi}}$${=3}^{+}$ band is found to have an isoscalar E4 strength=0.036 ${e}^{2}$${\mathrm{b}}^{4}$ (7 single particle units). A compilation plus reanalysis of earlier data exhibits unexpectedly strong E4 strength to the ${4}^{+}$ members of the lowest K${=2}^{+}$ and ${3}^{+}$ bands in strongly deformed rare earth nuclei. The octupole strength in this nucleus lies mainly in four ${3}^{\mathrm{\ensuremath{-}}}$ states at 1222, 1710, 1822, and 2030 keV with total isoscalar E3 strength of 0.147 ${e}^{2}$${\mathrm{b}}^{3}$. The results for the negative parity states are compared with the theory of Neerg\"ard and Vogel.

D-state effects in (α, d) reaction

The effect of the D-state of the alpha particle internal motion on the cross sections of the (α, d) reaction is investigated in the framework of a full finite range distorted-wave Born-approximation model. We have also performed calculations for this effect within a no-recoil peripheral model suggested previously. In both models the effect of the D-state is to enhance the cross sections for transitions to unnatural parity states and suppress them for transitions to natural parity states. However, the magnitude of this enhancement and suppression is much smaller than that reported earlier. In the no-recoil peripheral model only the absolute magnitudes of the differential cross sections are affected by the D-state. On the other hand, both absolute magnitudes as well as shapes of these cross sections are altered by the D-state effects in the full finite range calculations. This effect is particularly strong for momentum mismatched transitions where the D-state effects introduce large changes in the differential cross sections at relatively higher scattering angles leading to a better agreement between calculations and the experimental data.

Direct and sequential processes in the 16O( 7Li, 7Be) 16N reaction

Calculations are presented for the 16O( 7Li, 7Be) 16N charge exchange reaction. For the direct reaction, the tensor interaction leads to form factors with large spin and angular momentum transfer which are important for the unnatural parity states. The ( 7Li, 6Li)( 6Li, 7Be) sequential process exhibits a strong J-dependence and is the dominant contribution to the natural parity states.

Study on the 208Pb(α, 6He) 206Pb reaction at Eα = 109 MeV

The 208Pb(α, 6He) 206Pb reaction induced by 109 MeV α particles has been studied with 70 keV energy resolution. Twenty-five transitions up to 6.2 MeV in excitation energy have been analyzed. The shapes of the angular distributions are reproduced well by the zero-range distorted-wave Born approximation (DWBA) calculations. The spin and parity of the level at 6.10 MeV are proposed to be 9 −. It is interpreted as a weakly-coupled state of the collective 3 − state and the two-hole 6 + shell-model state. The energy dependence of the total cross sections of the (α, 6He) and (p, t) reactions has been studied systematically by using our present data and other data from the literatures. It reveals that there exists an empirical rule which allows one to compare quantitatively the ratios of the transition strengths of both reactions. The transition strength of the (α, 6He) reaction is found to be about 35 times smaller than that of the (p, t) reaction for the transitions to the natural parity states, while it is about 15 times smaller for the transition to the unnatural parity 3 + state. These small transition strengths are explained by the fact that this reaction occurs at the surface region of the nucleus.

Two-neutron excitations in 26Mg and 30Si

The reactions 24Mg(t, p) 26Mg and 28Si(t, p) 30Si have been studied at an incident energy of 18 MeV. Angular distributions have been measured for strongly excited states up to an excitation energy of about 10.5 MeV. A comparison with DWBA calculations using transition amplitudes resulting from a full (sd) shell model calculation generally shows good agreement up to an excitation energy of about 6 MeV, although a few states show significant discrepancies. At higher excitation energies the natural-parity states of the (f 7 2 d 5 2 ) multiplet, and the 2 + and 4 + states of the (f 7 2 ) 2 configuration can be identified in both 30Si and 26Mg. The 6 + state is identified in 30Si, but not in 26Mg. The expected 0 + states are not clearly identified in either case, although relatively strong transitions with “uncharacteristic” angular distributions are observed near the expected location of these states. DWBA calculations with a (f 7 2 ) 2 form factor suggest that these may in fact be the 0 + states of the (f 7 2 ) 2 configuration.

Continuum effects in Λ-hypernuclei

Calculations have been performed for the 12 ΛC and 16 ΛO states above Λ-threshold. It is demonstrated that continuum coupling reduces ( K −, π − strength assigned to a specific level. Natural parity states which begin to show some degree of collectivity are broad and become part of the quasi-elastic bump. The stretched states which appear in conventional nuclei also become broad and difficult to be identified experimentally.

Regular versus chaotic dynamics in nuclear spectra near the ground state

In an attempt to determine whether the low-lying parts of nuclear spectra are regular or chaotic, we analyse a recent set of data on low-lying levels in nuclei ranging from 24Na to 244Am. We evaluate the nearest-neighbour spacing distribution and the Δ 3 statistic. We find strong indications for regularity in rotational-like states in even-even nuclei, and some evidence that natural parity states in odd-odd nuclei are not completely chaotic. The other states in both types of nuclei seem to have statistical distributions which are consistent with complete chaoticity.

The nuclear structure of 168Er studied with the 170Er(p,t)168Er and 166Er(t,p)168Er reactions

The 170Er(p,t)168Er and 166Er(t,p)168Er reactions have been studied using 18-MeV protons and 17-MeV tritons, respectively. The reaction products were analyzed with magnetic spectrographs providing overall resolutions ranging from 10 to 15 keV full width at half maximum. The chief aim of these studies was to search for previously unknown 0+ states in 168Er, and one new 0+ level, at 1833.5 keV, has been identified. All the known excited 0+ states were populated much more strongly in the (t,p) reaction than in the (p,t) reaction. Numerous natural parity states in known bands were also observed in both reactions. The significance of these results for some recently proposed interpretations of 168Er is discussed. The states with I,Kπ = 0,0+ at 1422 keV and 2,2+ at 1848 keV are both populated much more strongly in the (t,p) reaction than the single-phonon γ vibration. Thus the interpretation given these levels in the interacting boson description, as predominantly multiple-phonon excitations involving at least one γ phonon, does not satisfactorily describe these data. The quasiparticle-phonon model of Soloviev and co-workers is the only model that does not conflict in some way with the presently available experimental data.

A spectroscopic study of 206,204Pb with the ( α, 6He) reaction

Large differences in the excitation of natural parity states have been observed between the (p, t) and ( α, 6He) reactions on 208,206Pb. These differences are well explained by including the components of relative angular momenta between the transferred two nucleons l ̃ ≠ 0 . The result suggests that the ( α, 6He) reaction may be a new spectroscopic tool to study l ̃ ≠ 0 two-nucleon correlations.

Decays of high-lying states in 12C.

States in $^{12}\mathrm{C}$ at 12.71, 16.11, 18.38, 19.55, and 20.62 MeV were populated strongly in the $^{11}\mathrm{B}$(d,n${)}^{12}$C reaction at a laboratory beam energy of 12 MeV. The charged-particle decays of these states were measured in coincidence with neutrons detected by time of flight techniques at 0\ifmmode^\circ\else\textdegree\fi{} relative to the beam. Decay protons and \ensuremath{\alpha} particles were detected and identified in a surface-barrier counter telescope placed at laboratory angles of 45\ifmmode^\circ\else\textdegree\fi{}, 60\ifmmode^\circ\else\textdegree\fi{}, 85\ifmmode^\circ\else\textdegree\fi{}, 110\ifmmode^\circ\else\textdegree\fi{}, and 135\ifmmode^\circ\else\textdegree\fi{}. Angular correlations and branching ratios were determined for the decay particles. The 19.55 MeV peak contains at least two states 300 keV apart with very different \ensuremath{\alpha} and proton decay rates. An \ensuremath{\alpha} decay branch to the ground state of $^{8}\mathrm{Be}$ indicates the presence of a natural parity state in the 18.38 MeV peak. Comparisons have been made between the measured angular correlations and calculations based on the $^{12}\mathrm{C}$ alignments predicted by the distorted-wave Born approximation.

Spectroscopy of even Sn nuclei and generalized-seniority breaking

Properties of even Sn nuclei are described in a broken-pair or generalized-seniority ( ν g ) scheme. Special attention is paid to the degree of ν g mixing in various types of low-lying states. A finite-range interaction as well as a surface-delta interaction (SDI) are employed and single-particle energies are deduced from spectra of odd Sn isotopes. It appears that up to 3 MeV no experimental indications for states with ν g > 4 exist. The only low-lying states which are not included in the model are the members of the well-known two-proton-hole band. With the SDI the ν g mixing is in general a factor two less than with the finite-range force. For the latter an improvement of the description of energy spectra as well as electromagnetic decay is obtained due to about 20% ν g = 4 admixtures in predominantly ν g = 2 states. Only ground states, 2 1 + and 3 1 − states have less than 10% of ν g = 4 admixtures. We argue that the main origin of ν g mixing is a particle-phonon coupling mechanism. A strong fragmentation of two-phonon 0 + , 2 + , 4 + states by ν g mixing emerges from the calculations. For the 0 + states the total two-phonon E2 transition strength is much less than predicted by phenomenological phonon or boson models. Excitation strengths for unnatural-parity states are reduced by 30–40% by ν g mixing. For natural-parity states this reduction is less; for 2 1 + and 3 1 − enhancements by ground-state correlations overcompensate the reduction by fragmentation.

Microscopic and macroscopic aspects of 135 MeV proton scattering from 16O

Differential cross sections have been measured for the scattering of 135 MeV protons from 16O and data from the transitions to 13 states (up to 19.5 MeV excitation) have been analysed using microscopic and macroscopic nuclear reaction models. Extensive collective model calculations have been made of the transitions to all natural-parity states. The deformation parameters for the 4p4h rotational band are in good agreement with theoretical models. The inelastic scattering data from the excitation of the negative-parity states have also been analysed in the distorted-wave approximation using microscopic (shell and RPA) models of nuclear structure and with density-dependent two-nucleon t-matrices. For positive-parity states, we report the first shell-model calculation using the complete 2ħω basis space and find that the triplet of 2p2h states (4 +, 2 +, 0 +) around 11 MeV excitation is quite well described by this model, as may be a 1 + state which is observed for the first time by proton scattering from 16O.

A study of 206Pb by inelastic scattering of 35 MeV protons

Using high-resolution techniques the inelastic scattering of 35 MeV protons by 206Pb was measured. Approximately 180 levels with excitation energies up to 6.8 MeV were identified and angular distributions of most of these states were measured. The L-transfers and deformation parameters are determined by comparison of the measured angular distributions to collectivemodel calculations. Microscopic calculations of natural-parity states are presented and allow a test of RPA and TDA wave functions. Unnatural-parity states were also studied microscopically and permit an examination of the central and noncentral forces in the effective interaction.

Spectroscopy of A = 16 from 13C( 6Li, t) 16O

The 13C( 6Li, t) 16O reaction has been studied at 34 MeV. Selective population of narrow states is observed up to 21 MeV excitation in 16O. This reaction populates strongly both unnatural-and natural-parity states that have little or no 12C + α 0 width. The measured angular distributions are compared with Hauser-Feshbach and finite-range DWBA calculations. Reasonable agreement with the DWBA calculations is found for most of the states strongly populated. The widths of the narrow states populated in the 16–20 MeV excitation region are presented. Comparison of the present data with that from medium-energy inelastic scattering and other multiparticle transfer reactions is made.