Charge radii of high-spin isomers measured using laser spectroscopy methods

The overview of experimental data on charge radii differences between the ground and the high-spin isomeric states is presented. Methods of high-resolution laser spectroscopy were used for measurements. Charge radii differences obtained in two ways are compared: from measurements of isomeric shifts of atomic levels of nuclei under study and from measurements of quadrupole moments in both states under the assumption that the radii differences are determined by the difference of their quadrupole deformations. Isomers formed at a rupture of one or several nucleon pairs and isomers with the configuration of the odd neutron 1h _11/2 for the nuclear region Cd-Ba and 1i _13/2 for the region Hg-Pb are considered. Observed deviations of the above charge radii differences for isomeric states of a different nature are discussed.     

Charge radii of neutral baryons

The charge structure of low lying spin 1/2 (8) baryons is investigated in terms of their radii, r², using the assumption of nonfactorizability of tranverse parton momentum distribution and the requirement that the u- and d-quarks inside a nucleon are described by separate spatial distributions. Explicit calculations lead to the startling prediction that the charge radii of all neutral baryons are negative in sign and nonvanishing in magnitude.I am grateful to Professor Abdus Salam, the International Atomic Energy Agency and UNESCO for hospitality at the International Centre for Theoretical Physics, Trieste, where this work was completed.     

Systematics of high-spin isomers in N = 83 isotones and a high-spin isomer beam

Isomers in N = 83 isotones of Z = 60-66, were studied systematically. Their spins and parities are 49/2⁺ and 27⁺ for odd and odd-odd nuclei, respectively. Nearly constant excitation energies of these isomers indicated a decrease of a Z = 64 shell gap energy as Z decreases from 64 to 60 within the framework of a deformed independent-particle model (DIPM). Their configurations are [ν(f _7/2 h _9/2 i _13/2),π(h _11/2)²]_49/2+ and [ν(f _7/2 h _9/2 i _13/2),π(h _11/2)²(d _5/2)^-1]₂₇₊ for odd and odd-odd nuclei, respectively. The shape of the yrast states changes suddenly at spin 49/2(odd) and 27(odd-odd) from a near spherical to an oblate shape. Transitions from isomers are highly hindered because of the shape changes. They may be categorized to be shape isomers. The development of a secondary beam produced by using these high-spin isomers is also described. Received: 1 May 2001 / Accepted: 4 December 2001     

New high-spin microsecond isomers in 131Sb

In this work we have identified and studied the decay of two new microsecond isomers 19/2^- and 23/2⁺ in ¹³¹Sb. This neutron-rich nucleus was produced by thermal neutron-induced fission of ²⁴¹Pu. The detection is based on time correlation between fission fragments selected by the LOHENGRIN spectrometer at ILL (Grenoble) and the γ-rays or conversion electrons from isomers. These new data on high-spin states complete the level scheme previously obtained from β-decay. A large fraction of the members of the πg _7/2ν(h _11/2 ^-1 d _3/2 ^-1) and πg _7/2νh _11/2 ^-2 multiplets are now known and were compared with a multi-particle shell model calculation. Received: 7 June 2000 / Accepted: 19 September 2000     

Charge radii in francium isotopes

Nuclear distributions affect many aspects of atomic spectra, making atomic physics a useful tool to study also nuclear properties. Relativistic coupled-cluster calculations for the 7s and 7p states in Fr are presented and applied to binding energies, and to electronic factors for the field isotope shift. The result, F     

Charge radii of light and heavy mesons

We calculate the electromagnetic (EM) form factors of the pseudoscalar mesons in the light-front framework. Specifically, these form factors are directly extracted from the relevant matrix elements, instead of choosing the Breit frame. The results show that the charge radius of the meson is related to both the first and second longitudinal momentum square derivatives of the momentum distribution function. The static properties of the EM form factors and the heavy quark symmetry of the charge radii are checked analytically in the heavy quark limit. In addition, we use the Gaussian-type wavefunction to obtain the numerical results. Received: 18 December 2001 / Revised version: 18 January 2002 / Published online: 15 March 2002     

Description of high-spin isomers in theN=82 region

The high spin states and of those especially the yrast isomers are studied in the region near the rare earth nuclei. The deformation energy surface is calculated with a method modelled in principle according to a shape constrained cranked HF theory (CHF). In practice, the expectation value of the many-body Hamiltonian is calculated with cranked Nilsson functions. One finds rotation around a slightly deformed oblate or prolate symmetry axis in front or behind the rare earth region, respectively. Near the Hf isotopes strongly prolate deformed nuclei rotating around the symmetry axis are found in agreement with the knownK isomers in this region. These results are explained also qualitatively with the help of the MONA (Maximisation of theOverlap ofNucleonic wave functions byAlignment of single particle angular momenta) effect. In the second part high spin states and yrast isomers in theN=82 region are caluclated in the cranked Hartree-Fock-Bogoliubov approach with four and six quasi-particle excitations. For the excitation energies in¹⁴⁶Gd and¹⁵²Dy and a measuredg factor one finds satisfactory agreement.     

Charge and mass radii of the tin isotopes

Data on the isotope shift of the nuclear charge densities of the tin isotopes and of their mean square charge radii are considered from the viewpoint of the Hartree-Fock and Droplet Models. Attention is paid to the electromagnetic corrections of order 1/m². Through a leptodermous analysis of charge and matter densities we find: (i) differences of m.s. charge radii are mainly sensitive to the external region, (ii) the electromagnetic corrections are important in that region, (iii) despite different leptodermous properties, forces Ska and GO-P lead to the same neutron skin thickness. The average rate of variation of the proton m.s. radius is interpreted as favouring either a low valueQ≈30 MeV for the droplet model asymmetry parameter, or a zero value for the saturation asymmetry parameterL.     

Description of high-spin isomers in theN=82 region

The high spin states and of those especially the yrast isomers are studied in the region near the rare earth nuclei. The deformation energy surface is calculated with a method modelled in principle according to a shape constrained cranked HF theory (CHF). In practice, the expectation value of the many-body Hamiltonian is calculated with cranked Nilsson functions. One finds rotation around a slightly deformed oblate or prolate symmetry axis in front or behind the rare earth region, respectively. Near the Hf isotopes strongly prolate deformed nuclei rotating around the symmetry axis are found in agreement with the knownK isomers in this region. These results are explained also qualitatively with the help of the MONA (Maximisation of theOverlap ofNucleonic wave functions byAlignment of single particle angular momenta) effect. In the second part high spin states and yrast isomers in theN=82 region are calculated in the cranked Hartree-Fock-Bogoliubov approach with four and six quasi-particle excitations. For the excitation energies in¹⁴⁶Gd and¹⁵²Dy and a measuredg factor one finds satisfactory agreement.     

Spectroscopic quadrupole moments of high-spin isomers in 193 Pb

The quadrupole interaction of high-spin isomers in ¹⁹³Pb implanted into solid Hg cooled at a temperature T = 170 K has been investigated by the time-differential perturbed -ray angular-distribution method. Spectroscopic quadrupole moment values of eb and 0.45(4) eb have been deduced for the 21/2^- and 33/2 ⁺ three-neutron states, respectively. A much higher value eb has been determined for the 29/2^- isomer, the band head of a magnetic rotational band.Received: 4 November 2002, Published online: 2 March 2004PACS: 21.10.Ky Electromagnetic moments - 27.80. + w      

Static and dynamic quadrupole moments of high-spin isomers in the Pb-region

Quadrupole moments of high-spin isomers in the Pb-region are studied by using core polarization charges induced by the coupling of single-particle states to giant resonances. We found that the core polarization charges are enough to reproduce the observed quadrupole moments of the isotones with neutron number N=126 quantitatively without any intrinsic deformation. The mass number dependence of the quadrupole moments in the Rn-isotopes is also discussed by taking into account the configuration mixing involving the neutron excited first 2⁺ state.     

Nuclear polarization and signs of quadrupole moments of high-spin Gd isomers

Time-differential perturbed-angular-distribution (TDPAD) experiments have been performed on polarized intermediate- and high-spin isomers ${}^{144}\text{Gd}\text{(10}{}^{\mathrm{+}}\text{)}\text{and}{}^{147}\text{Gd}\text{(}\text{13}\text{2}{}^{\mathrm{+}}\text{,}\text{27}\text{2}{}^{\mathrm{?}}\text{,}\text{49}\text{2}{}^{\mathrm{+}}\text{)}$. Excited Gd nuclei populated by $\text{(}{}^{28}\text{Si}\text{, x}\text{n}\text{)}$ reactions were polarized by the tilted-multifoil technique and implanted in a Gd single-crystal host. Observation of the subsequent electric quadrupole interaction with the known electric field gradient yielded negative values of the sign of the deformation for all isomers studied. The magnitude of the induced nuclear polarization P_I was also determined from the TDPAD data and compared to model calculations in order to deduce the average atomic angular momentum and polarization of Gd ions at v/c ～ 0.018.     

Charge radii from lattice relative charge distributions

Electromagnetic charge radii values are extracted from relative charge distribution data for pseudoscalars using lattice QCD techniques. This is done with Wilson fermions and SU(2) color at five values of the hopping parameter.     

Decay of high-spin isomers in Os nuclei by barrier penetration

A decay scheme for the 130±20 ns high-spin isomer in ¹⁸²Os has been established. The excitation energy of the isomer is 7049±1 keV and it has I^π = 25⁽⁺⁾. A 2.4% decay directly to the yrast 24⁺ level at 5988 keV is observed. In ¹⁸⁴Os a 20±5 ns isomer is observed at 2366±1 keV excitation energy with I^π = 10⁺. Again, direct transitions into the yrast 8⁺ and 10⁺ levels are observed. Contrary to previous speculations, there is no compelling evidence for stable triaxial shapes in the structure of the levels through which the isomers decay. The abnormally short half-lives observed, as well as the unusual decay patterns, are best understood in terms of a γ-soft nuclear potential. Motion in the γ-direction allows the isomer to decay via barrier penetration from an axially symmetric prolate shape with the angular momentum along the nuclear symmetry axis (deformation aligned state) via oblate shapes to another prolate shape with the angular momentum perpendicular to the nuclear symmetry axis (rotation-aligned state).     

Gamma-spectroscopy within the island of high-spin isomers nearN=82

A NaI sum-spectrometer combined with Ge-counters has been used to characterize the members of the island of high spin isomers nearN=82. On the basis of half lives, totalγ-decay energies and discreteγ-lines, assignments of 22 isomers are given or confirmed. The isomers are localized to the region 82≦N≦86 andZ≦68, and the excitation energies vary from 3 MeV to 12.2 MeV. An empirical relation between spin and excitation energy is presented and on this basis isomeric spin values up to (33±2)? are deduced. The isomers are thought to be due to strong alignment of 2 to 8 shell-model particles in a spherical or possibly weakly oblate potential.     

Charge radii and polarization effects in the oxygen region

When using reasonable monopole polarization charges, it is possible to fit the systematics of charge radii in the oxygen region, if core-excited components are taken into account.     

Calculations of electric quadrupole moments and charge radii for high-K isomers

Configuration-constrained potential-energy-surface calculations are performed to investigate high-K isomers in ⁹⁷Y, ¹³⁰Ba, ¹⁷⁶Yb, ¹⁷⁷Lu, and ¹⁷⁸Hf that were observed to have increased electric quadrupole moments but decreased charge radii relative to the states on which they are built. Taking into account the effects of deformation change and unpaired protons, our calculations can reproduce the enhancement of electric quadrupole moments for the isomers in ⁹⁷Y, ¹³⁰Ba, ¹⁷⁶Yb, ¹⁷⁷Lu and the K ^π = 8^? isomer in ¹⁷⁸Hf, and can reproduce the reduction of charge radii for the K ^π = 27/2^? isomer in ⁹⁷Y and the K ^π = 16⁺ isomer in ¹⁷⁸Hf.     

Charge radii and moments of strontium nuclei by laser spectroscopy

The isotope shifts and hyperfine splittings for 11 strontium isotopes (A=80–90) and two isomers for the optical transition λ=293.2 nm were measured. The magnetic dipole and electric quadrupole moments and the changes of the mean square charge radii are derived. The results are discussed with respect to the increasing nuclear deformation and the anomalous coupling scheme of light Sr nuclei.     

On the decrease in charge radii of multi-quasi particle isomers

We report changes in mean-square charge radii, δ〈r²〉$\delta 〈r^2〉$, magnetic moments and quadrupole moments for three multi-quasi particle isomers; ^97m2Y, ^176mYb and ^178m1Hf. All the isomers are observed to display a decrease in 〈r²〉$〈r^2〉$ compared to the lower-lying nuclear state on which the isomer is built. The decreases in 〈r²〉$〈r^2〉$ occur despite the isomers showing increases in quadrupole moment. Possible mechanisms for the effect, which is now seen for six multi-quasi particle isomers, are discussed.     

Systematics of high-spin isomers produced in nuclear reactions with intermediate-energy protons

Systematics is proposed for determining the isomeric ratios (and, consequently, the production cross sections) for high-spin isomeric states in nuclear reactions induced by intermediate-energy protons. It is based on experimental data obtained by bombarding tantalum targets with protons of energy 100 to 500 MeV. For reactions involving the emission of more than two nucleons, a linear dependence between the spin transfer and the logarithm of the isomeric ratio is observed; i.e.,