Odd Nuclei Research Articles

Shell quenching inNi78: A hint from the structure of neutron-rich copper isotopes

Recent progress in experimental techniques allows us to study very exotic systems like neutron-rich nuclei in the vicinity of $^{78}\mathrm{Ni}$. The spectroscopy of this region can nowadays be studied theoretically in the large scale shell model calculations. In this work, we perform a shell model study of odd copper nuclei with $N=40--50$, in a large valence space with the $^{48}\mathrm{Ca}$ core, using a realistic interaction derived from the CD-Bonn potential. We present the crucial importance of the proton core excitations for the description of spectra and magnetic moments, which are for the first time correctly reproduced in theoretical calculations. Shell evolution from $^{68}\mathrm{Ni}$ to $^{78}\mathrm{Ni}$ is discussed in detail. A weakening of the $Z=28$ gap when approaching the $N=50$ shell closure, suggested by the experimental evidence, is confirmed in the calculations.

Considering collective degrees of freedom in the β decay of odd nuclei

The β decay of around 30 odd nuclei was calculated within the dynamic collective model using expressions for the reduced matrix elements of the weak-interaction Hamiltonian for U-type and V-type β decay obtained earlier by the authors. All of the many-phonon states of the yrast band of an even-even core contributing to the formation of the excited states of nuclei were taken into account. For β transitions with an intensity of >1%, the calculated logft values differ from the experimental values by no more than 0.2.

Systematic calculation ofαdecay within a generalized density-dependent cluster model

We perform an extensive investigation on α decays in both even-A and odd-A nuclei within the new version of the generalized density-dependent cluster model. The microscopic deformed potential is numerically constructed in the double-folding model by the multipole expansion method. The coupled-channel effect resulting from nuclear deformation is included by using the coupled-channel Schrodinger equation with outgoing wave boundary conditions. The fine structure observed in α decay is well described by taking into account the angular momentum of the emitted α particle and the Boltzmann distribution of excitation spectrum in daughter nuclei. A good agreement between experiment and theory is achieved, and the results of our calculations are discussed in detail, together with the sensitivity of the calculated half-lives and branching ratios to some physical quantities used in the calculations.

QRAP: A numerical code for projected (Q)uasiparticle (RA)ndom (P)hase approximation

A computer code for quasiparticle random phase approximation – QRPA and projected quasiparticle random phase approximation – PQRPA models of nuclear structure is explained in details. The residual interaction is approximated by a simple δ-force. An important application of the code consists in evaluating nuclear matrix elements involved in neutrino–nucleus reactions. As an example, cross sections for 56Fe and 12C are calculated and the code output is explained. The application to other nuclei and the description of other nuclear and weak decay processes are also discussed. Program summary Title of program: QRAP ( Quasiparticle RAndom Phase approximation) Computers: The code has been created on a PC, but also runs on UNIX or LINUX machines Operating systems: WINDOWS or UNIX Program language used: Fortran-77 Memory required to execute with typical data: 16 Mbytes of RAM memory and 2 MB of hard disk space No. of lines in distributed program, including test data, etc.: ∼ 8000 No. of bytes in distributed program, including test data, etc.: ∼ 256 kB Distribution format: tar.gz Nature of physical problem: The program calculates neutrino– and antineutrino–nucleus cross sections as a function of the incident neutrino energy, and muon capture rates, using the QRPA or PQRPA as nuclear structure models. Method of solution: The QRPA, or PQRPA, equations are solved in a self-consistent way for even–even nuclei. The nuclear matrix elements for the neutrino–nucleus interaction are treated as the beta inverse reaction of odd–odd nuclei as function of the transfer momentum. Typical running time: ≈ 5 min on a 3 GHz processor for Data set 1.

Coriolis interaction in nuclear single-particle states with mixed parity

The Coriolis decoupling strength in nuclear single-particle (s.p.) states with mixed parity is examined within a reflection-asymmetric deformed shell model. A strong coupling scheme between the parity mixed s.p. state and a coherent quadrupole–octupole vibration mode in the core is considered for odd-mass nuclei. The Coriolis decoupling factor is obtained in a projected form corresponding to good total parity of the system. The average parity of the s.p. state and the decoupling factor are evaluated in several nuclei as functions of the quadrupole and octupole deformation parameters β2 and β3. It is found that the average s.p. parity obtains various dominant values in the (β2, β3)-plane. It is shown that by comparing the behaviour of the decoupling factor in the (β2, β3)-plane to values obtained in a collective quadrupole–octupole model and by requiring consistency between the calculated dominant parity and the experimentally established parity in the ground state one can determine physically reasonable deformation regions for the considered odd-A nuclei.

Nuclear reactions and the double beta decay

Charge-exchange reactions of ( n , p ) and ( p , n ) types at intermediate energies are introduced as a tool for the study of nuclear matrix element in β β decay. Here, the ( n , p ) type reactions are realized through ( d , 2 He ) , where 2He refers to two protons in a singlet 1 S 0 state and where both of these are momentum analyzed and detected by the same spectrometer and detector. These reactions have been developed and performed exclusively at KVI, Groningen (NL), using an incident deuteron energy of 183 MeV. The ( 3 He , t ) reaction is of ( p , n ) type and was developed at the RCNP facility in Osaka (JP) at incident energies of 420 MeV. Using both reaction types one can extract the Gamow–Teller transition strengths B ( G T + ) and B ( GT − ) , which define the two “legs” of the β β decay matrix elements for the 2 ν β β decay. The high resolution available in both reactions allows a detailed insight into the excitations of the intermediate odd–odd nuclei and, as will be shown, some unexpected features are being unveiled.

10.1007/s11450-008-3009-0

Dipole magnetic moments of more than 100 odd spherical nuclei are calculated within the theory of finite Fermi systems. For the effective interaction of nucleons within the theory of finite Fermi systems, use is made of a version that takes into account nuclear-medium-modified amplitudes for the exchange of one pion and one rho meson. A new tensor local charge ζ t is incorporated in the theory of finite Fermi systems in addition to the known orbital (ζ l ) and spin (ζ s ) local charges. Good agreement with experimental data, at a level of 0.1 to 0.2μ N , is obtained for the overwhelming majority of the nuclei considered here. Several cases of a significant discrepancy with experimental data, at a level of 0.3 to 0.5μ N , are revealed. Possibilities for removing these discrepancies are discussed. A detailed comparison with known results obtained within the multiparticle shell model is performed for 2p-to 1f-shell nuclei. Cases where the standard theory of finite Fermi systems must be extended by taking into account multiparticle configurations are found. Magnetic moments are analyzed for a number of long isotopic chains. Several new experimental values of magnetic moments for copper isotopes far from the beta-stability valleys are known. For the example of the copper-isotope chain, it is shown how the emergence of a deformation in the ground state of a nucleus can be revealed on the basis of a systematic analysis of magnetic moments.

New aspects of chiral symmetry breaking in atomic nucleus

The significant progresses of the chirality in atomic nuclei are briefly reviewed for both experimental and theoretical sides. A particle rotor model is developed which couples several valence protons and neutrons to a rigid triaxial rotor core and applied to investigating the chirality in odd-A nucleus 135Nd. Static chirality has been shown to be a transient phenomenon surrounding by chiral vibrations. It is found that the B(M1) staggering is associated strongly with the characters of nuclear chirality, i.e., the staggering is weak in chiral vibration region while strong in the static chirality region.

Description of the two-neutrino ββ decay of 100Mo by pnMAVA

The microscopic anharmonic vibrator approach (MAVA) is a scheme where the one- and two-phonon states of an even–even nucleus are treated consistently by using a realistic microscopic nuclear Hamiltonian. This model has recently been extended to describe odd–odd nuclei by adding proton–neutron phonons in a scheme called the proton–neutron MAVA (pnMAVA). In this paper, we apply pnMAVA to compute the nuclear matrix elements corresponding to the two-neutrino double beta (2νββ) decay of 100Mo to the ground state and the first excited 0+ state of 100Ru in a realistic single-particle space. We also compute the GT− and GT+ Gamow–Teller strength functions and compare them with the plain pnQRPA (proton–neutron QRPA) and available data. The redistribution of strength to four-quasiparticle degrees of freedom can be clearly seen in the GT+ function. The more striking effect is seen in the 2νββ matrix element corresponding to the ground-state transition where the incoherence of individual contributions is stronger for the pnMAVA than for the pnQRPA, and a 15% reduction in the magnitude of the matrix element is obtained for the pnMAVA. The 2νββ transition rate to the excited 0+ state is zero in a pnQRPA calculation, whereas the pnMAVA result is not far from the measured decay rate.

Isomer-tagged differential-plunger measurements in proton-unbound 144Ho

The lifetime of an excited state above a weakly populated isomer in the proton-unbound odd–odd nucleus 144Ho has been measured using the recoil distance Doppler shift method. This measurement represents the first differential-plunger lifetime measurement to utilize recoil-isomer tagging. The first excited I π = ( 10 + ) state above the two-quasiparticle π h 11 / 2 ⊗ ν h 11 / 2 ( 8 + ) isomer was determined to have a lifetime of τ = 6 ( 1 ) ps . Potential energy surface calculations, based on the configuration-constrained blocking method, predict the isomeric state to have γ-soft triaxial-nuclear shape with | γ | ≈ 24 ° . The lifetime of the ( 10 + ) state can be understood from these calculations if there is a degree of rotational alignment in this band, with the K value being lower than the bandhead spin. However, the validity of the K quantum number with large predicted triaxiality and gamma softness requires further theoretical study.

Extended Skyrme interaction: II. Ground state of nuclei and of nuclear matter

We study the effect of time-odd components of the Skyrme energy density functionals on the ground state of finite nuclei and in nuclear matter. The spin-density-dependent terms, which have been recently proposed as an extension of the standard Skyrme interaction, are shown to change the total binding energy of odd nuclei by only few tenths of keV, while the time-odd components of standard Skyrme interactions give an effect that is larger by one order of magnitude. The HFB-17 mass formula based on a Skyrme parametrization is adjusted including the new spin-density-dependent terms. A comprehensive study of binding energies in the whole mass table of 2149 nuclei gives a root mean square (rms) deviation of 0.575 MeV between experimental data and the calculated results, which is as good as the original HFB-17 mass formula. From the analysis of the spin instabilities of nuclear matter, restrictions on the parameters governing the spin-density-dependent terms are evaluated. We conclude that with the extended Skyrme interaction, the Landau parameters G0 and G′0 could be tuned with a large flexibility without changing the ground-state properties in nuclei or nuclear matter.

Odd-even mass difference and isospin dependent pairing interaction

The neutron and proton odd-even mass differences are studied with Hartree-Fock + BCS (HF + BCS) calculations with Skyrme interactions and an isospin dependent contact pairing interaction, which is recently derived from a microscopic nucleon-nucleon interaction. To this end, we perform HF + BCS calculations for even and odd semi-magic tin and lead isotopes together with even and odd Z isotones with N = 50 and 82. The filling approximation is applied to the last unoccupied particle in odd nuclei. Comparisons with the experimental data show a clear manifestation of the isospin dependent pairing correlations in both proton and neutron pairing gaps.

Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.: (VI) hfodd (v2.40h): A new version of the program

Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.: (VI) hfodd (v2.40h): A new version of the program

20 μsisomeric state in doubly odd61134Pm

Recoil-isomer tagging at the Accelerator Laboratory of the University of Jyvaeskylae has been used to establish the isomeric nature of a known (7{sup -}) excited state in the doubly odd nucleus {sup 134}Pm. The isomeric state was determined to have a half-life of 20(1) {mu}s and was populated from the decay of a {pi}h{sub 11/2} x {nu}h{sub 11/2} band using the {sup 92}Mo({sup 54}Fe,2{alpha}3pn) reaction at 305 and 315 MeV. The isomer decays by a 71-keV transition that provides an intermediate step in linking the established {sup 134}Pm high-spin level scheme to the lower-spin states observed from the {beta} decay of {sup 134}Sm. Electron-conversion analysis for the 71-keV {gamma}-ray transition reveals that it is of E1 character and its small reduced-transition probability suggests that {sup 134}Pm may have a nuclear shape more rigid than that of the neighboring nuclei.

Observation of Three-Quasiparticle Doublet Bands in 123I: Possible Evidence of Chirality

A new band in the odd proton nucleus 123I is identified via in-beam γ-ray spectroscopy using the 14N+116Cd reaction. This band shows up as doublets with the previously assigned πg7/2 ⊗ (νh11/2)2 band. Possible configurations of the new band are discussed in the framework of the cranked shell model and the geometrical model. It is argued that the new band might be a chiral partner of the previously known πg7/2 ⊗ (νh11/2) band.

Single particle states in neutron-richZr101,Mo103,105,107, andRu109,111

The multipole mixing ratios of $\ensuremath{\Delta}I=1$ transitions between levels in rotational bands built on single-particle states in odd neutron nuclei are dependent on the configurations of the states. In particular, the mixing ratio can be used to distinguish between several possible single-particle configurations if interpreted with the particle-axial-rotor model. This work features the first determination of the ground-state configurations of $^{109,111}\mathrm{Ru}$. The single-particle structures of the ground states of $^{101}\mathrm{Zr}$ and $^{103,105,107}\mathrm{Mo}$ as well as excited states in $^{103,107}\mathrm{Mo}$ are also investigated, with a new result found in $^{107}\mathrm{Mo}$.

Analytical approach to particle-rotor model for single j configuration, γ = 30°

The analytical method is developed to describe yrast states in odd triaxial nuclei. Simple expressions for the energies and the wave functions are obtained. B(M1) transition probabilities inside the yrast band are considered.

New description of the doublet bands in doubly odd nuclei

The experimentally observed $\ensuremath{\Delta}I=1$ doublet bands in some odd-odd nuclei are analyzed within the orthosymplectic extension of the interacting vector boson model (IVBM). A new, purely collective interpretation of these bands is given on the basis of the obtained boson-fermion dynamical symmetry of the model. It is illustrated by its application to three odd-odd nuclei from the $A~130$ region, namely $^{126}\mathrm{Pr}$, $^{134}\mathrm{Pr}$, and $^{132}\mathrm{La}$. The theoretical predictions for the energy levels of the doublet bands as well as $E2$ and $M1$ transition probabilities between the states of the yrast band in the last two nuclei are compared with experiment and the results of other theoretical approaches. The obtained results reveal the applicability of the orthosymplectic extension of the IVBM.

Enhanced Radiative Strength in the Quasicontinuum ofSn117

The radiative strength function of 117Sn has been measured up to the neutron separation energy using the (3He, 3He' gamma) reaction. An increase in the slope of the strength function around E gamma=4.5 MeV indicates the onset of a resonancelike structure, giving a significant enhancement of the radiative strength function compared to standard models in the energy region 4.5<or=E gamma<or=8.0 MeV. For the first time, the functional form of this resonancelike structure has been measured in an odd tin nucleus below neutron threshold in the quasicontinuum region.

Chirality in odd-A nucleus 135Nd in particle rotor model

A particle rotor model is developed which couples several valence protons and neutrons to a rigid triaxial rotor core. It is applied to investigating the chirality in odd-A nucleus 135Nd with πh11/22⊗νh11/2−1 configuration for the first time in a fully quantal approach. For the two chiral sister bands, the observed energies and the B(M1) and B(E2) values for the in-band as well as interband transitions are reproduced excellently. Root mean square values of the angular momentum components and their probability distributions are used for discussing in detail the chiral geometry of the aplanar rotation and its evolution with angular momentum. Chirality is found to change from a soft chiral vibration to nearly static chirality at spin I=39/2 and back to another type of chiral vibration at higher spin.