Odd Proton Research Articles

Deformation of Odd Nuclei 27Al, 31P and 35Cl in Single-Particle States

Using the evolutionary approach recently developed by us, the shapes of odd s-d-shell 27Al, 31P and 35Cl nuc­lei in the ground and single-particle excited states have been extracted from the experimental data on the energies, spins, and parities of these states, as well as the measured probabilities of electromagnetic transitions between them. The key ingredient of our procedure is the evolutionary algorithm that evolves the population of the bad-quality data-fitting nuclear shapes to the high-quality data-fitting nuclear shapes. We have found that the studied nuclei in the ground states are abnormally weakly deformed, which is not expected for the nuclei in the shell middle. Even in their low-laying single-particle excited states, the nuclei 27Al and 31P are found to be weakly deformed, too. With the increase of the single-particle excitation energy, the change of the state of the only one nucleon – the valence proton the spin and parity of which determine the spin and parity of the 35Cl nucleus – causes the shape phase transition from the high-symmetry phase – spherical ground state – to the low-symmetry phase – deformed excited states. The angular part of the 27Al and 31P nuclei shape is de­scribed by two harmonics – quadrupole and hexadecapole. The angular part of the 35Cl nucleus shape is de­scribed by three harmonics – quadrupole, hexadecapole, and hexacontatetrapole, but the contribution of hexadecapole deformation is not independent. At present, there are no fundamental nuclear models that account for or predict the dominant hexacontatetrapole deformation, especially for light and medium nuclei. We have found that the spin and parity of the 27Al, 31P and 35Cl nuc­lei are determined by the spin and parity of the last odd (valence) proton. At the same time, some of the nucleons of the nucleus core change their characteristics, too. Thus, the electromagnetic transitions between the single-particle states of the 27Al, 31P and 35Cl nuc­lei are the multi-particle processes.

Examination of nuclear chirality with a magnetic moment measurement of the I=9 isomeric state in Cs128

The $g$ factor of the isomeric $I={9}^{+}$ bandhead of the yrast states in $^{128}\mathrm{Cs}$ is obtained from the time differential perturbed angular distribution measurement performed with the electromagnet at IPN Orsay. An external magnetic field of 2.146 T at the target position was attained with GAMIPE reaction chamber surrounded by four high-purity germanium detectors, of which two were low-energy photon spectrometer type. The results are in accordance with $\ensuremath{\pi}{h}_{11/2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}^{\ensuremath{-}1}\phantom{\rule{4pt}{0ex}}I={9}^{+}$ bandhead assignment and are discussed in the context of chiral interpretation of the $^{128}\mathrm{Cs}$ nucleus as a composition of the odd proton, odd neutron, and even-even core with their angular momentum vectors. The obtained $g$-factor value was compared with predictions of the particle-rotor model. The experimental $g$ factor corresponds to the nonchiral geometry of the isomeric bandhead. This observation indicates the existence of the chiral critical frequency in $^{128}\mathrm{Cs}$ and may explain the absence of the chiral doublet members for $I<13\ensuremath{\hbar}$.

Level structure in the transitional nucleus Fr215

The level scheme of $^{215}\mathrm{Fr}$ is extended up to 55/2 $\ensuremath{\hbar}$ and 4.8 MeV excitation energy with the addition of 52 new $\ensuremath{\gamma}$-ray transitions. Previously established isomers and their half-lives, except for the ${47/2}^{+}$ state, are revisited. The discrepancy in the half-life of the ${39/2}^{\ensuremath{-}}$ state is resolved, and its half-life is revised to 11.4(14) ns. An overall good agreement is observed between the experimental results and the shell-model calculations performed using the CD-Bonn $NN$ interaction derived from the ${V}_{\text{low-}k}$ renormalization approach. A weak coupling of the odd proton to the even-even core is observed to account for the level structure at lower energies, which strongly resembles a decoupled nonrotational band. A new positive-parity sequence is also established which is observed to originate from the coupling of the ${i}_{13/2}$ proton at low excitation energy.

Conflicting Coupling of Unpaired Nucleons and the Structure of Collective Bands in Odd-Odd Nuclei

The conflicting coupling of unpaired nucleons in odd-odd nuclei is discussed. A very simple explanation is suggested for the damping of the energy spacing of the lowest levels in the rotational bands in odd-odd nuclei with the ``conflicting'' coupling of an odd proton and an odd neutron comparative to those of the bands based on the state of a strongly coupled particle in the neighboring odd nucleusentering the "conflicting" configuration.

A new boson approach for the wobbling motion in even–odd nuclei

A triaxial core rotating around the middle axis, i.e. two-axis, is cranked around the one-axis, due to the coupling of an odd proton from a high j orbital. Using the Bargmann representation of a new and complex boson expansion of the angular momentum components, the eigenvalue equation of the model Hamiltonian acquires a Schrödinger form with a fully separated kinetic energy. From a critical angular momentum, the potential energy term exhibits three minima, two of them being degenerate. Spectra of the deepest wells reflects a chiral-like structure. Energies corresponding to the deepest and local minima respectively, are analytically expressed within a harmonic approximation. Based on a classical analysis, a phase diagram is constructed. It is also shown that the transverse wobbling mode is unstable. The wobbling frequencies corresponding to the deepest minimum are used to quantitatively describe the wobbling properties in 135Pr. Both energies and e.m. transition probabilities are described.

Core of F25 in the rotational model

In a recent experiment, carried out at RIBF/RIKEN, the $^{25}$F$(p,2p)$$^{24}$O reaction was studied at 270 MeV/A in inverse kinematics. Derived spectroscopic factors suggest that the effective core of $^{25}$F significantly differs from a free $^{24}$O nucleus. We interpret these results within the Particle-Rotor Model and show that the experimental level scheme of $^{25}$F can be understood in the rotation-aligned coupling scheme, with its $5/2^+_1$ ground state as the band-head of a decoupled band. The excitation energies of the observed $1/2_1^+$ and $9/2_1^+$ states correlate strongly with the rotational energy of the effective core, seen by the odd proton, and allow us to estimate its $2^+$ energy at $\approx$ 3.2 MeV and a moderate quadrupole deformation, $\epsilon_2 \approx 0.15$. The measured fragmentation of the $\pi d_{5/2}$ single-particle strength is discussed and some further experiments suggested.

Proton drip line nuclei in the Relativistic Hartree-Bogoliubov model

The Relativistic Hartree Bogoliubov (RHB) theory is applied to the description of ground-state properties of proton-rich odd-Z nuclei. The model predicts the location of the proton drip-line, the ground-state quadrupole deformations and one-proton separation energies at and beyond the drip-line, the deformed single-particle Orbitals occupied by the odd valence proton, and the corresponding spectroscopic factors. The results of fully self-consistent RHB calculations are compared with experimental data on deformed and transitional proton emitters and the predictions of various mass models.

Global microscopic calculations of odd-odd nuclei

The macroscopic-microscopic finite-range droplet model is combined with a particle-rotor coupling model in order to systematically describe low-energy spectra of odd-odd nuclei. The odd proton and neutron are allowed to interact through effective nuclear forces representing the residual neutron-proton interaction. In particular, ground-state spins and parities are calculated and compared to data, where all 268 axially symmetric nuclei which have reliable spin and parity assignments in the Nubase 2016 database are considered. Using a residual neutron-proton interaction composed of both central and tensor terms the agreement with experimental ground-state spins and parities reaches 41% for spherical nuclei and 31% for deformed nuclei. The model is applied to study possible $\ensuremath{\alpha}$-decay chains in superdeformed odd-odd nuclei, and ${Q}_{\ensuremath{\alpha}}$ values are calculated considering favored decay-paths as compared to ground-state paths.

Pygmy resonances: what’s in a name?

The centroid, width and percentage of energy weighted sum rule of dipole resonances can be strongly affected by dynamical fluctuations and static deformations of the nuclear surface, deformations and fluctuations which, in turn, depend on pairing, and thus on Cooper pairs. Because of angular momentum conservation, such insight is restricted, to lowest order, to fluctuations/deformations of quadrupole and monopole type. The latter being closely connected with the neutron (excess) skin and thus with soft dipole modes. From the values (N − Z)/A ≈ 0.18, 0.21, and 0.45 for the nuclei 122Sn, 208Pb, and 11Li, it is expected that the latter system, which is weakly bound by pairing effects (spatially extended single Cooper pair and odd proton acting as spectator), constitutes an attractive laboratory to study the properties of soft E1-modes and thus of isospin nuclear deformation. From the calculation of the full dipole response function in QRPA, discretizing the continuum in a spherical box of radius of 40 fm, one finds a GDR with centroid Ex ≈ 24 MeV, width Γ ≈11 MeV and carrying 90% of the EWSR, and a low-lying collective resonance characterized by EX = 0.75 MeV, Γ = 0.5 MeV and 6.2% EWSR. The wave function of the latter resonance is built out of about fifteen components (both protons and neutrons), typical of a collective mode. The transition densities indicate this soft E1-mode to be generated by surface density oscillation of the neutron (halo) skin (Δrnp ≈ 1.71 fm) relative to an approximately isospin-saturated core. Through a detailed study of the full dipole response of 11Li we will draw a comparison between the soft E1-mode of this halo nucleus and the PDR of heavy stable nuclei, pointing to the physical similarities and also to the basic differences.

Spectroscopy of odd-odd nuclei within the interacting boson-fermion-fermion model based on the Gogny energy-density functional

We present a method to calculate spectroscopic properties of odd-odd nuclei within the framework of the Interacting Boson-Fermion-Fermion Model based on the Gogny energy density functional. The $(\beta,\gamma)$-deformation energy surface of the even-even (boson-)core nucleus, spherical single-particle energies and occupation probabilities of the odd neutron and odd proton, are provided by the constrained self-consistent mean-field calculation within the Hartree-Fock-Bogoliubov method with the Gogny-D1M functional. These quantities are used as a microscopic input to fix most of the parameters of the IBFFM Hamiltonian. Only a few coupling constants for the boson-fermion Hamiltonian and the residual neutron-proton interaction are specifically adjusted to reproduce experimental low-energy spectra in odd-mass and odd-odd nuclei, respectively. In this way, the number of free parameters involved in the IBFFM framework is reduced significantly. The method is successfully applied to the description of the low-energy spectra and electromagnetic transition rates in the odd-odd $^{194,196,198}$Au nuclei.

\u201cSpin-dependent\u201d varvec{mu rightarrow e} conversion on light nuclei

The experimental sensitivity to mu rightarrow e conversion will improve by four or more orders of magnitude in coming years, making it interesting to consider the “spin-dependent” (SD) contribution to the rate. This process does not benefit from the atomic-number-squared enhancement of the spin-independent (SI) contribution, but probes different operators. We give details of our recent estimate of the spin-dependent rate, expressed as a function of operator coefficients at the experimental scale. Then we explore the prospects for distinguishing coefficients or models by using different targets, both in an EFT perspective, where a geometric representation of different targets as vectors in coefficient space is introduced, and also in three leptoquark models. It is found that comparing the rate on isotopes with and without spin could allow one to detect spin-dependent coefficients that are at least a factor of few larger than the spin-independent ones. Distinguishing among the axial, tensor and pseudoscalar operators that induce the SD rate would require calculating the nuclear matrix elements for the second two. Comparing the SD rate on nuclei with an odd proton vs. odd neutron could allow one to distinguish operators involving u quarks from those involving d quarks; this is interesting because the distinction is difficult to make for SI operators.

The equation of motion phonon method and its application in the neutron rich oxygen region

An equation of motion phonon method, developed for even-even nuclear systems and extended to odd nuclei, is applied to 22O and to its odd neighbors 23O and 23F. A calculation using the chiral potential NNLOopt is carried out in a space encompassing up to two phonons. The computed dipole cross section in 22O and the spectra of 22O and 23O are in a satisfactory agreement with the experimental data. However, the calculation describes poorly the spectrum of 23F. This discrepancy originates from the strong coupling between the odd proton and the 22O phonons of neutron nature. This coupling pushes down in energy several states enhancing the level density at low energy. We suggest that a viable route for the solution of this problem could be the inclusion of the three-body interaction using the new chiral potential NNLOsat.

Enhanced effect of CP -violating nuclear magnetic quadrupole moment in a HfF+ molecule

The ${\mathrm{HfF}}^{+}$ cation is a very promising system to use in the search for the electron electric dipole moment (EDM), and a corresponding experiment is carried out by JILA group [H. Loh, K. C. Cossel, M. C. Grau, K.-K. Ni, E. R. Meyer, J. L. Bohn, J. Ye, and E. A. Cornell, Science 342, 1220 (2013); K.-K. Ni, H. Loh, M. Grau, K. C. Cossel, J. Ye, and E. A. Cornell, J. Mol. Spectrosc. 300, 12 (2014). Here we theoretically investigate the cation to search for another effect which violates time-reversal ($T$) and spatial parity ($P$) symmetries---the nuclear magnetic quadrupole moment (MQM) interaction with electrons. We report an accurate ab initio relativistic electronic structure calculations of the molecular parameter ${W}_{M}=0.494 \frac{{10}^{33}\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}}{e\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2}}$ that is required to interpret the experimental data in terms of the MQM of the Hf nucleus. For this we have implemented and applied the combined Dirac-Coulomb(-Gaunt) and relativistic effective core potential approaches to treat electron correlation effects from all of the electrons and to take into account high-order correlation effects using the coupled cluster method with single, double, triple and noniterative quadruple cluster amplitudes. We discuss interpretation of the MQM effect in terms of the strength constants of $T,P$-odd nuclear forces, proton and neutron EDMs, the QCD parameter $\ensuremath{\theta}$, and quark chromo-EDMs.

Investigation of the structure of core-coupled odd-proton Copper nuclei in fpg valence space using the Projected Shell Model

By employing a systematically parametrized Hamiltonian and the best fit of the various input parameters, high-spin yrast energy states for an isotopic chain of odd mass 59-69Cu nuclei have been investigated by using a novel computational quantum mechanical framework-projected shell model. Comparison of calculations and experiments yields good agreement. The present study of various intriguing nuclear structure properties along the yrast lines in these odd proton isotopes reflects some interesting informative nuclear physics results. The calculations successfully describe the formation of the yrast level structures from multi-quasi-particle configurations based on $\pi f \otimes \nu g$ bands for 59-69Cu isotopes. The present calculations indicate the evolution of the nuclear structure near the magic nuclei, Ni, and also provide an indication of coexistence of both, collective as well as single-particle, levels for 69Cu nucleus at N=40.

Single-particle structures, high-spin isomers, and a strongly coupled band in odd-oddSb120

Excited states in $^{120}\mathrm{Sb}$ have been investigated using the $^{116}\mathrm{Cd}(^{7}\mathrm{Li},3n)^{120}\mathrm{Sb}$ reaction at a beam energy of 34 MeV. A total of 15 new $\ensuremath{\gamma}$ rays were added into the level scheme of $^{120}\mathrm{Sb}$. Most of the observed single-particle states can be interpreted in terms of weak coupling of the odd proton and odd neutron to an excited $^{118}\mathrm{Sn}$ core involving either vibrational states or broken neutron pairs. The previously known strongly coupled rotational band based on the $\ensuremath{\pi}{g}_{9/2}^{\ensuremath{-}1}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}$ configuration has been extended up to the ${(15}^{\ensuremath{-}})$ state. The configuration-fixed constrained triaxial relativistic mean-field approaches and the particle rotor model are employed to discuss the high-spin isomers and strongly coupled rotational band, respectively.

Fast-timing lifetime measurements of excited states inCu67

The half-lives of the 9/2 + , 13/2+ , and 15/2+ yrast states in the neutron-rich 67Cu nucleus were determined by using the in-beam fast-timing technique. The experimentally deduced E3 transition strength for the decay of the 9/2+ level to the 3/2- ground state indicates that the wave function of this level might contain a collective component arising from the coupling of the odd proton p3/2 with the 3- state in 66Ni. Theoretical interpretations of the 9/2+ state are presented within the particle-vibration weak-coupling scheme involving the unpaired proton and the 3- state from 66Ni and within shell-model calculations with a 56Ni core using the jj44b residual interaction. The shell model also accounts reasonably well for the other measured electromagnetic transition probabilities.

Exotic decay modes of odd-Z (105–119) superheavy nuclei

Half-lives of proton emission for proton emitters with Z = 51 to 83 are calculated, in the frame-work of unified fission model with the penetrability calculated using the WKB approximation. For all the ground and isomeric state of the proton, the deformation degree of freedom is included. Calculated half-lives are in good agreement with the experimental ones. Experimentally for a few isotopes, proton and alpha branches are reported. Hence we have calculated the half-lives of alpha decay for these elements. For parent nuclei 157Ta, 166Ir, 167Ir, 176Tl and 177Tl, the alpha decay mode is preferred over the proton emission. Further, the calculations are extended to find half-lives of superheavy element with odd proton number in the range Z = 105 to 119, for both proton, alpha and for a few cluster decays. Calculations on superheavy elements reveal that cluster radioactivity has half-lives comparable with proton emissions. It is found that proton emission is the primary competing decay mode with respect to alpha decay for superheavy elements. Among considered clusters, 12C, 20Ne and 24Mg are found to have lowest half-lives among other N = Z clusters and for a few clusters the half-lives are found to be comparable with that of proton emission.

Medium-spin states in135Cs

Limited information is currently known on medium- and higher-spin states for ${}^{135}$Cs, a neutron-rich nucleus amenable to shell-model calculations due to its proximity to the shell closures in ${}^{132}$Sn. In order to extend the level structure of ${}^{135}$Cs to higher excitations, this nucleus was studied via prompt $\ensuremath{\gamma}$-ray spectroscopy of fragments following the fission of the compound nucleus ${}^{226}$Th formed in the ${}^{18}$O (91 MeV) $+$ ${}^{208}$Pb fusion-fission reaction. Medium-spin states up to spin (23/2) and $\ensuremath{\sim}$3.3 MeV excitation energy have been established. The observed states were compared with those in the neighboring $N=82$${}^{137}$Cs nucleus, as well as with states in the neighboring $N=80$ isotones. The coupling of the odd proton occupying the ${g}_{7/2}$ orbital to the yrast states in the ${}^{134}$Xe and ${}^{136}$Ba cores could account for the lower excited states of ${}^{135}$Cs. The experimental results are compared with predictions from shell-model calculations.

Competition betweenT=1andT=0pairing inpf-shell nuclei withN=Z

The pairing correlation energy for two-nucleon configurations with the spin-parity and isospin of $J^\pi=0^+$, $T$=1 and $J^\pi=1^+$, $T$=0 are calculated with $T$=1 and $T$=0 pairing interactions, respectively. To this end, we consider the $(1f2p)$ shell model space, including single-particle angular momenta of $l=3$ and $l=1$. It is pointed out that a two-body matrix element of the spin-triplet $T$=0 pairing is weakened substantially for the $1f$ orbits, even though the pairing strength is much larger than that for the spin-singlet $T$=1 pairing interaction. In contrast, the spin-triplet pairing correlations overcome the spin-singlet pairing correlations for the $2p$ configuration, for which the spin-orbit splitting is smaller than that for the $1f$ configurations, if the strength for the T=0 pairing is larger than that for the T=1 pairing by 50% or more. Using the Hartree-Fock wave functions, it is also pointed out that the mismatch of proton and neutron radial wave functions is at most a few % level, even if the Fermi energies are largely different in the proton and neutron mean-field potentials. These results imply that the configuration with $J^\pi=0^+$, $T$=1 is likely in the ground state of odd-odd $pf$ shell nuclei even under the influence of the strong spin-triplet $T$=0 pairing, except at the middle of the $pf$ shell, in which the odd proton and neutron may occupy the $2p$ orbits. These results are consistent with the observed spin-parity $J^{\pi}=0^+$ for all odd-odd $pf$ shell nuclei except for $^{58}_{29}$Cu, which has $J^{\pi}=1^+$.

New Levels in the Structure of the 36Cl by72Ge(35Cl, n) Reaction

The structure of odd–odd nuclei, such as 36Cl, offers a scope for investigating the underlying proton– neutron residual interaction. Such nuclei exhibit highly complex level structures due to the large number of possible couplings of the odd proton and neutron to the even–even core. In the analysis of the experimental data for the 36Cl nucleus, a few new gamma rays was also obtained; they were carefully placed in the level structure using coincidence techniques and relative intensities. The directional correlation from oriented nuclei ratios for the new as well as the known γ-ray transitions was also calculated.