Odd Neutron Research Articles

Microscopic calculation of fission product yields for odd-mass nuclei

Fission data are essential inputs to reaction networks involved in nucleosynthesis simulations and nuclear forensics. In such applications as well as in the description of multi-chance fission, the characteristics of fission for odd-mass nuclei are just as important as those for even-even nuclei. The fission theories that aim at explicitly describing fission dynamics are typically based on some variant of the nuclear mean-field theory. In such cases, the treatment of systems with an odd number of particles is markedly more involved, both formally and computationally. In this article, we use the blocking prescription of the Hartree-Fock-Bogoliubov theory with Skyrme energy functionals to compute the deformation properties of odd-mass uranium isotopes. We show that the resulting fission fragment distributions depend quite significantly on the spin of the odd neutron. By direct calculation of the spin distribution of the fissioning nucleus, we propose a methodology to rigorously predict the charge and mass distributions in odd-mass nuclei.

Fusion enhancement within a collective clusterization approach applied to the isotopic chain of neutron-rich light-mass compound nuclei

The dynamics of neutron-rich light-mass compound nuclei $^{24,25,26,27}\mathrm{Mg}^{*}$ formed in $^{12,13,14,15}\mathrm{C}+^{12}\mathrm{C}$ fusion reactions, respectively, is explored at different ${E}_{\mathrm{c}.\mathrm{m}.}$ values within the dynamical cluster decay model (DCM). DCM is based on the quantum mechanical fragmentation theory, which treats the binary fragmentation of emitting compound nucleus as light particles (LPs), intermediate mass fragments (IMFs), as well as symmetric mass fragments (SMFs), on equal footing, which is not the case with other fission and statistical models. All calculations are made for spherical considerations and angular momenta taken up to the $\ensuremath{\ell}$-critical value for the respective reactions. A fusion enhancement is observed as we go from compound nuclei (CN) having an even number of neutrons ($^{24,26}\mathrm{Mg}^{*}$) to CN with the odd number of neutrons ($^{25,27}\mathrm{Mg}^{*}$). Interestingly, we find that the only parameter of the DCM, the neck-length parameter $\mathrm{\ensuremath{\Delta}}R$ related to the barrier lowering, is in linear relation with ${\ensuremath{\sigma}}_{\mathrm{Fusion}}$ at chosen incident laboratory energy. The fusion enhancement is found to be larger for odd neutron number nuclei, which indicates the influence of unpaired neutrons on fusion cross sections. Within the formalism of DCM, the phenomenon of fusion enhancement finds its base in the process of collective clusterization, which is quite evident from the larger values of summed-up preformation probability for the reactions having odd mass projectiles or forming odd mass CN. The DCM calculated fusion cross sections are in good agreement with the available experimental data for the given reactions.

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 $I<13\ensuremath{\hbar}$.

Possible shape coexistence in odd-A Ne isotopes and the impurity effects of Λ hyperons * *Supported by the National Natural Science Foundation of China (U2032141), the Natural Science Foundation of Henan Province (202300410479), the Foundation of Fundamental Research for Young Teachers of Zhengzhou University (JC202041041), and the Physics Research and Development Program of Zhengzhou University (32410217)

In this study, shape evolution and possible shape coexistence are explored in odd-A Ne isotopes in the framework of the multidimensionally constrained relativistic-mean-field (MDC-RMF) model. By introducing and hyperons, the impurity effects on the nuclear shape, energy, size, and density distribution are investigated. For the interaction, the PK1 parameter set is adopted, and for the interaction, the PK1-Y1 parameter set is used. The nuclear ground state and low-lying excited states are determined by blocking the unpaired odd neutron in different orbitals around the Fermi surface. Moreover, the potential energy curves (PECs), quadrupole deformations, nuclear r.m.s. radii, binding energies, and density distributions for the core nuclei as well as the corresponding hypernuclei are analyzed. By examining the PECs, possibilities for shape coexistence in Ne and a triple shape coexistence in 31Ne are found. In terms of the impurity effects of Λ hyperons, as noted for even-even Ne hypernuclear isotopes, the hyperon exhibits a clear shrinkage effect, which reduces the nuclear size and results in a more spherical nuclear shape. The hyperon occupying the orbital is prolate, which causes the nuclear shape to be more prolate, and the hyperon occupying the orbital displays an oblate shape, which drives the nuclei to be more oblate.

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.

Lifetime measurements of excited states in 169,171,173Os: Persistence of anomalous B(E2) ratios in transitional rare earth nuclei in the presence of a decoupled i13/2 valence neutron

Lifetimes of low-lying excited states in the νi13/2+ bands of the neutron-deficient osmium isotopes 169,171,173Os have been measured for the first time using the recoil-distance Doppler shift and recoil-isomer tagging techniques. An unusually low value is observed for the ratio B(E2;21/2+→17/2+)/B(E2;17/2+→13/2+) in 169Os, similar to the “anomalously” low values of the ratio B(E2;41+→21+)/B(E2;21+→0gs+) previously observed in several transitional rare-earth nuclides with even numbers of neutrons and protons, including the neighbouring 168,170Os. Furthermore, the evolution of B(E2;21/2+→17/2+)/B(E2;17/2+→13/2+) with increasing neutron number in the odd-mass isotopic chain 169,171,173Os is observed to follow the same trend as observed previously in the even-even Os isotopes. These findings indicate that the possible quantum phase transition from a seniority conserving structure to a collective regime as a function of neutron number suggested for the even-even systems is maintained in these odd-mass osmium nuclei, with the odd valence neutron merely acting as a “spectator”. As for the even-even nuclei, the phenomenon is highly unexpected for nuclei that are not situated near closed shells.

Band structures, lifetimes, and shape coexistence in La130

The level structure of $^{130}\mathrm{La}$ has been investigated using the $^{121}\mathrm{Sb}(^{12}\mathrm{C}$, 3n) reaction with the ROSPHERE array at IFIN-HH, Bucharest. The level scheme was significantly extended with the observation of 45 new states and 100 new transitions. Several band structures have been identified and a clear connection with the lower-lying states has been established. A lifetime of $\ensuremath{\tau}=3.6(2)$ ns has been measured for the 346-keV ${6}^{\ensuremath{-}}$ state by the in-beam fast timing technique. The lifetimes of 18 high-spin states have been determined by applying the Doppler-shift attenuation method. The deformations derived from the experimental $B(E2)$ transition strengths indicate distinct coexisting shapes at high spins in $^{130}\mathrm{La}$. The experimental properties of both low- and high-spin states were compared with theoretical calculations performed in the frame of the two-quasiparticles-plus-rotor model. Two new negative-parity decoupled bands, with a deduced quadrupole deformation ${\ensuremath{\beta}}_{2}=0.150(15)$, were interpreted by coupling the proton in the 1/2[550] and 3/2[541] orbitals with the odd neutron occupying mainly the low-$\mathrm{\ensuremath{\Omega}}$ orbitals from the ${d}_{3/2}$ and ${s}_{1/2}$ states. A quadrupole deformation ${\ensuremath{\beta}}_{2}=0.220(17)$ was derived for a newly identified positive-parity decoupled band. This enhanced deformation was attributed to the involvement in the band configuration of the $\mathrm{\ensuremath{\Omega}}=1/2$ $({f}_{7/2},{h}_{9/2})$ intruder neutron orbital. The multiparticle configuration $\ensuremath{\pi}{g}_{7/2}{({h}_{11/2})}^{2}\ensuremath{\bigotimes}\ensuremath{\nu}({h}_{11/2})$ was assigned to a high-spin negative-parity dipole band, based on the comparison of the experimental $B(M1)$ transition strengths with values calculated by applying the geometrical model of D\onau and Frauendorf.

Cluster decay half-lives and preformation probabilities

An improved semi-analytic approach to the barrier penetration probability is developed in the frame work of the Wentzel-Kramers-Brillouin (WKB) approximation. It is used to calculate decay half-lives and preformation probabilities for a set of 304 cluster emitters in the range 87 ≤ Z ≤ 96 and a set of 390 α-emitters in the range 52 ≤ Z ≤ 120. For cluster decay, the validity of our approach is tested against Coulomb and proximity potential model (CPPM) by comparing decay half-lives and barrier penetration probabilities. Our results are found to be in a good agreement with CPPM calculations and with the available experimental data. In case of α-decay, our calculations are tested against the experimental data and also a very good agreement is achieved. In both cases, results are also compared with calculations of some other well known universal decay laws that are used in many recent studies. Our approach shows a better agreement with experimental data than most of the other models. Our study is extended to calculate the assault frequency and preformation probability of the cluster inside the parent nucleus. A strong correlation is obtained for all these parameters with each other. Neutron shell closures are found to be more important in the cluster decay process than proton shell closure. It is also noted that the odd–even staggering behavior dominates the decay processes involving the emission of clusters with odd neutron number.

Microscopic study of electromagnetic properties and band spectra of neutron deficient 133,135,137Sm

A microscopic high spin study of neutron deficient and normally deformed 133,135,137Sm has been carried out in projected shell model framework. The theoretical results have been obtained for the spins, parities and energy values of yrast and excited bands. Besides this, the band spectra, band head energies, moment of inertia and electromagnetic transition strengths are also predicted in these isotopes. The calculations successfully give a deeper understanding of the mechanism of the formation of yrast and excited bands from the single and multi-quasi particle configurations. The results on moment of inertia predict an alignment of a pair of protons in the proton (1h11/2)2 orbitals in the yrast ground state bands of 133-137Sm due to the crossing of one quasiparticle bands by multi-quasiparticle bands at higher spins. The discussion in the present work is based on the deformed single particle scheme. Any future experimental confirmation or refutation of our predictions will be a valuable information which can help to understand the deformed single particle structure in these odd mass neutron deficient 133-137Sm.

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.

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.

Investigating the fusion enhancement for neutron-rich mid-mass nuclei using the dynamical cluster-decay model

The mechanism involved in compound nucleus formation through heavy ion induced fusion reactions at near- and sub-barrier energies has been stimulating the interest of both experimentalists and theoreticians. The study of fusion reactions is important not only for the production of superheavy elements but also to unfold the mysteries involved in the evolution of neutron stars and nucleosynthesis of elements in astrophysical scenarios. The detection of gravitational waves originating from the merging of two black holes, and the possibility of observing similar events originating from black-hole--neutron-star mergers, highlighted the necessity of understanding the behavior of neutron-rich nuclear matter. One of the potential methods to understand the character of neutron-rich matter is through the study of fusion of an isotopic chain of reactions. Recently, the first experimental evidence of fusion enhancement at near-barrier energies for neutron-rich nuclei was reported for the light and mid-mass regime. To understand the dynamics involved in such reactions, the investigation of K-induced reactions has been performed using the quantum mechanical fragmentation based dynamical cluster-decay model (DCM). The experimental fusion cross sections of $^{39,47}\mathrm{K}+^{28}\mathrm{Si}$ are reproduced using DCM and, further, the fusion cross sections are predicted for other isotopes of K beam on $^{28}\mathrm{Si}$ to investigate the fusion enhancement as a function of neutron number. It has been observed that fusion enhancement is significant at near-barrier energies for neutron-rich nuclei. The fusion enhancement observed is larger for odd neutron number nuclei as compared to adjacent neutron nuclei. This indicates the influence of unpaired neutrons on fusion cross sections. Also, the fusion cross sections predicted in the present work will act as input for planning more experimental measurements.

\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.

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.

Band structure inSn113

The structure of collective bands in $^{113}\mathrm{Sn}$, populated in the reaction $^{100}\mathrm{Mo}(^{19}\mathrm{F},\phantom{\rule{0.16em}{0ex}}p5n)$ at a beam energy of 105 MeV, has been studied. A new positive-parity sequence of eight states extending up to 7764.9 keV and spin $(39/{2}^{+})$ has been observed. The band is explained as arising from the coupling of the odd valence neutron in the ${g}_{7/2}$ or the ${d}_{5/2}$ orbital to the deformed 2p-2h proton configuration of the neighboring even-$A$ Sn isotope. Lifetimes of six states up to an excitation energy of 9934.9 keV and spin $47/{2}^{\ensuremath{-}}\mathrm{belonging}$ to a $\mathrm{\ensuremath{\Delta}}I=2$ intruder band have been measured for the first time, including an upper limit for the last state, from Doppler-shift-attenuation data. A moderate average quadrupole deformation ${\ensuremath{\beta}}_{2}=0.22\ifmmode\pm\else\textpm\fi{}0.02$ is deduced from these results for the five states up to spin $43/{2}^{\ensuremath{-}}$. The transition quadrupole moments decrease with increase in rotational frequency, indicating a reduction of collectivity with spin, a feature common for terminating bands. The behavior of the kinematic and dynamic moments of inertia as a function of rotational frequency has been studied and total Routhian surface calculations have been performed in an attempt to obtain an insight into the nature of the states near termination.

Algebraic approach to the structure of the low-lying states inA≈100Ru isotopes

The structure of the low-lying states in the odd- and even-mass $A\ensuremath{\approx}100$ Ru isotopes is studied in the framework of two algebraic models. The even-mass Ru nuclei are first described within the interacting boson model 1 (IBM-1). The output of these calculations was then used to calculate the odd-$A$ isotopes within the interacting boson-fermion model 1 (IBFM-1), where a coupling of the odd neutron to the even-even core is considered. The level energies and transition probabilities calculated in the present work are tested against the experimental data. One-nucleon transfer spectroscopic factors as well as electromagnetic moments were also calculated for the odd-$A$ Ru and compared to the experimental values. The transitional character of the isotopes is studied. Most of the low-lying positive-parity states in the odd-$A$ Ru nuclei below 2 MeV are interpreted on the basis of $\ensuremath{\nu}{d}_{5/2}$ and $\ensuremath{\nu}{g}_{7/2}$ configurations. The role of the $\ensuremath{\nu}{s}_{1/2}$ orbital in the nuclear structure of the odd-mass Ru nuclei at low energies is also studied. The negative-parity states are interpreted as $\ensuremath{\nu}{h}_{11/2}$ excitations coupled to the core. The evolution of the IBM-1 and IBFM-1 parameters is discussed.

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.

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.

CHARACTERISTICS OF TWO-QUASIPARTICLE CHIRAL BANDS

The two-quasiparticle-plus-triaxial-rotor model was applied to study chiral configurations in the 100, 130 and 190 mass regions. It was shown that in order for a degeneracy in the two-quasiparticle partner bands to occur, one needs mutually orthogonal angular momenta of the odd proton, odd neutron and the collective rotation. The staggering in the B(M1) reduced transition probabilities as an indication of strongly broken symmetry was studied too.