Negative Parity Research Articles

Microscopic description of quadrupole-octupole coupling in neutron-rich actinides and superheavy nuclei with the Gogny-D1M energy density functional

The interplay between quadrupole and octupole degrees of freedom is discussed in a series of neutron-rich actinides and superheavy nuclei with $92 \le$ Z $\le 110$ and $186 \le$ N $\le 202$. In addition to the static Hartree-Fock-Bogoliubov approach, dynamical beyond-mean-field correlations are taken into account via both parity restoration and symmetry-conserving Generator Coordinate Method calculations based on the Gogny-D1M energy density functional. Physical properties such as correlation energies, negative-parity excitation energies as well as reduced transition probabilities $B(E1)$ and $B(E3)$ are discussed in detail. It is shown that, for the studied nuclei, the quadrupole-octupole coupling is weak and to a large extent the properties of negative parity states can be reasonably well described in terms of the octupole degree of freedom alone.

Various collective states in the I124 nucleus

The level structure of $^{124}\mathrm{I}$ ($Z=53, N=71$) has been studied via the $^{122}\mathrm{Sn}(^{7}\mathrm{Li},5n)^{124}\mathrm{I}$ reaction with a beam energy of 54 MeV. Through in-beam and out-of-beam $\ensuremath{\gamma}$-ray spectroscopy, the sophisticated low-lying levels including isomeric states and numerous collective states have been established for the first time. A positive-parity collective band built on the ${10}^{+}$ state at 1297 keV is interpreted as being associated with the combination of a proton and a neutron in the same intruder ${h}_{11/2}$ orbital, namely the $\ensuremath{\pi}{h}_{11/2}\ensuremath{\nu}{h}_{11/2}$ configuration. This band shows a typical quadrupole vibrational character. In contrast, the negative parity bands based on the $\ensuremath{\pi}{g}_{7/2}\ensuremath{\nu}{h}_{11/2}$ configuration show a soft triaxial rotation. An isomeric ${8}^{\ensuremath{-}}$ state at 689 keV with a half-life of 14 ns can be explained as a K isomer due to a proton with an ${\mathrm{\ensuremath{\Omega}}}_{p}=9/2$ in the ${g}_{9/2}$ orbital coupled to a neutron with an ${\mathrm{\ensuremath{\Omega}}}_{n}=7/2$ in the ${h}_{11/2}$ orbital. The excited states based on this $\ensuremath{\pi}{g}_{9/2}\ensuremath{\nu}{h}_{11/2}$ configuration show a coupled rotational structure. Another coupled rotational band built on the ${6}^{+}$ state at 714 keV is thought to be based on the $\ensuremath{\pi}{g}_{9/2}\ensuremath{\nu}{d}_{3/2}$ configuration.

Two-body neutral Coulomb system in a magnetic field at rest: From hydrogen atom to positronium

A simple locally accurate uniform approximation for the nodeless wave function is constructed for a neutral system of two Coulomb charges of different masses $(\ensuremath{-}q,{m}_{1})$ and $(q,{m}_{2})$ at rest in a constant uniform magnetic field for the states of positive and negative parity, $(1{s}_{0})$ and $(2{p}_{0})$, respectively. It is shown that by keeping the mass and charge of one of the bodies fixed, all systems with different second-body masses are related. This allows one to consider the second body as infinitely massive and to take such a system as basic. Three physical systems are considered in detail: the hydrogen atom with (in)finitely massive proton (deuteron, triton) and the positronium atom $(\ensuremath{-}e,e)$. We derive the Riccati-Bloch and generalized Bloch equations, which describe the domains of small and large distances, respectively. Based on the interpolation of the small- and large-distance behavior of the logarithm of the wave function, a compact ten-parametric function is proposed. Taken as a variational trial function, it provides accuracy of not less than six significant digits (SDs) ($\ensuremath{\lesssim}{10}^{\ensuremath{-}6}$ in relative deviation) for the total energy in the whole domain of considered magnetic fields $[0\phantom{\rule{0.16em}{0ex}},\phantom{\rule{0.16em}{0ex}}{10}^{4}]$ a.u. and not less than three SDs for the quadrupole moment ${Q}_{zz}$. To get reference points, the Lagrange mesh method with 16 K mesh points was used to get from ten to six SDs in energy from small to large magnetic fields. Based on the Riccati-Bloch equation, the first 100 perturbative coefficients for the energy, in the form of rational numbers, are calculated and, using the Pad\'e-Borel resummation procedure, the energy is found with not less than ten SDs at magnetic fields $\ensuremath{\le}1\phantom{\rule{0.16em}{0ex}}\mathrm{a}.\mathrm{u}.$

Quantum interference between spin-orbit split partial waves in the F + HD → HF + D reaction.

The effect of electron spin-orbit interactions on chemical reaction dynamics has been a topic of much research interest. Here we report a combined experimental and theoretical study on the effect of electron spin and orbital angular momentum in the F + HD → HF + D reaction. Using a high-resolution imaging technique, we observed a peculiar horseshoe-shaped pattern in the product rotational-state-resolved differential cross sections around the forward-scattering direction. The unusual dynamics pattern could only be explained properly by highly accurate quantum dynamics theory when full spin-orbit characteristics were considered. Theoretical analysis revealed that the horseshoe pattern was largely the result of quantum interference between spin-orbit split-partial-wave resonances with positive and negative parities, providing a distinctive example of how spin-orbit interaction can effectively influence reaction dynamics.

Evidence of antimagnetic rotational motion in Pd103

Lifetime measurements have been carried out for the levels of the negative parity yrast sequence in $^{103}\mathrm{Pd}$ nucleus using the Doppler shift attenuation method. The levels were populated via $^{94}\mathrm{Zr}(^{13}\mathrm{C}, 4n\ensuremath{\gamma})^{103}\mathrm{Pd}$ fusion-evaporation reaction at a beam energy of 55 MeV. De-exciting $\ensuremath{\gamma}$ rays were detected by utilizing the Indian National Gamma Array. The extracted transition probabilities and other auxiliary observations indicate that the sequence may be resulting from the antimagnetic rotational (AMR) motion of valence nucleons. The key characteristic feature of the AMR motion is the steady decrease of the $B(E2)$ transition probability with spin, which is seen in the present measured transitions for $^{103}\mathrm{Pd}$. The experimental results are compared with the theoretical predictions of tilted axis cranked approach based on the covariant density functional theory. It is noted that the properties of the AMR band structure for $^{103}\mathrm{Pd}$ predicted in this model analysis are in good agreement with the present experimental findings. Further, semi-classical particle-rotor model has been employed to substantiate the AMR interpretation of the observed band structure in $^{103}\mathrm{Pd}$ and it is shown that results are similar to the band structures observed in the neighboring isotopes, which have also been considered as candidates for AMR motion.

Decay properties of N*(1895)

The nature of nucleon resonances is still being debated, while much experimental data are accumulated. In this work, we focus on the negative parity resonance ${N}^{*}(1895)$ which is located in the scattering region of various meson-baryon coupled channels, and such dynamics can be crucial in understanding its properties. To test the relevance of such hadron dynamics, we investigate the decay properties of ${N}^{*}(1895)$ in detail. We examine how a two pole nature of ${N}^{*}(1895)$ is compatible with its observed decay properties. Moreover, we find that the resonance decays into final states involving $\mathrm{\ensuremath{\Lambda}}(1405)$ and $\mathrm{\ensuremath{\Sigma}}(1400)$, where the latter is not yet observed experimentally. Such decay processes can be useful to study the properties of the aforementioned hyperon resonances.

A detailed study of nuclear structure of odd-mass Pm isotopes near N = 82 shell closure

A systematic study of the positive as well as negative parity yrast structure for the odd-mass 145−149Pm isotopes is carried out by using the angular momentum projection technique implemented in the projected shell model (PSM). By assuming an axial symmetry in the deformed basis, we have been able to calculate the yrast states up to a maximum spin of 47/2 for both positive and negative parity, and as a result, a good agreement is obtained with available experimental data for all isotopes. The intrinsic structure of positive and negative parity yrast states has been found to be built on πg7/2 $$ \otimes $$ νh11/2 and πh11/2 $$ \otimes $$ νh11/2 configurations, respectively. The phenomenon of back-bending has also been discussed in the present work. Reduced electric and magnetic transitions probabilities [B(E2) and B(M1)] are also calculated using the PSM wave functions. Since experimental data on B(E2) and B(M1) are not available, these results can serve as motivation for experimentalists to look for these data. However, the theoretical values of transition strength ratio B(M1)/B(E2) have been found to be matching excellently with the experimental ones.

Investigation of Alignment Effects of Neutron and Proton Pairs in High Spin States of Band Crossing for <sup>159,160</sup>Sm Isotopes Using Projected Shell Model (PSM)

Energy spectrum of nucleus is one the important information for better recognition of nuclear force and interaction of nucleon inside of the nucleus. Energy levels of nucleus are measured by detecting gamma- ray energy spectrum when a target nucleus bombarded with a special projectile to excite it in to levels higher than ground state. On the other hand, there are several models to calculate nuclear energy levels. Solution of the Schrödinger equation by considering a suitable potential is direct method to obtain energy levels of a quantum mechanical system like nucleus. Projected shell model is a model of this type that is developed by solving the Schrödinger equation for a set of potentials along with role of spin. Band structure and yrast bands for even-even and odd-even isotopes of Samarium (^159,160Sm) are calculated using a Fortran code founded based on the projected shell model (PSM). Energy levels of negative and positive parity bands of ¹⁵⁹Sm and ¹⁶⁰Sm isotopes of Samarium nucleus are obtained separately for each spin. Kinetic and dynamic moments of inertias are also calculated for these isotopes. The acquired results are compared with the experimental data. The electromagnetic reduced transition probabilities, B(M1)/B(E2) the behavior of dynamic moment of inertia J², rotational kinetic energy and moment of inertia J¹ as a function of spin have also been investigated and proper comparison is made between the calculated results and the experimental data. The alignment phenomena of neutron-proton pairs in view of the rotational movement in high spin states has also been studied with reference to band crossing.

Evolution of the N=20 and 28 shell gaps and two-particle-two-hole states in the FSU interaction

The FSU $spsdfp$ cross-shell interaction for the shell model was successfully fitted to a wide range of mostly intruder negative parity states of the $sd$ shell nuclei. This paper reports the application of the FSU interaction to systematically trace out the relative positions of the effective single-particle energies of the $0f_{7/2}$ and $1p_{3/2}$ orbitals, the evolution from normally ordered low-lying states to the "Island of Inversion" (IoI), and the behavior of a wide range of excited states with a $0f_{7/2}$ proton and neutron coupled to maximum spin of $7 \hbar$. Above a proton number of about 13 the $0f_{7/2}$ orbital lies below that of $1p_{3/2}$, which is considered normal ordering, but systematically at $Z = 10$ to $12$ the orbitals cross. The calculations reproduce well the 2p2h - 0p0h inversion in the configurations of nuclei inside the IoI, they reproduce the absolute binding energies and the transition to normal ordering as the proton number approaches that of the neutrons. The important role of $1p_{3/2}$ neutron pairs in the IoI is also demonstrated. The calculations account well for the energies of the fully aligned states with 0, 1, or 2 individual $sd$ nucleon aligned in spin with the aligned $\pi 0f_{7/2}$ - $\nu 0f_{7/2}$ pair and reproduce well their systematic variation with $A$ and number of aligned $sd$ nucleons. The results presented in this paper give hope for the predictive power of the FSU interaction for more exotic nuclei to be explored in near future.

Interplay between single particle and collective excitation in 49V

High spin states of 49V populated through 48Ti(4He, 2np)49V reaction with 48 MeV 4He beam, have been studied using the Indian National Gamma Array (INGA) facility. The relative intensities, RDCO and polarization measurements have been carried out for a few transitions in 49V. The level lifetimes have been extracted for a few negative parity yrast levels using Doppler shift attenuation method. Large basis shell model calculations have been performed to understand the microscopic structure of these levels.

Microscopic description of quadrupole-octupole coupling in actinides with the Gogny-D1M energy density functional

The interplay between quadrupole and octupole degrees of freedom is discussed in a series of U, Pu, Cm and Cf isotopes both at the mean-field level and beyond. In addition to the static Hartree–Fock–Bogoliubov approach, dynamical beyond-mean-field correlations are taken into account via both parity restoration and symmetry-conserving generator coordinate method calculations based on the parametrization D1M of the Gogny energy density functional. Physical properties such as correlation energies, negative-parity excitation energies as well as reduced transition probabilities B(E1) and B(E3) are discussed in detail and compared with the available experimental data. It is shown that, for the studied nuclei, the quadrupole-octupole coupling is weak and to a large extent the properties of negative parity states can be reasonably well described in terms of the octupole degree of freedom alone.

Competition between Allowed and First-Forbidden β Decay: The Case of ^{208}Hg→^{208}Tl.

The β decay of ^{208}Hg into the one-proton hole, one neutron-particle _{81}^{208}Tl_{127} nucleus was investigated at CERN-ISOLDE. Shell-model calculations describe well the level scheme deduced, validating the proton-neutron interactions used, with implications for the whole of the N>126, Z<82 quadrant of neutron-rich nuclei. While both negative and positive parity states with spin 0 and 1 are expected within the Q_{β} window, only three negative parity states are populated directly in the β decay. The data provide a unique test of the competition between allowed Gamow-Teller and Fermi, and first-forbidden β decays, essential for the understanding of the nucleosynthesis of heavy nuclei in the rapid neutron capture process. Furthermore, the observation of the parity changing 0^{+}→0^{-}β decay where the daughter state is core excited is unique, and can provide information on mesonic corrections of effective operators.

Lifetime measurements in 104Pd

High spin states in 104Pd were populated via 94Zr(13C, 3nγ) fusion-evaporation reaction at a beam energy of 55 MeV. The Indian National Gamma Array was utilized to detect the de-exciting γ-rays. Lifetimes of states in the negative parity bands have been determined using the Doppler shift attenuation method. The present lifetime results suggest a moderate quadrupole deformation (β 2 ≈ 0.2) for the negative parity bands. The Woods–Saxon total Routhian surface calculations have also been carried out which predicted a similar deformation for these bands. In addition, lifetimes of states in the positive parity band have also been determined. Present results found in agreement with the earlier reported values of lifetimes and hence agreed with the antimagnetic rotational character of the band as interpreted earlier.

Charmonium spectroscopy motivated by general features of pNRQCD

Mass spectrum of charmonium is computed in the framework of potential non-relativistic quantum chromodynamics. O(1/m) and O(1/m2) relativistic corrections to the Cornell potential and spin-dependent potential have been added, and is solved numerically. New experimentally observed and modified positive and negative parity states like ψ(4230), ψ(4260), ψ(4360), ψ(4390), ψ(4660), χc1(4140) and χc1(4274) near open-flavor threshold have also been studied. We explain them as admixtures of S-D wave states and P-wave states. Apart from these states, some other states like X(3915), χc1(3872), ψ(3770) and ψ(4160) have been identified as 23P0, 23P1, 13D1 and 23D1 states. Subsequently, the electromagnetic transition widths and γγ, e+e−, light hadron and γγγ decay widths of several states are calculated at various leading orders. All the calculated results are compared with experimental and results from various theoretical models.

First Observation of Multiple Transverse Wobbling Bands of Different Kinds in ^{183}Au.

We report the first observation of two wobbling bands in ^{183}Au, both of which were interpreted as the transverse wobbling (TW) band but with different behavior of their wobbling energies as a function of spin. It increases (decreases) with spin for the positive (negative) parity configuration. The crucial evidence for the wobbling nature of the bands, dominance of the E2 component in the ΔI=1 transitions between the partner bands, is provided by the simultaneous measurements of directional correlation from the oriented states ratio and the linear polarization of the γ rays. Particle rotor model calculations with triaxial deformation reproduce the experimental data well. A value of spin, I_{m}, has been determined for the observed TW bands below which the wobbling energy increases and above which it decreases with spin. The nucleus ^{183}Au is, so far, the only nucleus in which both the increasing and the decreasing parts are observed and thus gives the experimental evidence of the complete transverse wobbling phenomenon.

Theoretical study of Nb isotope productions by muon capture reaction on Mo100

The isotope $ {}^{99} \rm{Mo} $, the generator of $ {}^{99m} \rm{Tc} $ used for diagnostic imaging, is supplied by extracting from fission fragments of highly enriched uranium in reactors. However, a reactor-free production method of $ {}^{99} \rm{Mo} $ is searched over the world from the point of view of nuclear proliferation. Recently, $ {}^{99} \rm{Mo} $ production through a muon capture reaction was proposed and it was found that about $ 50 \, \% $ of $ {}^{100} \rm{Mo} $ turned into $ {}^{99} \rm{Mo} $ through $ {}^{100} \rm{Mo} \left( \mu^-, n \right) $ reaction [arXiv:1908.08166]. However, the detailed physical process of the muon capture reaction is not completely understood. We, therefore, study the muon capture reaction of $ ^{100} \rm{Mo} $ by a theoretical approach. We used the proton-neutron QRPA to calculate the muon capture rate. The muon wave function is calculated with considering the electronic distribution of the atom and the nuclear charge distribution. The particle evaporation process from the daughter nucleus is calculated by a statistical model. From the model calculation, about $ 38 \, \% $ of $ {}^{100} \rm{Mo} $ is converted to $ {}^{99} \rm{Mo} $ through the muon capture reaction, which is in a reasonable agreement with the experimental data. It is revealed that negative parity states, especially $ 1^- $ state, play an important role in $ {}^{100} \rm{Mo} \left( \mu^-, n \right) {}^{99} \rm{Nb} $. The feasibility of $ {}^{99} \rm{Mo} $ production by the muon capture reaction is also discussed. Isotope production by the muon capture reaction strongly depends on the nuclear structure.

Strong decays of fully-charm tetraquarks into di-charmonia

We study strong decays of the possible fully-charm tetraquarks recently observed by LHCb, and calculate their relative branching ratios through the Fierz rearrangement. Together with our previous QCD sum rule study, our results suggest that the broad structure around 6.2–6.8 GeV can be interpreted as an S-wave ccc¯c¯ tetraquark state with JPC=0++ or 2++, and the narrow structure around 6.9 GeV can be interpreted as a P-wave one with JPC=0-+ or 1-+. These structures were observed in the di-J/ψ invariant mass spectrum, and we propose to confirm them in the di-ηc,J/ψhc,ηcχc0, and ηcχc1 channels. We also propose to search for their partner states having the negative charge-conjugation parity in the J/ψηc,J/ψχc0,J/ψχc1, and ηchc channels.

Indication of γ-vibration in 123,125,127I

High spin states in 127I were populated via 124Sn(7Li, 4nγ) fusion-evaporation reaction at Ebeam = 33 MeV. Level scheme of 127I has been updated by placing new γ-rays and also by confirming the spin/parity of several energy levels. Two new levels at Ex = 2628 and 3199 keV have been identified which are found to decay into the negative parity πh11/2 band. These two states and two earlier reported states at 3502 and 3989 keV have been interpreted as the γ-vibrational states on the basis of their decay pattern. Two positive parity three-quasiparticle bands above Iπ = 23/2+ states at 2901 and 3060 keV have been identified to be a possible candidate of chiral band. A comparison in the isotopic and isotonic chains reveals the possible existence of γ-vibration and chiral rotation in 123–127I.

Total Routhian surface calculations to study the abrupt band termination phenomenon in 121,123I

The phenomenon of abrupt band termination in [Formula: see text]I has been revisited in the light of total Routhian surface (TRS) calculations. Both axial ([Formula: see text]) and nonaxial ([Formula: see text]) quadrupole deformation parameters have been estimated for the negative parity states. The calculation has also been extended for [Formula: see text]I and the theoretical result has been compared with the available experimental information. The calculated transition quadrupole moments ([Formula: see text]) are matching nicely upto [Formula: see text] MeV. The noncollective oblate shapes become yrast at higher angular frequency in [Formula: see text]I. At lower spin, all of these nuclei exhibit a collective prolate shape. This sudden change in shape at [Formula: see text] is indicative of the loss of collectivity at [Formula: see text]–[Formula: see text] MeV.

Detailed spectroscopy of doubly magic Sn132

The structure of the doubly magic $^{132}_{50}$Sn$_{82}$ has been investigated at the ISOLDE facility at CERN, populated both by the $\beta^-$decay of $^{132}$In and $\beta^-$-delayed neutron emission of $^{133}$In. The level scheme of $^{132}$Sn is greatly expanded with the addition of 68 $\gamma$-transitions and 17 levels observed for the first time in the $\beta$ decay. The information on the excited structure is completed by new $\gamma$-transitions and states populated in the $\beta$-n decay of $^{133}$In. Improved delayed neutron emission probabilities are obtained both for $^{132}$In and $^{133}$In. Level lifetimes are measured via the Advanced Time-Delayed $\beta\gamma\gamma$(t) fast-timing method. An interpretation of the level structure is given based on the experimental findings and the particle-hole configurations arising from core excitations both from the \textit{N} = 82 and \textit{Z} = 50 shells, leading to positive and negative parity particle-hole multiplets. The experimental information provides new data to challenge the theoretical description of $^{132}$Sn.