Relative Orbital Angular Momentum Research Articles

New developments in fission studies within the time-dependent density functional theory framework

We have extended significantly the microscopic description of the fission process by examining a larger set of observables. We extract neutron and proton numbers of fission fragments, their spins and fission fragment relative orbital angular momentum and their correlations, investigate neutrons emitted at or shortly after scission, excitation energy sharing mechanism, total kinetic energy of fission fragments, and the entanglement entropy. I will present a short overview of our simulations obtained with two independent nuclear energy density functionals.

Three-Space from Quantum Mechanics

The spin geometry theorem of Penrose is extended from SU(2) to E(3) (Euclidean) invariant elementary quantum mechanical systems. Using the natural decomposition of the total angular momentum into its spin and orbital parts, the distance between the centre-of-mass lines of the elementary subsystems of a classical composite system can be recovered from their relative orbital angular momenta by E(3)-invariant classical observables. Motivated by this observation, an expression for the ‘empirical distance’ between the elementary subsystems of a composite quantum mechanical system, given in terms of E(3)-invariant quantum observables, is suggested. It is shown that, in the classical limit, this expression reproduces the a priori Euclidean distance between the subsystems, though at the quantum level it has a discrete character. ‘Empirical’ angles and 3-volume elements are also considered.

Angular correlation between the fission fragment intrinsic spins

The generation of fission fragment (FF) spins and of their relative orbital angular momentum has been debated for more than six decades, and no consensus has been achieved so far. The interpretation of recent experimental results of Wilson et al., Nature (London) 590, 566 (2021) has been challenged by several recent theoretical studies, which are not in agreement with one another. According to the interpretation by Wilson et al., Nature (London) 590, 566 (2021), the FF spins emerge very long after scission occurrs. Randrup and Vogt Phys. Rev. Lett. 127, 062502 (2021), while agreeing that the FF spins are uncorrelated, conclude on the basis of a phenomenological model that these spins are uncorrelated already before scission. Bulgac et al., Phys. Rev. Lett. 128, 022501 (2022) in a fully microscopic study demonstrate that the primordial FF spin final values are defined before the emission of prompt neutrons and statistical gammas and are strongly correlated with a relative angle between spins close to $2\ensuremath{\pi}/3$, a result in full agreement with the present independent analysis. The prompt neutrons and statistical gammas carry a significant amount of angular momentum according to the study of Stetcu et al., Phys. Rev. Lett. 127, 222502 (2021), which can lead to a decorrelation of the FF bandhead spins of the yrast lines measured by Wilson et al., Nature (London) 590, 566 (2021), and which also provides arguments why these measured spins are so different from the primordial FF spins evaluated by Bulgac et al., Phys. Rev. Lett. 128, 022501 (2022). Here, I show that the unexpected character of the angular correlation between the primordial FF intrinsic spins, recently evaluated by Bulgac et al., Phys. Rev. Lett. 128, 022501 (2022), which favors FF intrinsic spins pointing predominantly in opposite directions, can be understood by using simple general phase space arguments. The observation by Wilson et al., Nature (London) 590, 566 (2021) that the FF spins are uncorrelated follows from both the results of the microscopic calculation of Bulgac et al., Phys. Rev. Lett. 128, 022501 (2022) and the present analysis of the full correlated probability distribution of the FF spins together with the relative orbital angular momentum of the primordial FFs. These arguments may apply also to heavy-ion collisions and, since there is no use of specifics of the particle interactions, the present results might apply to atomic and molecular systems as well.

Fragment Intrinsic Spins and Fragments’ Relative Orbital Angular Momentum in Nuclear Fission

We present the first fully unrestricted microscopic calculations of the primary fission fragment intrinsic spins and of the fission fragments' relative orbital angular momentum for ^{236}U^{*}, ^{240}Pu^{*}, and ^{252}Cf using the time-dependent density functional theory framework. Within this microscopic approach, free of restrictions and unchecked assumptions and which incorporates the relevant physical observables for describing fission, we evaluate the triple distribution of the fission fragment intrinsic spins and of their fission fragments' relative orbital angular momentum and show that their dynamics is dominated by their bending collective modes in contradistinction to the predictions of the existing phenomenological models and some interpretations of experimental data.

Edge current and orbital angular momentum of chiral superfluids revisited

Cooper pairs in chiral superfluids carry quantized units of relative orbital angular momentum (OAM). Various predictions of the intrinsic OAM density or the macroscopic OAM of a two-dimensional chiral superfluid differ by several orders of magnitude, which constitute the so-called Angular Momentum Paradox. Following several previous studies, we substantiate the semiclassical Bogoliubov-de Gennes theory of the single-particle edge current and OAM in two-dimensional chiral superfluids in the BCS limit. The analysis provides a simple intuitive understanding for the vanishing of OAM for a non-p-wave chiral superfluid (such as $d+id$) confined in a rigid potential. When generalized to anisotropic chiral superconductors and three-dimensional chiral superfluids, the theory similarly returns an accurate description. We also present a detailed numerical study of the chiral phases in the BEC limit. Our study suggests that, in both BCS and BEC phases the relative OAM of the individual Cooper pairs contribute to the total OAM additively, and that in both phases the corresponding macroscopic OAM density distribution is localized at the boundary.

Gravitational transition form factors of N(1535)→N

We employ the quark part of the symmetric energy-momentum tensor current to calculate the transition gravitational form factors of the $N(1535) \rightarrow N$ by means of the light cone QCD sum rule formalism. In numerical analysis, we use two different sets of the shape parameters in the distribution amplitudes of the $ N(1535) $ baryon and the general form of the nucleon's interpolating current. It is seen that the momentum squared dependence of the gravitational form factors can be well described by the p-pole fit function. The results obtained by using two sets of parameters are found to be quite different from each other and the $N(1535) \rightarrow N$ transition gravitational form factors depend highly on the shape parameters of the distribution amplitudes of the $N(1535)$ state that parametrize relative orbital angular momentum of the constituent quarks.

Bottomonium resonances with I=0 from lattice QCD correlation functions with static and light quarks

We discuss, how to study $I = 0$ quarkonium resonances decaying into pairs of heavy-light mesons using static potentials from lattice QCD. These static potentials can be obtained from a set of correlation functions containing both static and light quarks. As a proof of concept we focus on bottomonium with relative orbital angular momentum $L = 0$ of the $\bar{b} b$ pair corresponding to $J^{P C} = 0^{- +}$ and $J^{P C} = 1^{- -}$. We use static potentials from an existing lattice QCD string breaking study and compute phase shifts and $\mbox{T}$ matrix poles for the lightest heavy-light meson-meson decay channel. We discuss our results in the context of corresponding experimental results, in particular for $\Upsilon (10860)$ and $\Upsilon (11020)$.

Orbital angular momentum of a laser beam behind an off-axis spiral phase plate.

Here we obtain a simple formula for the relative total orbital angular momentum (OAM) of a paraxial light beam with arbitrary rotationally symmetric complex amplitude, passed through an off-axis spiral phase plate (SPP). The formula shows that the OAM is zero if the incident light is bounded by a diaphragm, and the SPP center is outside it. Another consequence of the obtained formula is that if the incident light is limited by an annular diaphragm then the full angular momentum is the same, regardless of the position of the SPP center inside the shaded circle of the annular diaphragm. This means that it is more appropriate to illuminate the SPP by beams with an annular intensity distribution because, in this case, the inaccurate alignment of the SPP center and the center of the annular intensity distribution do not affect the total OAM of the beam. In addition, we obtain a formula for the OAM density of such a light beam in the initial plane. The experimentally measured OAM is in good agreement with that calculated by the obtained formula.

Orbital angular momentum of an arbitrary axisymmetric light field after passing through an off-axis spiral phase plate

We obtain a simple formula for the relative total orbital angular momentum (OAM) of a paraxial light beam with arbitrary rotationally symmetric complex amplitude passed through a spiral phase plate (SPP) whose center is shifted from the optical axis. The formula shows that the OAM equals zero if the incident beam is bounded by an aperture and the SPP center is outside this aperture. For the incident beam bounded by an annular aperture, there is another interesting consequence of the obtained expression. The total OAM of such a beam is the same regardless of the position of the SPP center within the shaded circle of the aperture. Thus, it would be appropriate to illuminate the SPP by beams with an annular intensity distribution, since in this case an inaccurate alignment of the SPP center and the center of the annular intensity distribution does not affect the total OAM of the beam. We also obtain an expression for the OAM density of such a beam in the initial plane.

Making two dysprosium atoms rotate —Einstein-de Haas effect revisited

We present a numerical study of the behaviour of two magnetic dipolar atoms trapped in a harmonic potential and exhibiting the standard Einstein-de Haas effect while subject to a time-dependent homogeneous magnetic field. Using a simplified description of the short-range interaction and the full expression for the dipole-dipole forces we show that under experimentally realisable conditions two dysprosium atoms may be pumped to a high value of the relative orbital angular momentum.

Reply to “Comment on ‘Structure effects in theN15(n,γ)N16radiative capture reaction from the Coulomb dissociation ofN16'”

We reply to the comments (arXiv:1605.07499 [nucl-th]) on "Structure effects in the $^{15}$N($n,\gamma$)$^{16}$N radiative capture reaction from the Coulomb dissociation of $^{16}$N". We have investigated the issue of "energy dependence of branching ratios" and believe that this energy dependence is due to the proper inclusion of the non-resonant continuum in the post-form reaction theory. Interestingly, this energy dependence is sensitive to the relative orbital angular momentum content of the state. We reiterate that we have attempted to resolve the discrepancy in the spectroscopic factors of low-lying $^{16}$N levels and that it is essential to know the low energy $^{15}$N($n,\gamma$)$^{16}$N capture cross section, especially below 0.25 MeV.

Excess neutron nucleus 11Be as a product of reaction (t, p)

The (t, p) reaction on the 9Be nucleus is analyzed using the mechanisms of dineutron stripping and 8Li heavy cluster stripping. It is shown that in the shell model, the wave function of the 11Be(1/2+) nucleus formed by adding two neutrons to the 9Be nucleus is constructed from a 10Be(0+) core and a 2s-neutron. This concept of the 11Be(1/2+) structure allows us to calculate the reduced width of tritium and a dineutron with a relative orbital angular momentum equal to 1. The differential cross section of the (t, p) reaction is calculated with allowance for the contribution from both mechanisms. The agreement between the theoretical and experimental cross sections of dineutron stripping at narrow angles θp confirms the shell model can be used to describe the states of nuclei with complex structure and mixed configurations of different shells.

Peculiarities of quasifission reactions in heavy ion collisions

The probability of the formation and decay of a dinuclear system is investigated for a wide range of relative orbital angular momentum values. The mass and angular distributions of the quasifission fragments are studied to understand the reaction mechanisms of the heavy ion collision of 78Kr (10A MeV) + 40Ca within dinuclear system model. The quasifission products are found to contribute to the mass-symmetric region of the mass distribution in collisions with a large orbital angular momentum. The analysis of mass and angular distributions of quasifission fragments shows the possibility of the 180° rotation of the system so that projectile-like products can be observed in the forward hemisphere with large cross sections, which can explain the phenomenon observed recently in the ISODEC experiment.

Nucleon-Nucleon t-matrix Effective Interaction for (p, 2p) Reactions

In (p, 2p) reactions the p-p interaction is the main knockout interaction which acts in its full glory. Recent finite range (p, 2p) calculations used a parametrized spin-isospin dependent finite range tNN (r) - effective interaction operator which is a function of the distance between the nucleons alone. In the present work we have evaluated the nucleon-nucleon (N-N) t-matrix effective interaction using the Reid soft core N-N interaction potential. In this we find that the proper t- matrix effective interaction is not only a function of spin and isospin of the interacting nucleons but is a strong function of the relative orbital angular momentum, L also. The radial behaviour of the tL (r) is also found to be very unconventional in that it is found to go to zero at r = 0 while in the conventional usage the t(r) is taken to peak at r = 0 because of its representation in terms of Yukawa functions. This very different behaviour of our calculated N-N t-matrix effective interaction operator is expected to make large changes in the Finite Range (FR-DWIA) predictions for (p, 2p) reaction cross sections. Besides this it is hoped that the marked differences one obtains in the behaviour of these tL(r)'s from different realistic N-N interactions through their resulting fits obtained for the (p, 2p) reactions will provide us a tool to select the proper N-N interaction out of the many available in literature.

Exchange mechanism of dα interaction and vertex constants of 6Li

In this work, we use a model for describing the dα interaction in a 6Li nucleus, in which the dα nuclear potential is written as the sum of the local folding potential and a nonlocal term originating from the deuteron exchange mechanism and corresponding to a three-deuteron component of the 6Li wave function. This model was used to calculate the nuclear vertex constants and the corresponding asymptotic normalization coefficients of 6Li in the dα channel. Both values L = 0 and L = 2 of relative dα orbital angular momentum L were considered. Calculations were performed with and without allowance for the Coulomb dα interaction.

Dispersion interactions and reactive collisions of ultracold polar molecules

Progress in ultracold experiments with polar molecules requires a clear understanding of their interactions and reactivity at ultralow collisional energies. Two important theoretical steps in this process are the characterization of interaction potentials between molecules and the modeling of the reactive scattering mechanism. Here, we report on the ab initio calculation of isotropic and anisotropic van der Waals interaction potentials for polar KRb and RbCs colliding with each other or with ultracold atoms. Based on these potentials and two short-range scattering parameters, we then develop a single-channel scattering model with flexible boundary conditions. Our calculations show that, at low temperatures (and in the absence of an external electric field), the reaction rates between molecules or between molecules and atoms have a resonant character as a function of the short-range parameters. We also find that both the isotropic and anisotropic van der Waals coefficients have significant contributions from dipole coupling to excited electronic states. Their values can differ dramatically from those solely obtained from the permanent dipole moment. A comparison with recently obtained reaction rates of fermionic 40K87Rb shows that the experimental data cannot be explained by a model where the short-range scattering parameters are independent of the relative orbital angular momentum or partial wave.

Persistent currents in cold atoms

We propose a scheme to realize persistent mass and spin currents in cold atoms using optically generated gauge potentials. Two degenerate dark states can be created by coupling ``tripod'' atoms to three Laguerre-Gaussian laser beams carrying relative orbital angular momentum. Atoms in these dark states feel opposite effective magnetic fields of the flux-tube type and circulate in opposite directions around the axis of the tube, generating persistent mass currents in the system. Persistent spin currents can also be generated, with or without spin polarization.

Global quark polarization in noncentralA+Acollisions

Partons produced in the early stage of noncentral heavy-ion collisions can develop a longitudinal fluid shear because of the unequal local number densities of participant target and projectile nucleons. Under such fluid shear, local parton pairs with nonvanishing impact parameters have finite local relative orbital angular momentum along the direction opposite to the reaction plane. Such a finite relative orbital angular momentum among locally interacting quark pairs can lead to global quark polarization along the same direction because of spin-orbital coupling. Local longitudinal fluid shear is estimated within both the Landau fireball and the Bjorken scaling model of initial parton production. Quark polarization through quark-quark scatterings with the exchange of a thermal gluon is calculated beyond the small-angle scattering approximation in a quark-gluon plasma. The polarization is shown to have a nonmonotonic dependence on the local relative orbital angular momentum dictated by the interplay between electric and magnetic interactions. It peaks at a value of relative orbital angular momentum which scales with the magnetic mass of the exchanged gluons. With the estimated small longitudinal fluid shear in semiperipheral Au+Au collisions at energies currently available at the BNL Relativistic Heavy Ion Collider (RHIC), the final quark polarization is found to be small $|{P}_{q}|<0.04$ in the weak coupling limit. Possible behavior of the quark polarization in the strong coupling limit and implications on the experimental detection of such global quark polarization at RHIC and CERN Large Hadron Collider (LHC) are also discussed.

Subthreshold photofission of even-even nuclei

Within quantum-mechanical fission theory, the angular distributions of fragments originating from the subthreshold photofission of the even-even nuclei 232Th, 234U, 236U, 238U, 238Pu, 240Pu, and 242Pu are analyzed for photon energies below 7 MeV. Special features of various fission channels are assessed under the assumption that the fission barrier has a two-humped shape. It is shown that the maximum value of the relative orbital angular momentum Lm of fission fragments can be found upon taking into account deviations from the predictions of A. Bohr’s formula for the angular distributions of fission fragments. The result is Lm ≈ 30. The existence of an “isomeric shelf” for the angular distributions of fragments from 236U and 238U photofission in the low-energy region is confirmed.

Globally Polarized Quark-Gluon Plasma in NoncentralA+ACollisions

Produced partons have a large local relative orbital angular momentum along the direction opposite to the reaction plane in the early stage of noncentral heavy-ion collisions. Parton scattering is shown to polarize quarks along the same direction due to spin-orbital coupling. Such global quark polarization will lead to many observable consequences, such as left-right asymmetry of hadron spectra and global transverse polarization of thermal photons, dileptons, and hadrons. Hadrons from the decay of polarized resonances will have an azimuthal asymmetry similar to the elliptic flow. Global hyperon polarization is studied within different hadronization scenarios and can be easily tested.