Coupled-channel Calculations Research Articles

Reaffirmation of probe dependence of the mass deformation length for low-lying excitations in Sn112,116,118,120,122,124 isotopes

Background: A transparent approach for the study of nuclear shapes and sizes in excited states requires knowledge about dynamic deformations of both neutron and proton distributions, by means of their independent excitations at the same energy. Heavy-ion scattering could be a reliable approach, facilitating a simultaneous study of deformations of charge and matter densities in nuclei.Purpose: Measurement of angular distributions of the inelastic scattering cross sections for excitations to low-lying ${2}_{1}^{+}$ and ${3}_{1}^{\ensuremath{-}}$ states in $^{112,116,118,120,122,124}\mathrm{Sn}$ nuclei using $^{12}\mathrm{C}$ beam as a probe at ${E}_{\mathrm{lab}}=60\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$, and determination of neutron and proton transition matrix elements involved in each excitation.Methods: Projectilelike fragments have been detected using ten sets of Si-surface barrier detector telescopes to measure the cross sections for elastic and inelastic scattering channels. Coupled reaction channels calculations are performed to understand the measured differential cross sections.Results: Homogeneous nature of surface vibrations (similar deformation for proton and neutron distributions) for the ${2}_{1}^{+}$ and ${3}_{1}^{\ensuremath{-}}$ states in Sn isotopes is observed.Conclusions: A comparison with recent results using $^{7}\mathrm{Li}$ projectile at similar ${E}_{\mathrm{c}.\mathrm{m}.}/{V}_{\mathrm{B}}$, which showed damped neutron vibrations particularly for the ${3}_{1}^{\ensuremath{-}}$ state, confirms that such measurements are probe dependent. Intrinsic transition matrix elements of nuclei can be deduced by removing the effects of finite projectile size in the extraction of nuclear shapes.

Role of target shell structure in direct reactions involving weakly bound Li7

The effect of the shell structure of the target nuclei ($^{89}\mathrm{Y}$ and $^{93}\mathrm{Nb}$) on reaction mechanisms involving the weakly bound $^{7}\mathrm{Li}$ projectile has been investigated via a comparative study of different processes. Measurements of direct breakup, nucleon transfer leading to the ejectile in bound as well as unbound states, and elastic scattering have been carried out for the $^{7}\mathrm{Li}+^{89}\mathrm{Y}$ system at three different energies near the Coulomb barrier. An extensive analysis of this comprehensive data set was carried out using coupled channel calculations and compared with a previous similar study for the $^{7}\mathrm{Li}+^{93}\mathrm{Nb}$ system. The observed cross sections at low target excitations for nucleon transfer reactions correlate with the vacancies in the valance orbitals.

Near-threshold photodissociation of cool OH+ to O + H+ and O+ + H.

We have measured the spectrum of laser photodissociation of OH+ molecular ions to O + H+ and O+ + H fragments for photon energies of 38 100-40 900 cm-1. The OH+ ions were stored as a fast beam (5.50 MeV) in the storage ring TSR for several seconds to achieve rovibrational cooling into the lowest rotations N'' = 0-11 of the vibrational ground state X3Σ-(v'' = 0), close to room temperature (≈300 K). The many resonances in the spectra reveal the energies, widths, and O/O+ branching ratios of 44 predissociating quasibound levels (Feshbach resonances) that lie between the fine-structure states of the O fragment and belong to the last, near-threshold vibrational states v' = 9 and 10 of the A3Π electronic state. For the A3Π0,1 substates, isolated levels with v' = 11 are observed and attributed to double-well distortions of these curves due to nonadiabatic interactions. Another five isolated levels are assigned to the v' = 0 and 1 states of the shallow 15Σ- electronic state, borrowing oscillator strength from nearby A3Π levels. Together, the near-threshold levels deliver a new value D0 = 40 253.8(1.1) cm-1 for the dissociation energy of OH+. Through a two-step photodissociation process, 72 levels from the lower bound states A3Π(v' = 7-8) appear as well and are rotationally analyzed. The level energies are used to construct improved A3Π and 15Σ- Born-Oppenheimer potentials. The totality of the spectral data (energies, widths, intensities, and branching ratios) can provide tight constraints for the potentials and nonadiabatic interactions assumed in future coupled-channel calculations of OH+ photodissociation or of the related charge-exchange reaction O + H+ → O+ + H.

Elastic and inelastic scattering of O16 on Al27 and Si28 at 240 MeV

The nuclear scattering at energies well above the Coulomb barrier allows for a fairly sensitive examination of the parameters of the optical potential when the relevant couplings are included into the calculations. In this work we present experimental angular distribution data for the elastic and inelastic scatterings of $^{16}\mathrm{O}$ impinging on $^{27}\mathrm{Al}$ and $^{28}\mathrm{Si}$ target nuclei at ${E}_{\mathrm{lab}}=240\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$. The experimental data were measured at ${7}^{\ifmmode^\circ\else\textdegree\fi{}}<{\ensuremath{\theta}}_{\text{c.m.}}<{16}^{\ifmmode^\circ\else\textdegree\fi{}}$ with good angular resolution. Experimental data are compared with coupled channel calculations with the inclusion of couplings to excited states in the target and projectile. We show that the shape of angular distributions are sensitive to the mass diffuseness parameter and the best agreement is achieved for $a=0.62\phantom{\rule{0.28em}{0ex}}\mathrm{fm}$.

Nuclear potentials model for heavy-ion reactions

Here, we present a nuclear potential model for heavy- ion reactions consisting of four central, spin, iso-spin and Iτ terms. The potential model presented here, predicts more accurate values for the barrier height of 6Li+24Mg→30P* and 7Li+24Mg→31P* reactions compared to the other potential models such as Proximity potential (Prox.77 and Prox.88) and Age Wither potential model (AW 95). A detailed comparative study of the fusion excitation functions of 6Li+24Mg and 7Li+24Mg reactions has been performed in 1–25 MeV energy interval. For energies below the Coulomb barrier and above the 15 MeV, our proposed potential model exhibits a better agreement with the experimental data than the above-mentioned potential models and leads to about 10 to 20 percent improvement in the previous results. Also, the analysis of S factor and the logarithmic derivatives showed that the coupled channel calculation based on our purposed potential is in good agreement with the corresponding experimental data at these energy ranges.

Spin-orbit effects in the 8Li+58Ni elastic scattering

In this work we present an elastic scattering angular distribution for the 8Li+58Ni system measured at Elab = 26.1 MeV. The 8Li beam was produced in the Radioactive Ion Beams in Brasil (RIBRAS) facility using the 7Li primary beam delivered by the 8-UD Pelletron accelerator. The angular distribution covers the angular range from 20 to 85 degrees in the center of mass frame. The data have been analysed by optical model and coupled channels calculations, including couplings to low-lying states in 8Li and the spin-orbit interaction. Our results indicate that the inclusion of the spin-orbit interaction in the calculations is important to describe the data at backward angles.

Sub-barrier fusion involving odd mass nuclei: The case of 36S + 50Ti, 51V

Sub-barrier fusion of the two near-by systems 36S + 50Ti, 51V has been measured at the Laboratori Nazionali di Legnaro (INFN). Motivation for the experiment came from the possible effect of the non-zero spin of the ground state of the 51V nucleus on the sub-barrier excitation function, and in particular on the shape of the barrier distribution. No previous data were available for these two systems near the barrier. Our results show that the two measured excitation functions are very similar down to the level of 20-30μb. The same is true for the two barrier distributions. Coupled-channel calculations have been performed including the low energy excitations of both projectile and the two targets. We have indication that the low-lying levels in 51V can be interpreted in the weak-coupling scheme, that is, 51V (I) = 50Ti(2+) ⊗ p(1f7/2) and that the extra proton in the $ 1f_{7/2}$ shell does not have a significant influence on sub-barrier fusion.

Fusion barrier distribution and superheavy elements

The barrier distribution, originated from channel coupling effects in heavy-ion fusion reactions, has been extracted experimentally for many systems using either a fusion excitation function or an excitation function of large-angle quasi-elastic scattering. In this article, we discuss an application of the latter method to the 48Ca+248 Cm system, which is relevant to hot fusion reactions to synthesize superheavy elements. To this end, we carry out coupled-channels calculations for this system, taking into account the deformation of the target nucleus, and discuss the role of deformation in a formation of evaporation residues.

First microscopic coupled-channels calculation of cross sections for inelastic α scattering off O16

The $\alpha$ inelastic scattering on $^{16}$O is investigated with the coupled-channel calculation using the $\alpha$-nucleus coupled-channel potentials, which are microscopically derived by folding the the Melbourne $g$-matrix $NN$ interaction with the $^{16}$O and $\alpha$ densities. The matter and transition densities of $^{16}$O are calculated by a microscopic structure model of the variation after the spin-parity projections combined with the generator coordinate method of $^{12}$C+$\alpha$ in the framework of the antisymmetrized molecular dynamics. The calculation reproduces the observed elastic and inelastic cross sections at incident energies of $E_\alpha$=104 MeV, 130 MeV, 146 MeV, and 386 MeV. The coupled-channel effect on the cross sections is also discussed.

α scattering cross sections on C12 with a microscopic coupled-channels calculation

$\alpha$ elastic and inelastic scattering on $^{12}$C is investigated with the coupled-channel calculation using microscopic $\alpha$-$^{12}$C potentials, which are derived by folding the Melbourne $g$-matrix $NN$ interaction with the matter and transition densities of $^{12}$C. These densities are obtained by a microscopic structure model of the antisymmetrized molecular dynamics combined with and without the $3\alpha$ generator coordinate method. The calculation reproduces satisfactorily well the observed elastic and inelastic cross sections at incident energies of $E_\alpha=130$~MeV, 172.5~MeV, 240~MeV, and 386~MeV with no adjustable parameter. Isoscalar monopole and dipole excitations to the $0^+_2$, $0^+_3$, and $1^-_1$ states in the $\alpha$ scattering are discussed.

K-shell ionization cross sections of atoms by muons and pions

The K-shell ionization cross sections of copper and silver atoms by muons and pions with negative and positive charge have been calculated with the classical trajectory Monte Carlo method and the plane-wave Born approximation with corrections for the Coulomb-deflection and binding-energy effects. Both results are in good agreement with each other. The obtained cross sections for muons on copper are also compared with the coupled-channels calculations. The dependence of the K-shell ionization cross sections on the sign of the projectile as well as on the projectile mass is discussed.Graphical abstract

Elastic rate coefficients forLi+H2collisions in the calibration of a cold-atom vacuum standard

Ongoing efforts at the National Institute of Standards and Technology in creating a cold-atom vacuum standard device have prompted theoretical investigations of atom-molecule collision processes that characterize its operation. Such a device will operate as a primary standard for the ultrahigh-vacuum and extreme-high-vacuum regimes. This device operates by relating loss of ultracold lithium atoms from a conservative trap by collisions with ambient atoms and molecules to the background density and thus pressure through the ideal gas law. The predominant background constituent in these environments is molecular hydrogen H2. We compute the relevant Li+H2 Born-Oppenheimer potential energy surface, paying special attention to its uncertainty. Coupled-channel calculations are then used to obtain total rate coefficients, which include momentum-changing elastic and inelastic processes. We find that inelastic rotational quenching of H2 is negligible near room temperature. For a (T = 300)-K gas of H2 and 1.0-μK gas of Li atoms prepared in a single hyperfine state, the total rate coefficients are 6.0(1) × 10-9 cm3/s for both 6Li and 7Li isotopes, where the number in parentheses corresponds to a one-standard-deviation combined statistical and systematic uncertainty. We find that a 10-K increase in the H2 temperature leads to a 1.9% increase in the rate coefficients for both isotopes. For Li temperatures up to 100 μK, changes are negligible. Finally, a semiclassical Born approximation significantly overestimates the rate coefficients. The difference is at least ten times the uncertainty of the coupled-channel result.

Analysis of fusion excitation functions of reactions 6He +209Bi and 7Li +209Bi around Coulomb barrier

Here, we have studied the sensitivity of fusion excitation functions of reactions induced by weakly bound projectiles [Formula: see text] and [Formula: see text] on [Formula: see text] target on nuclear potential parameters and on number of partial waves. The Kemble version of WKB approximation and Hill–Wheeler formula has been used to predict the fusion transmission probability below and above the Coulomb barrier, respectively, and the optimum values for radius (r0) = 1.17 fm, diffuseness (a) = 0.5 fm and for partial waves (l) = up to 60 are proposed. The coupled channel calculations have also been performed and it is found that the matching between data and predictions have been enhanced on inclusion of coupling effects. Further, the breakup effects are also taken into account through the dynamic polarization potential (DPP) approach. It further improves matching between data and predictions.

Low-lying quadrupole and octupole collective excitations in the Sn112,116,118,120,122,124 isotopes

Background: In recent years, considerable interest has been focused on the study of the effect of neutron skin on the collective properties of vibrational nuclei. This can be best evidenced by exclusively determining neutron and proton transition matrix elements involved in a particular excitation by investigating the Coulomb-nuclear interference feature of inelastic scattering.Purpose: Measurement of angular distributions of the inelastic scattering cross sections for excitations to low-lying ${2}_{1}^{+}$ and ${3}_{1}^{\ensuremath{-}}$ states in $^{112,116,118,120,122,124}\mathrm{Sn}$ using $^{7}\mathrm{Li}$ beam as probe at ${E}_{\mathrm{lab}}=28\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and determination of neutron and proton transition matrix elements involved in each excitation.Methods: Projectilelike fragments were detected using six sets of Si-surface barrier detector telescopes to measure the cross sections for elastic and inelastic scattering channels. Optical model analysis of elastic scattering data, coupled reaction channels, and continuum discretized coupled channels calculations were performed to understand the measured differential cross sections. An attempt has been made to extract the microscopic mass and charge deformation lengths.Results: For the ${2}_{1}^{+}$ state, experimental $B(E2)$ values are in good agreement with existing results obtained by electromagnetic methods. Charge and mass quadrupole vibrations are homogeneous. Significant differences are observed for excitation to the ${3}_{1}^{\ensuremath{-}}$ state across the Sn isotopic chain. Available structural information for collective octupole vibrations could not reproduce the present data for this excitation. Results show much lower values of octupole mass deformation parameters.Conclusions: Isoscalar nature of surface vibrations for the ${2}_{1}^{+}$ state in Sn isotopes is verified, with ${M}_{n}/{M}_{p}\ensuremath{\sim}N/Z$. For the ${3}_{1}^{\ensuremath{-}}$ state, damped mass vibration is the primary observation. On comparison with existing estimates, a significant deviation from isoscalar nature is conjectured for this excitation, when probed with $^{7}\mathrm{Li}$.

Restricted basis set coupled-channel calculations on atom-molecule collisions in magnetic fields.

Rigorous coupled-channel quantum scattering calculations on molecular collisions in external fields are computationally demanding due to the need to account for a large number of coupled channels and multiple total angular momenta J of the collision complex. We show that by restricting the total angular momentum basis to include only the states with helicities K ≤ Kmax, it is possible to obtain accurate elastic and inelastic cross sections for low-temperature He + CaH, Li + CaH, and Li + SrOH collisions in the presence of an external magnetic field at a small fraction of the computational cost of the full coupled-channel calculations (where K is the projection of the molecular rotational angular momentum on the atom-diatom axis). The optimal size of the truncated helicity basis set depends on the mechanism of the inelastic process and on the magnitude of the external magnetic field, with the minimal basis set (Kmax = 0) producing quantitatively accurate results for, e.g., ultracold Li + CaH and Li + SrOH scattering at low magnetic fields, leading to nearly 90-fold gain in computational efficiency. Larger basis sets are required to accurately describe the resonance structure in the magnetic field dependence of Li + CaH and Li + SrOH inelastic cross sections in the few partial wave-regime as well as indirect spin relaxation in He + CaH collisions. Our calculations indicate that the resonance structure is due to an interplay of the spin-rotation and Coriolis couplings between the basis states of different K and the couplings between the rotational states of the same K induced by the anisotropy of the interaction potential.

Influence of the deformation and orientation on the interaction potential of the 28Si+28Si system and its fusion process

We investigated the orientation behavior of the interaction potential between highly-deformed oblate [Formula: see text]Si nuclei and its influences on the fusion process. The deformed–deformed potential is calculated using the double-folding model based on the realistic M3Y-Reid nucleon–nucleon interaction. We found that the Coulomb barrier parameters and the sub-barrier fusion data strongly depend on the polar orientation angles of the involved deformed nuclei, with a rather less dependence on the azimuthal angles. For interacting oblate nuclei, the elongated configuration corresponding to the lowest Coulomb barrier is obtained at orthogonal polar orientations, while the hexadecapole deformation determines the compact configuration obtained at nonzero polar orientations. The orientation behavior of the Coulomb barrier radius (height and curvature) consistently follow (inversely reflex) the orientation variation of the sum of the half-density radii of the two deformed nuclei, along their centers-of-mass separation vector. The deformations of the colliding nuclei increase their fusion cross-section at sub- and around-barrier energies. The calculations based on the parabolic barrier approximation overestimate the sub-barrier cross-section. The coupled channels calculations with couplings up to the 2[Formula: see text] and 4[Formula: see text] excitation states of [Formula: see text]Si nuclei are needed to reproduce the [Formula: see text] fusion cross-section, and the corresponding logarithmic slope and barrier distribution, over the full energy region.

Interplay of neutron transfer and collective degrees of freedom in the fusion dynamics of 16O +76Ge and 18O +74Ge reactions

This work examined the fusion dynamics of [Formula: see text] and [Formula: see text] reactions within the framework of the static Woods–Saxon potential model, the energy dependent Woods–Saxon potential (EDWSP) model and coupled channel formulation. The effects of inelastic surface excitations, static deformation of colliding pairs and /or neutron transfer channels on fusion process are investigated through the coupled channel method. The calculations based upon static Woods–Saxon potential in conjunction with one-dimensional Wong formula strongly under predict the fusion data of [Formula: see text] and [Formula: see text] reactions at sub-barrier energies. However, such discrepancies are removed if one uses couplings to nuclear structure degrees of freedom of reacting nuclei. The coupled channel calculations obtained by considering the vibrational nature of the colliding nuclei fairly reproduce the fusion data of [Formula: see text] reactions. For this reaction, the neutron transfer channels, which are expected to influence strongly the fusion yields at below barrier energies, in reality contribute very weakly to fusion process. While in case of [Formula: see text] reaction, the consideration of vibrational couplings as well as the rotational couplings for target provides a reasonable explanation to the fusion cross-section data at near and above barrier energies. In distinction, the energy dependence in the nucleus–nucleus potential causes barrier modulation effects and subsequently modifies the barrier profile of the interaction barrier in such a way that the effective fusion barrier between the colliding pair reduces. This ultimately brings larger fusion cross-sections over the outcomes of one-dimensional barrier penetration model and the EDWSP model based calculations appreciably explained the fusion dynamics of chosen reaction at energy spanning around the Coulomb barrier. Both models (EDWSP and coupled channel model) lead to barrier lowering effects and modeled quantum tunneling in different way, henceforth, adequately explore the fusion dynamics of the studied reactions in near and above barrier energy regions.

Hidden-bottom pentaquarks

The LHCb Collaboration has recently reported strong evidences of the existence of pentaquark states in the hidden-charm baryon sector, the so-called $P_c(4380)^+$ and $P_c(4450)^+$ signals. Five-quark bound states in the hidden-charm sector were explored by us using, for the quark-quark interaction, a chiral quark model which successfully explains meson and baryon phenomenology, from the light to the heavy quark sector. We extend herein such study but to the hidden-bottom pentaquark sector, analyzing possible bound-states with spin-parity quantum numbers $J^P=\frac12^\pm$, $\frac32^\pm$ and $\frac52^\pm$, and in the $\frac12$ and $\frac32$ isospin sectors. We do not find positive parity hidden-bottom pentaquark states; however, several candidates with negative parity are found with dominant baryon-meson structures $\Sigma_b^{(\ast)}\bar{B}^{(\ast)}$. The calculated distances among any pair of quarks within the bound-state reflect that molecular-type bound-states are favored when only color-singlet configurations are considered in the coupled-channels calculation whereas compact pentaquarks, which are also deeply bound, can be found when hidden-color configurations are added. Finally, our findings resemble the ones found in the hidden-charm sector but, as expected, we find in the hidden-bottom sector larger binding energies and bigger contributions of the hidden-color configurations.

Surface diffuseness parameter with quasi-elastic scattering for some heavy-ion systems

Itemised studies of the surface property of the inter-nucleus potential in heavy-ion reactions have been achieved using large-angle quasi-elastic scattering at sub-barrier energies close to the Coulomb barrier height for 63Li + 6430Zn and 73Li + 6430Zn systems. In this paper, the nuclear potential has been expressed using Wood Saxon (WS) formula. The effect of rotational deformation was included for the nucleus 6430Zn with ground state rotational band up to the 4+ states. The Single-Channel (SC) and Coupled-Channels (CC) calculations have been carried out to elicit the diffuseness parameter of the nuclear potential as well as the potential depth, these calculations have been performed by using (CQEL) program which is considered the latest version of computer code (CCFULL). The chi square method, χ², played an important role in determining the best-fitted value of the diffuseness parameter. Through CC calculations with inert projectile and rotational target for 63Li + 6430Zn and 73Li + 6430Zn systems, full compatibility of diffuseness parameter has been achieved with the standard value 0.63 fm with χ² = 0.130 and χ² = 0.163 respectively, while the SC calculations give 0.64 fm and 0.65 fm, respectively.

Three-body description of 12C: From the hyperspherical formulation to the algebraic cluster model and its application to α + 12C inelasticscattering

Form factors for α+12C inelastic scattering are obtained within two theoretical (α+α+α) approaches:The hyperspherical framework for three identical bosons, and the algebraic cluster model assuming the D3h symmetry of an equilateral triangle subject to rotations and vibrations. Results show a good agreement, with form factors involving the Hoyle state having a slightly larger extension within the hyperspherical approach. Coupled-channel calculations using these form factors are ongoing.