Vector correlations in the F + HD reaction

A theoretical study of the orientation of product rotational angular momenta for two chemical reaction channels: F + HD(ν _r = 0, j _r = 0) → HF(ν, j) + D and F + HD(ν _r = 0, j _r = 0) → DF(ν, j) + H at a E _coll = 78.54 meV collision energy was performed. Angular momentum orientation was described on the basis of irreducible tensor operators (state multipoles) expressed through anisotropy transfer coefficients, which contained quantum-mechanical scattering T matrices determined on the basis of exact solutions to quantum scattering equations obtained using the hyperquantization algorithm. The possibility of the existence of substantial orientation of the angular momentum of reaction products j in the direction perpendicular to the scattering plane was demonstrated. The dependences of differential reaction cross sections and state multi-poles on the ν and j quantum numbers were calculated and analyzed. A experimental scheme based on the multiphoton ionization method was suggested. The scheme can be used to detect predicted reaction product angular momentum orientation.     

Product polarization distribution: Stereodynamics of the reaction of atom H and radical NH

The product angular momentum polarization of the reaction of H+NH is calculated via the quasiclassical trajectory method (QCT) based on the extended London-Eyring-Polanyi-Sato (LEPS) potential energy surface (PES) at a collision energy of 5.1 kcal/mol. The calculated results of the vector correlations are denoted by using the angular distribution functions. The polarization-dependent differential cross sections (PDDCSs) demonstrate that the rotational angular momentum of the product H2 is aligned and oriented along the direction perpendicular to the scattering plane. Vector correlation shows that the angular momentum of the product H₂ is aligned in the plane perpendicular to the velocity vector. It suggests that the reaction proceeds preferentially when the reactant velocity vector lies in a plane containing all three atoms. The orientation and alignment of the product angular momentum affects the scattering direction of the product molecules. The polarization-dependent differential cross sections (PDDCSs) reveal that scattering is predominantly in the backward hemisphere.      

Product polarization distribution: Stereodynamics of the reaction of atom H and radical NH

The product angular momentum polarization of the reaction of H+NH is calculated via the quasiclassical trajectory method (QCT) based on the extended London-Eyring-Polanyi-Sato (LEPS) potential energy surface (PES) at a collision energy of 5.1 kcal/mol. The calculated results of the vector correlations are denoted by using the angular distribution functions. The polarization-dependent differential cross sections (PDDCSs) demonstrate that the rotational angular momentum of the product H₂ is aligned and oriented along the direction perpendicular to the scattering plane. Vector correlation shows that the angular momentum of the product H₂ is aligned in the plane perpendicular to the velocity vector. It suggests that the reaction proceeds preferentially when the reactant velocity vector lies in a plane containing all three atoms. The orientation and alignment of the product angular momentum affects the scattering direction of the product molecules. The polarization-dependent differential cross sections (PDD-CSs) reveal that scattering is predominantly in the backward hemisphere.     

Q- and Z-dependence of angular momentum transfer in deeply inelastic collisions of 86Kr with 209Bi

The dependence of the in-plane and out-of-plane angular correlations of fragments from fissioning heavy products on the kinetic energy and Z of the light reaction partner have been measured. From the dependence of the angular correlations on Q-value and hence energy loss, together with existing data from which the total angle-integrated cross section as a function of energy loss can be extracted, we have determined the dependence of the angular momentum transferred to the heavy product on the initial orbital angular momentum or impact parameter. The resulting dependence is qualitatively consistent with the sticking limit for a reaction intermediate of touching deformed fragments. More specific nuclear models generally underestimate the angular momentum transfer, although the one-body proximity-friction model accounts for the major fraction of the angular momentum transfer. A recent model incorporating both one-body proximity friction and collective excitations accounts quite well for the observed angular momentum transfer. The Z-dependendence of the anisotropy shows the importance of angular momentum fractionation for the less probable events, where the Z of the fissioning system is appreciably less than that of the target. The transferred angular momentum is shown to be fairly strongly aligned along the perpendicular to the reaction plane, with alignment values of 0.6 to 0.8. The component of angular momentum not along the perpendicular to the reaction plane is found to be primarily oriented perpendicular rather than parallel to the recoil direction. The absolute fission probabilities are found to be qualitatively consistent with J-dependent calculations using the J-values deduced from the angular correlations.     

Rotational band crossings in the actinides

In the actinides bothi _13/2 protons andj _15/2 neutrons are close to the Fermi surface. At rapid rotation these high-j particles will unpair and align their orbital angular momentum along the axis of rotation giving rise tos-bands that cross the ground-state band. Coulomb excitation of the odd nuclei ₂₃₇ ⁹³ Np (established up to the 45/2⁺ state) and ₂₃₅ ⁹² U (established up to the 51/2^? state) provides specific information about these band crossings: From the saturating alignment of the odd high-j particle in both nuclei at intermediate rotational frequencies we find the aligned angular momentum of thei _13/2 protons-band to be 6.6? while the corresponding value for thej _15/2 neutrons-band is 5.5?. At more rapid rotation above ?ω=0.18 MeV we observe additional alignment in²³⁵U. This is ascribed to the interaction of the protons-band. From the gradual onset of the additional alignment we deduce that forZ=92 the protons-band interacts strongly with the ground-state band and from a comparison of the actual amount of alignment with the full value of 6.6? we estimate the crossing to occur around ?gw _c ^p =0.25 MeV.     

Vector correlations of the reaction O(1D) + H2 on the DK potential energy surface

This paper reports on the angular momentum polarization of the products of the reaction O(¹D₂) + H₂ via the quasiclassical trajectory (QCT) calculation on the DK (Dobbyn and Knowles) potential energy surface (PES). The four polarization-dependent differential cross-sections (PDDCS) (0, 0), (2, 0), (2, 2), (2, ?1) were calculated at different collision energies. The vector correlation between reagent velocity and product angular moment, the vector correlation between reagent, product velocity and product angular moment were studied. From the calculations, it can be obtained that the OH products are produced mainly in the plane of H–O–H plane. The changes of OH products angular momentum j ′ direction along with the increasing collision energies were ascribed to the existence of a new reaction mechanism.     

12C + 7Li Reaction measurements and the 12C(7Li,t)16O reaction

A measurement of the residues from the ¹²C + ⁷Li reaction has been obtained for ⁷Li energies from 10 to 38 MeV. From these measurements the fusion cross sections and critical angular momenta for the ¹²C + ⁷Li system have been deduced. Cross sections for the ⁷Li(¹²C, t)¹⁶O reaction have been obtained for ¹²C energies from 54 to 62 MeV at θ_lab = 2.7°. The critical angular momenta obtained from the fusion cross sections have been used to perform Hauser-Feshbach calculations for the ¹²C(⁷Li, t)¹⁶O reaction. These calculations have been compared to measured angular distributions over a wide energy range. By comparing the fusion cross sections required by the Hauser-Feshbach calculations to fit the ¹²C(⁷Li, t)¹⁶O(8.87 MeV) reaction and the measured residue cross section it is estimated that at least 80 % of the measured residues are fusion products. The calculations also indicate that direct processes dominate the population of many ¹⁶O levels at forward angles and the 10.35 MeV state at backward angles. The necessity for using a critical angular momentum in Hauser-Feshbach calculations is discussed.     

Study of the total reactive dynamics of the H + DCl reaction within the framework of the quantum approach

The reactive dynamics of the H + DCl reaction was studied by the wave-packet method at an arbitrary total angular momentum. Two reaction channels (exchange and abstraction) are considered. The reaction cross sections calculated depending on collision energies up to 2.5 eV and initial states of the DCl molecule remain unchanged for the rotational levels j ₀ = 0, 1, 4 at a vibrational level v ₀ = 0. The reaction threshold and cross section agree with the known experimental data.     

Spin alignment of yrast levels populated by pre-equilibrium (α, xnγ) reactions

Angular momenta of yrast levels following pre-equilibrium (α, xnγ) reactions at E_α, = 110 MeV were found to be aligned as well as those following the equilibrium (compound) (α, xnγ) reactions at E_α = 20–50 MeV. They are uniform against the neutron multiplicity x. The degrees of the spin (angular momentum) alignment with rank 2 for the yrast levels with spins 8–12 average about α₂ ≈ 0.87 ± 0.05. The good spin alignment indicates that both the neutron emission and the γ-emission are stretched in angular momentum space. This supports the pre-equilibrium neutron emission process, where the momenta carried away by the neutrons are not in random directions but rather in the beam direction. The result is well reproduced by the pre-equilibrium neutron emission process followed by neutron evaporation and the K-band γ-deexcitation process.     

Quantum stereodynamics study for the reaction F + HD

This paper studies the quantum stereodynamics of the F + HD(υ = 0, j = 0) → HD + F/HF + D reaction at the collision energies of 0.52 and 0.87~kcal/mol. The quantum scattering calculations, based on Stark-Werner potential energy surfaces, show that the differential cross sections for the HF(υ' = 2) + D and DF(υ' = 3) + H channels are consistent with the recent theoretical results. Furthermore, the product rotational angular momentum orientation and alignment have been determined for some selected rovibrational states of the HF + D and DF + H channels.     

The doubling of the anomalous magnetic moment of electron in a very strong constant homogeneous electric field

Calculated by the author previously [8], the anomalous magnetic moment (AMM) of the electron in an intense constant electric field changes nonmonotonically as the field increases, passing through a minimum and tending to the doubled Schwinger value for very strong fields. In the present paper, it is supposed that the AMM is related by the Lande factor to the angular momentum of a virtual electron accompanied by a virtual photon. This factor changes its effective value because of the influence of the external field on the motion of the virtual electron and its self-action. With increase of the electric field strength, the virtual electron can successively occupy the excited states l = 1, j = 1/2 and l = 1, j = 3/2 in addition to the original state with the orbital angular momentum l = 0 and the total angular momentum j = 1/2. The first of these excited states decreases the AMM and the second increases and doubles it if only this state is occupied for a very strong field. The latter condition is equivalent to the alignment of the spin and the orbital angular momentum of the electron along the field, while the total angular momentum of the entire system of the virtual electron and the virtual photon remains equal to 1/2.     

Theoretical study of the stereodynamics for the reaction F+HBr

The vector correlation between products and reagents for exothermic reaction F + HBr → HF + Br has been studied using a quasi-classical trajectory (QCT) method on the latest extended Lond–Eyring–Polanyi–Sato (LEPS) potential energy surface at three collision energies of 0.1 eV, 0.2 eV and 0.3 eV. Four polarization- dependent generalized differential cross-sections (2π/σ)(dσ₀₀/dω _t ), (2π/σ)(dσ₂₀/dω _t ), (2π/σ)(dσ₂₂₊/dω _t ), (2π/σ)(dσ_21?/dω _t ) have been presented in the centre of mass frame, respectively. The distribution of dihedral angle P(φ _r ), the distribution of angle between k and j ′ , P(θ _r ), are calculated. Both the influence of the collision energy and the influence of the reagent rotation on the product polarization have been studied in the present work, and the results indicate that the product rotational angular momentum j ′ is not only aligned, but also oriented along the direction perpendicular to the scattering plane. The orientation of the HF product rotational angular momentum vector j ′ depends very sensitively on the reagent rotation and also effected by the collision energy.     

The stereodynamic properties of the F+HO(v,j) → HF+O reaction on~1 A' and ~3A' potential energy surfaces by quasi-classical trajectory calculations:Initial excitation effect(v=1-3, j=0 and v= 0, j=1-3)

The stereodynamic properties of the F ＋ HO （v, j） reaction are explored by quasi-classical trajectory （QCT） calculations performed on the 1At and 3At potential energy surfaces （PESs）. Based on the polarization-dependent differential cross sections （PDDCSs） and the angular distributions of the product angular momentum with the reactant at different values of initial v or j, the results show that the product scattering and product polarization have strong links with initial vibrationalrotational numbers of v and j. The significant manifestation of the normal DCSs is that the forward scattering gradually becomes predominant with the initial vibrational excitation increasing, and the scattering angle of the HF product taking place on the 3At potential energy surface is found to be more sensitive to the initial value of v. The product orientation and alignment are strongly dependent on the initial rovibrational excitation effect. With enhancement in the initial rovibrational excitation effect, there is an overall decrease in the product orientation as well as in the product alignment either perpendicular to the reagent relative velocity vector k or along the direction of the y axis, for which the initial rotational excitation effect is much more noticeable than the vibrational excitation effect. Moreover, the initial rovibrational excitation effect on the product polarization is more pronounced for the 3At potential energy surface than for the 1At potential energy surface.     

Theoretical study of stereodynamics for the reaction O(3P) +D2 (v=0, j=0) to OD+D and isotope effect

Quasi-classical trajectory (QCT) calculations have been performed to study the product polarization behaviours in the reaction O(³P) + D₂ (v= 0, j= 0)→OD + D. By running trajectories on the ³A′ and ³A″ potential energy surfaces (PESs), vector correlations such as the distributions of the polarization-dependent differential cross sections (PDDCSs), the angular distributions of P(θ_r) and P(ø_r) are presented. Isotope effect is discussed in this work by a comprehensive comparison with the reaction O(³P) + H₂ (v= 0, j= 0) → H + H. Common characteristics as well as differences are discussed in product alignment and orientation for the two reactions. The isotope mass effect differs on the two potential energy surfaces: the isotope mass effect has stronger influence on P(θ_r) and PDDCSs of the ³A′ PES while the opposite on P(ø_r) of the ³A″ potential energy surface.     

The special features of rotationally resolved differential cross sections of the F + H2 reaction at small scattering angles

We studied the nature and collision energy dependence of the maximum that appears in the angular distributions of the HF (v′ = 3) product of the F + H₂ (v = 0; j = 0, 1, 2) → H + HF (v′, j′) reaction at small scattering angles θ in the center-of-mass frame. This maximum and its increase as the collision energy increased were discovered in the well-known experiment described by D.M. Neumark, A.M. Wodtke, G.N. Robinson, C.C. Hayden, and Y.T. Lee, J. Chem. Phys. 82 (7), 3045 (1985). In order to determine the nature of the maximum, we performed quantum-mechanical simulation of the reaction on the Stark-Werner ground state potential energy surface at collision energies of 1.84, 2.74, and 3.42 kcal/mol corresponding to the above-mentioned experiment and calculated the vibrationally and rotationally resolved differential cross sections dσ_v′j′/dΩ of the reaction. The maximum under consideration was found to be due to a superposition of two effects, namely, the absence of HF (v′ = 3; j′) products with large j′ because of energy restrictions and an increase in the relative amplitude of quantum-mechanical oscillations on dσ_v′j′/dΩ cross sections at small j′ and θ as v′ increased. Oscillations on dσ_3j′ /dΩ cross sections with small j′ are responsible for the maximum observed.     

Proton-hole states in 115In observed in the 116Sn(d, 3He) reaction

The ¹¹⁶Sn(d, ³He)¹¹⁵In reaction has been investigated at E_d = 50 MeV. Thirteen transitions to states up to 3 MeV excitation energy were studied. The measured angular distributions were compared with DWBA calculations and transferred angular momenta and spectroscopic factors were deduced. Levels at 1.04, 2.23 and 2.52 MeV were found to be excited most likely by l = 3 angular momentum transfer in contrast to previous investigations at lower incident energies in which no l = 3 transitions have been observed.     

Stereodynamics of the reaction He+H<Stack><Subscript>2</Subscript><Superscript>+</Superscript></Stack> → HeH<Superscript>+</Superscript> + H: a theoretical study

Quasiclassical trajectory method for the title reaction He +H₂⁺ → HeH⁺ + H was carried out on the potential energy surface which was revised by Aquilanti et al. [Chem. Phys. Lett. 469, 26 (2009)]. The initial vibrational quantum number of reactant was set as v=1, v=2 and v=3. Stereodynamics information of the reaction was obtained, such as the distributions of product angular momentum P(θ _r ), P(ϕ _r ),p(ϕ _r , θ _r ) and the two commonly used polarization-dependent differential cross sections (PDDCSs) (2π/σ)(dσ ₀₀/dω _t ) and (2π/σ)(dσ ₂₀/dω _t ), to get the alignment and orientation of product molecules. The results show that the influence of both the collision energy and vibrational quantum number (v) to the reaction are highly sensitive.     

Theoretical study of stereodynamics for the O（3P） ＋ H2 → OH ＋ H reaction

This paper employs the quasi-classical trajectory calculations to study the influence of collision energy on the title reaction on the potential energy surface of the ground ³A' triplet state developed by Rogers et al. (J. Phys. Chem. A 2000 104 2308). It calculates the product angular distribution of P(θ_r), P(φ_r) and P(θ_r, φ_r) which reflects vector correlation. The distribution P(θ_r) shows that product rotational angular momentum vectors j' of the products are strongly aligned along the relative velocity direction k. The distribution of P(φ_r) implies a preference for left-handed product rotation in planes parallel to the scattering plane. Four different polarisation-dependent cross-sections are also presented in the centre-of-mass frame. Results indicate that OH is sensitively affected by collision energies of H₂.     

Correspondence between classical and quantummechanical Boltzmann equations

To compare quantummechanical and classical Boltzmann equations for molecular gases, a correspondence is proposed for functions of angular momentum. Equivalence between irreducible tensors of both kinds is prescribed in a unique way by demanding that trace-averages of binary operator products be equal to solid-angle averages of products of the classical equivalents. Application to the linearized Waldmann-Snider equation for rigid linear molecules leads to an equivalent system for a set of functions φ_j(r, υ, ω, t), j = 0, 1, 2,…. If the quantum number j is approximated by a continuous variable, the system goes over into a single classical equation.