Partial Wave Contributions Research Articles

Quantum Dynamics of O(3P)+HBr→OH+Br Reaction: Integral Cross Sections and Rate Constants and their Initial State Dependence.

The integral cross sections (ICSs) and rate constants (RCs) for the title reaction are calculated by means of accurate quantum wave packet method employing the recent ab initio potential energy surface developed by Peterson and co-workers. Hundreds of partial wave contributions (up to J=150) are calculated explicitly taking Coriolis coupling into account. The ICSs are found to increase monotonically with energy and their energy dependences are smooth except in the energy range below the potential energy barrier, where several resonance peaks are observed. The temperature dependences of the RCs obey in general the Arrhenius law. These behaviors manifest the dominance of abstract mechanism. Initial rotational state (ji) excitations are found to greatly enhance the reactivity starting from ji=4, while exhibiting a complicated dependence for ji<4. From Boltzmann average of the initial state specified RCs (for ji=0-15) we obtained thermal RCs which are in reasonable agreement with available experimental results.

Dynamics and energetics of the K([formula omitted]) + H[formula omitted] ([formula omitted]) reaction: Significance of orientational and (ro)vibrational contribution

The significance of orientational and (ro)vibrational excitations on the K(2S) + H2 (X1Σg+) reaction dynamics is presented here by performing the exact time-dependent wavepacket calculations using the Coriolis coupling (CC) approach. Employing the new accurate ab initio ground electronic surface 1 2A′ reported by Yuan et al. (2018), the dynamical quantities such as integral cross sections and thermal rate constants are computed within the CC and CS (centrifugal sudden) methods. All partial wave contributions of J (total angular momentum) up to 90 are required to get the convergence in dynamical results up to the collision energy of 3.5 eV. The present study attests that the ground and first vibrational level dynamics is insignificant. For v=2, the reaction probability is monotonically increasing, followed by the onset noted near 1.25 eV, as a function of collision energy up to 3.5 eV. Further, the kinematic effects (replacing H by D atom) on the title system is also performed and found that the KH product formation is more favored than the KD product via HD depletion path.

Unveiling Quantum Interference in the D+ + H2 Nonadiabatic Reaction Dynamics at Low Collision Energies.

Fully converged nonadiabatic dynamics calculations of the D+ + H2 → H+ + HD reaction are performed at low temperatures using the time-dependent wave packet approach based on a set of precise 3 × 3 diabatic potential energy surfaces (PESs) ( Phys. Chem. Chem. Phys., 2021, 23, 7735-7747, DOI: 10.1039/D0CP04100A). The D+ + H2 reaction is mediated by a dense manifold of resonances associated with the deep potential well on the ground-state PES. The calculated results show that the nonadiabatic coupling can affect the resonance positions, deviating from the expectation based solely on adiabatic considerations. Furthermore, significant forward-backward asymmetry in total differential cross sections (DCSs) is revealed, which is markedly influenced by nonadiabatic effects. The nonadiabatic effects not only affect the contribution of partial waves in the reaction but also make the interference patterns in the DCSs change significantly.

Spin entanglement in neutron-proton scattering

In this Letter, I work out spin entanglement properties of neutron-proton scattering using the exact S-matrix, considering both S-wave and higher partial wave contributions. The dependence of spin entanglement on relative momentum, scattering angle, and initial spin configuration is investigated for realistic nuclear forces, while low-energy properties of spin entanglement are analyzed within the framework of pionless effective field theory at leading order. New connections are found between spin entanglement and symmetry emergence of strong interactions. These results lead to a more complete understanding of how spin entanglement is generated via neutron-proton interaction. They also lay the theoretical foundation for controllable production of entangled nucleon-nucleon pairs in future experiments.

Dynamics of Correlated Double-Ionization of Two-Electron Quantum Dots in Laser Fields.

Using an ab initio, time-dependent calculational method, we study the non-linear dynamics of a two-electron quantum dot in the presence of ultrashort Thz laser pulses. The analysis of the contribution of the various partial waves to two-electron joint radial and energy distribution patterns revealed strongly correlated electron ejection channels. In the double-ionization process, regardless of the photon energy, the two-electron wave packets are born and remain concentrated until the pulse's peak; at later times, and depending on the photon energy of the field, distinctly different patterns emerge. Our calculations also showed the gradual transition of the radial and energy patterns from a single-peak to a doubly peaked structure, associated with the direct and the sequential double-ionization mechanisms, respectively.

Dynamical and Mechanical Insights into the Li(2 S)+ HCl( ) Reaction: A Detailed Quantum Wavepacket Study.

Quantum wave packet dynamics of the Li(2 S)+HCl( ) reaction in its electronic ground state is studied. The initial state-selected and energy-resolved dynamical attributes such as reaction probability, integral cross section, and thermal rate constant for the Cl-abstraction and H-abstraction pathways are reported. All partial wave contributions of J up to 120 were found to be necessary for the title reaction up to the collision energy of ∼1.0 eV. The dynamical results reveal that the Cl-abstraction is more favored over the H-abstraction for the different rovibrational (v, j) excitations. Due to the existence of an early barrier in the potential energy surface, the cross sections increase with increasing collision energy. The rate constants also monotonously increase with temperature for both channels. Resonances are identified and characterized in terms of eigenfunctions and lifetimes. Nearly 120 well-resolved eigenstates are reported for the LiHCl complex, and they are categorized as van der Waals (vdW), barrier and product states according to the nodal progressions along (R, r, γ). The vdW resonances reveal a local-mode behavior of quasibound type at low energies and extended progressions at high energies. Further, the single-quantized periodic orbit type is also observed in the barrier region, which decays very fast. Finally, the lifetime analysis reveals that the vdW resonances can survive as long as ∼2.2 ps, which is much longer than the lifetime of the resonances in the barrier region.

Final bound-state formation effect on dark matter annihilation * *Supported in part by the One Hundred Talent Program of Sun Yat-sen University, China

If two annihilation products of dark matter (DM) particles are non-relativistic and couple to a light force mediator, their plane wave functions are modified due to multiple exchanges of the force mediator. This gives rise to the final state Sommerfeld (FSS) effect. It is also possible that the final state particles form a bound state. Both the FSS effect and final bound-state (FBS) effect need to be considered in the calculation of the DM relic abundance. The annihilation products can be non-relativistic if their masses are comparable to those of the annihilating DM particles. We study the FSS and FBS effects in the mass-degenerate region using two specific models. Both models serve to illustrate different partial-wave contributions in the calculations of the FSS and FBS effects. We find that the FBS effect can be comparable to the FSS effect when the annihilation products couple strongly with a light force mediator. Those effects significantly modify the DM relic abundance.

Exact quantum dynamics study of the H(2S)+SiH+(X1Σ+) reaction on a new potential energy surface of SiH * *Project supported by the National Natural Science Foundation of China (Grant Nos. 11674198 and 11804193), the Shandong Provincial Natural Science Foundation of China (Grant No. ZR2019PA012), and the First-class Discipline Construction Foundation of Shandong Agricultural University.

Based on a new global potential energy surface of , the exact quantum dynamical calculation for the H(2 S) + SiH+(X1Σ+) → H2 + Si+ reaction has been carried out by using the Chebyshev wave packet method. The initial state specified (ν i = 0, j i = 0) probabilities, integral cross sections (ICS) and thermal rate constants of the title reaction are calculated. All partial wave contributions up to J = 90 are calculated in exact quantum calculation including the full Coriolis coupling (CC) effect. The dynamical behaviors of probabilities, ICSs and rate constants are found to be in accord with an exothermic reaction without potential barrier. By comparing the probabilities of CC with the corresponding centrifugal sudden (CS) approximation ones, it can be concluded that neglecting CC effect will decrease the collision time, increase the amplitude of oscillation and lead to overestimation or underestimation of the reaction probability. For ICSs and rate constants, it is found that the deviation of CC and CS ICSs is small in the most of collision energy range except for the range of 0 eV–0.05 eV, while the deviation of both rate constants is considerable in the temperature range of 16 K–1000 K.

A combined experimental and theoretical study of photodouble ionization of water at 32 eV excess energy and unequal energy sharing

The photodouble ionization of water at about 32 eV excess energy has been investigated both experimentally and theoretically. In an energy and angular resolved photoelectron–photoelectron coincidence experiment, the two photoelectrons in unequal energy sharing (25 and 7 eV) condition, have been detected in a plane perpendicular to the propagation direction of the linearly polarized radiation. The measured angular distributions have been compared with, molecular orientation averaged, triple differential cross sections calculated with a recently developed theoretical model (Randazzo et al 2020 Phys. Rev. A 101 033407). The model uses separable products of orbitals as initial electronic state of the water molecule taken as a two-electron target and describes accurately the correlated two electron continuum. The combination of calculated cross sections corresponding to different dication states capture most of the measured features in terms of the evolution of both the shape and the intensity as a function of the faster electron direction which is set at 0°, 30° and 60° with respect to the polarization vector of the incident radiation. A detailed analysis in terms of the different dication states as well as of the partial wave contributions to the electron pair wave function sheds light on the origin of such features.

Suppression of the nuclear rainbow in the inelastic nucleus–nucleus scattering

The nuclear rainbow observed in the elastic $$\alpha $$ -nucleus and light heavy-ion scattering is proven to be due to the refraction of the scattering wave by a deep, attractive real optical potential. The nuclear rainbow pattern, established as a broad oscillation of the Airy minima in the elastic cross section, originates from an interference of the refracted far-side scattering amplitudes. It is natural to expect a similar rainbow pattern also in the inelastic scattering of a nucleus–nucleus system that exhibits a pronounced rainbow pattern in the elastic channel. Although some feature of the nuclear rainbow in the inelastic nucleus–nucleus scattering was observed in experiment, the measured inelastic cross sections exhibit much weaker rainbow pattern, where the Airy oscillation is suppressed and smeared out. To investigate this effect, a novel method of the near-far decomposition of the inelastic scattering amplitude is proposed to explicitly reveal the coupled partial-wave contributions to the inelastic cross section. Using the new decomposition method, our coupled channel analysis of the elastic and inelastic $$^{12}$$ C + $$^{12}$$ C and $$^{16}$$ O + $$^{12}$$ C scattering at the refractive energies shows unambiguously that the suppression of the nuclear rainbow pattern in the inelastic scattering cross section is caused by a destructive interference of the partial waves of different multipoles. However, the inelastic scattering remains strongly refractive in these cases, where the far-side scattering is dominant at medium and large angles like that observed in the elastic scattering.

Experimental and theoretical investigation of resonances in low-energy NO-H2 collisions.

The experimental characterization of scattering resonances in low energy collisions has proven to be a stringent test for quantum chemistry calculations. Previous measurements on the NO-H2 system at energies down to 10 cm-1 challenged the most sophisticated calculations of potential energy surfaces available. In this report, we continue these investigations by measuring the scattering behavior of the NO-H2 system in the previously unexplored 0.4 cm-1-10 cm-1 region for the parity changing de-excitation channel of NO. We study state-specific inelastic collisions with both para- and ortho-H2 in a crossed molecular beam experiment involving Stark deceleration and velocity map imaging. We are able to resolve resonance features in the measured integral and differential cross sections. Results are compared to predictions from two previously available potential energy surfaces, and we are able to clearly discriminate between the two potentials. We furthermore identify the partial wave contributions to these resonances and investigate the nature of the differences between collisions with para- and ortho-H2. Additionally, we tune the energy spreads in the experiment to our advantage to probe scattering behavior at energies beyond our mean experimental limit.

Uniform description of the helium isoelectronic series down to the critical nuclear charge with explicitly correlated basis sets derived from regularized Krylov sequences.

An efficient computational scheme for the calculation of highly accurate ground-state electronic properties of the helium isoelectronic series, permitting uniform description of its members down to the critical nuclear charge Zc, is described. It is based upon explicitly correlated basis functions derived from the regularized Krylov sequences (which constitute the core of the free iterative CI/free complement method of Nakatsuji) involving a term that introduces split length scales. For the nuclear charge Z approaching Zc, the inclusion of this term greatly reduces the error in the variational estimate for the ground-state energy, restores the correct large-r asymptotics of the one-electron density ρ(Z; r), and dramatically alters the manifold of the pertinent natural amplitudes and natural orbitals. The advantages of this scheme are illustrated with test calculations for Z = 1 and Z = Zc carried out with a moderate-size 12th-generation basis set of 2354 functions. For Z = Zc, the augmentation is found to produce a ca. 5000-fold improvement in the accuracy of the approximate ground-state energy, yielding values of various electronic properties with between seven and eleven significant digits. Some of these values, such as those of the norms of the partial-wave contributions to the wavefunction and the Hill constant, have not been reported in the literature thus far. The same is true for the natural amplitudes at Z = Zc, whereas the published data for those at Z = 1 are revealed by the present calculations to be grossly inaccurate. Approximants that yield correctly normalized ρ(1; r) and ρ(Zc; r) conforming to their asymptotics at both r → 0 and r → ∞ are constructed.

Properties of nuclear matter in relativistic Brueckner–Hartree–Fock model with high-precision charge-dependent potentials

Properties of nuclear matter are investigated in the framework of relativistic Brueckner–Hartree–Fock model with the latest high-precision charge-dependent Bonn (pvCD-Bonn) potentials, where the coupling between pion and nucleon is adopted as a pseudovector form. These realistic pvCD-Bonn potentials are renormalized to effective nucleon–nucleon (NN) interactions, G matrices. They are obtained by solving the Blankenbecler-Sugar (BbS) equation in nuclear medium. Then, the saturation properties of symmetric nuclear matter are calculated with pvCD-Bonn A, B, C potentials. The energies per nucleon are around −10.72 MeV to −16.83 MeV at saturation densities, 0.139 fm−3 to 0.192 fm−3 with these three potentials, respectively. It clearly demonstrates that the pseudovector coupling between pion and nucleon can generate reasonable saturation properties comparing with pseudoscalar coupling. Furthermore, these saturation properties have strong correlations with the tensor components of NN potentials, i.e., the D-state probabilities of deuteron, PD to form a relativistic Coester band. The equations of state of pure neutron matter from pvCD-Bonn potentials are almost identical, since the prominent difference of pvCD Bonn potentials are the components of tensor force, which provides very weak contributions in the case of total isospin T = 1. In addition, the charge symmetry breaking (CSB) and charge independence breaking (CIB) effects are also discussed in nuclear matter from the partial wave contributions with these high-precision charge-dependent potentials. In general, the magnitudes of CSB from the differences between nn and pp potentials are about 0.05 MeV, while those of CIB are around 0.35 MeV from the differences between np and pp potentials.

Coriolis coupling effects on the H(2S) + CH+(X1Σ+) reaction dynamics in the ground electronic state

We investigated the effect of Coriolis coupling (CC) on the initial state-selected dynamics of the H(2S) + CH+() reaction in its electronic ground state () using a time-dependent wavepacket approach. Here, the exact dynamical calculations were carried out by considering the CC terms and the results were compared with our previous study within the centrifugal sudden (CS) approximation. All partial wave contributions up to the total angular momentum J = 60 were required to obtain the converged integral cross section upto collision energy ∼1.0 eV, and the rotational (j) level of CH+ reagent was varied upto 3. The projection quantum number Ω, ], facilitates the coupling between the neighboring substates Ω ± 1. There is no noticeable effect of CC in the dynamics for low-J values when compared to the CS result. As J increases, they effectively reduce the threshold shift observed in the CS probabilities and also vanish the resonance oscillations. The CC treats CH+ destruction (R1) and CH+ retention (R2) channels in the ratio of ∼(3:1), whereas the CS favors only R1 channel even for high-J values. The CC increases the dynamical quantities such as cross sections and rate constants with j-excitations and the values are generally higher than the CS result. Finally, we conclude that neglecting the CC terms generally underestimates the dynamical results for the title reaction which proceeds via the complex-forming mechanism, on the other hand, CC predicts the exact rate constants on par with the experimental results especially at low-T ranges of the astrochemical interest.

Theoretical study of photoionization cross sections of Al-like Sc

Photoionization (PI) cross sections of the ground state 3s23p 2P°1/2 and metastable state 3s23p 2P°3/2 of Al-like Sc are investigated using the Dirac R-matrix method. The current energy levels and radiative transition rates are consistent with experimental results and previous theory. Our calculated ionization energies of the ground and metastable states are in accordance with the experimental values. The PI cross sections show good agreement between length and velocity forms. Partial-wave contributions to the total PI of ground and metastable states are discussed. Moreover, the PI cross sections are dominated by a large number of resonances from the Rydberg series of autoionizing states. In addition to providing data for the Opacity Project TOPbase, the present work promotes plasma simulation and diagnosis.

Wave packet quantum dynamics of &lt;inline-formula&gt;&lt;tex-math id="Z-20200417045027-1"&gt;\begin{document}${\bf{C}}{(^3}{\bf{P}}) + {{\bf{H}}_2}({{\bf{X}}^1} \Sigma _{\bf{g}}^ + ) $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20200132_Z-20200417045027-1.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20200132_Z-20200417045027-1.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; &lt;inline-formula&gt;&lt;tex-math id="Z-20200418100246-1"&gt;\begin{document}$ \to {\bf{H}}{(^2}{\bf{S}}) + {\bf{CH}}{(^2} \Pi ) $\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20200132_Z-20200418100246-1.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20200132_Z-20200418100246-1.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; reaction based on new CH&lt;sub&gt;2&lt;/sub&gt;(&lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}${\tilde {\bf X}{}^3}\bf A''$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20200132_M2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20200132_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;) surface

The C(&lt;sup&gt;3&lt;/sup&gt;P) + H&lt;sub&gt;2 &lt;/sub&gt;→ CH+H reaction in a collision energy range of 1.0–2.0 eV with the initial state &lt;inline-formula&gt;&lt;tex-math id="M6"&gt;\begin{document}$\nu = 0{\rm{ }},j = 0$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20200132_M6.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20200132_M6.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; is investigated based on the new potential energy surface (PES) by using the Chebyshev wave packet method. All partial wave contributions up to &lt;i&gt;J&lt;/i&gt; = 60 are calculated explicitly by the coupled state (CS) approximation method and the Coriolis coupling (CC) effect. Dynamic properties such as reaction probabilities, integral cross sections, and state specific rate constants are calculated. The calculated probabilities and integral reaction cross sections display an increasing trend with the increase of the collision energy and an oscillatory structure due to the CH&lt;sub&gt;2&lt;/sub&gt; well on the reaction path. The thermal rate constants of the endoergic reaction with a temperature ranging from 1000 K to 2000 K are obtained also. The calculated rate constants increase in the entire temperature range, showing a sharp &lt;i&gt;T&lt;/i&gt; dependence in a range of 1400–2000 K. The rate constants are sensitive to the temperature due to the high threshold of the title reaction. In addition, the results of the exact calculations including CC effect are compared with those from the CS approximation. For smaller &lt;i&gt;J&lt;/i&gt;, the CS probabilities are larger than the CC results, while for larger &lt;i&gt;J&lt;/i&gt;, they are smaller than the CC ones. For reaction cross sections and rate constants, the CS results and the CC ones are in good agreement with each other at lower energy. However, they turn different at higher energy. The comparison between the CC and CS results indicates that neglecting the Coriolis coupling leads the cross sections and the rate constants to be underestimated due to the formation of a CH&lt;sub&gt;2&lt;/sub&gt; complex supported by stationary point of CH&lt;sub&gt;2&lt;/sub&gt;(&lt;inline-formula&gt;&lt;tex-math id="M7"&gt;\begin{document}${\tilde{\rm X}}{}^3 \rm A''$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20200132_M7.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20200132_M7.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;) PES. It is suggested that the CH&lt;sub&gt;2&lt;/sub&gt; complex plays an important role in the process of the title reaction. However, it seems to overestimate the CS and CC rate constants because the barrier recrossing is neglected. Unfortunately, the results obtained in the present work have no corresponding theoretical or experimental data to be compared with, therefore these results provide simply a certain reference significance to the follow-up study of the title reaction.

Complete and incomplete fusion cross-sections for 7Li+119Sn reaction using different approaches

In reference to complete fusion (CF) and incomplete fusion (ICF) processes, the analysis of 7 Li+ 119 Sn reaction forming 126 I compound nucleus (CN) is carried out at incident energies spread across the Coulomb barrier. Firstly, the total fusion (TF) cross-sections are calculated using the Wong formula. Since, it overestimates the experimental data, so ℓ-summed Wong approach is employed to address the TF cross-section, which limits the contribution of partial waves up to ℓ max value. Within ℓ-summed Wong model, the energy dependent selection function is used to separate out the contributions of CF and ICF from the TF cross-sections. This phenomenological selection function seems to give adequate distribution of CF and ICF cross-sections at higher energies. Beside this, the CF and ICF contributions are also separated out on the basis of angular momentum window and by using the energy correction formula. In the angular momentum distribution case, CF and ICF cross-sections are estimated in view of ℓ-windows, 0≤ℓ&lt;ℓ critical (for CF) and ℓ critical ≤ ℓ ≤ℓ max (For ICF). Finally, in energy normalization case, the incident energy of 7 Li beam ( 7 Li→ 4 He + 3 H) is distributed among alpha and tritium fragments, and the ICF cross-sections for 3 H+ 119 Sn ICF channel are estimated using the ℓ-summed Wong model.

Electron attachment and quantum coherence in molecular hydrogen

Single electron attachment to a molecule may invoke quantum coherence in different angular momentum transfer channels. This has been observed in the 14 eV dissociative electron attachment resonance in molecular hydrogen where a coherent superposition of two negative ion resonant states of opposite parity is created, with the s and p partial waves of the electron contributing to the attachment process. Interference between the two partial wave contributions leads to a forward – backward asymmetry in the angular distribution of the product negative ions. Since these two resonant states dissociate to the same n = 2 state of H and H−, this asymmetry is further modified due to interference between the two paths of the dissociating molecular negative ion along different potential energy curves. This interference manifests as a function of the electron energy as well as isotopic composition. This case is akin to the quantum interference observed in photodissociation by one-photon vs two-photon absorption.

Search for CP violation with kinematic asymmetries in the D0→K+K−π+π− decay

We search for $CP$ violation in the singly-Cabibbo-suppressed decay $D^{0}\rightarrow K^{+}K^{-}\pi^{+}\pi^{-}$ using data corresponding to an integrated luminosity of $988\text{ }{\rm fb}^{-1}$ collected by the Belle detector at the KEKB $e^{+}e^{-}$ collider. We measure a set of five kinematically dependent $CP$ asymmetries, of which four asymmetries are measured for the first time. The set of asymmetry measurements can be sensitive to $CP$ violation via interference between the different partial-wave contributions to the decay and performed on other pseudoscalar decays. We find no evidence of $CP$ violation.

Importance of d-wave contributions in the charge symmetry breaking reaction [formula omitted

This letter reports a first quantitative analysis of the contribution of higher partial waves in the charge symmetry breaking reaction dd→4Heπ0 using the WASA-at-COSY detector setup at an excess energy of Q=60MeV. The determined differential cross section can be parametrized as dσ/dΩ=a+bcos2⁡θ⁎, where θ⁎ is the production angle of the pion in the center-of-mass coordinate system, and the results for the parameters are a=(1.55±0.46(stat)+0.32−0.8(syst))pb/sr and b=(13.1±2.1(stat)−2.7+1.0(syst))pb/sr. The data are compatible with vanishing p-waves and a sizable d-wave contribution. This finding should strongly constrain the contribution of the Δ isobar to the dd→4Heπ0 reaction and is, therefore, crucial for a quantitative understanding of quark mass effects in nuclear production reactions.