Higher Partial Waves Research Articles

Electron-F2Ocollision study using theR-matrix method

The present study deals with the calculation of differential, elastic integral, momentum transfer, and excitation cross sections for electron-${\mathrm{F}}_{2}\mathrm{O}$ collision in a 16-state $R$-matrix method. Configuration interation (CI) wave functions are used to represent the target states. The CI model gave an adequate description of the vertical excitation spectrum from the equilibrium geometry of the ground state ${X}^{1}\phantom{\rule{0.2em}{0ex}}{A}_{1}$ of the ${\mathrm{F}}_{2}\mathrm{O}$ molecule that spans the energy range $4.21--10.21\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Our calculated dipole moment of $0.224\phantom{\rule{0.3em}{0ex}}\mathrm{D}$ is in good agreement with the experimental value $0.297\phantom{\rule{0.3em}{0ex}}\mathrm{D}$. We also found two broad shape resonances in $^{2}A_{1}$ and $^{2}B_{2}$ scattering symmetries and both resonances support dissociative electron attachment. A born correction is applied for the elastic and dipole allowed transitions to account for higher partial waves $(lg4)$ excluded in the $R$-matrix calculation. All cross sections are presented for incident electron energies up to $15\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Our results are compared with cross sections of ${\mathrm{Cl}}_{2}\mathrm{O}$ calculated at the same level of complexity using the $R$-matrix method.

Quasi-Hermitian pseudopotential for higher partial wave scattering

We formulate a quasi-Hermitian delta-shell pseudopotential for higher partial wave scattering, and show that any such potential must have an energy-dependent regularization. The quasi-Hermiticity of the Hamiltonian leads to a complete set of biorthogonal wave functions that can be used as a basis to expand and diagonalize other two-body Hamiltonians. We demonstrate this procedure for the case of ultracold atoms in a polarization-gradient optical lattice, interacting pairwise when two atoms are transported together from separated lattice sites. Here the pseudopotential depends explicitly on the trapping potential. Additionally, we calculate the location of trap-induced resonances for higher partial waves, which occur when a molecular eigenstate is shifted to resonance with a trap eigenstate. We verify the accuracy of the pseudopotential approach using a toy model in which a square well acts as the true interaction potential, and see excellent agreement.

ROLE OF THE TENSOR CORRELATIONS IN 4HE and 5HE

We investigate the roles of the tensor correlation on the structures of 4 He and 5 He . For 4 He , we take the high angular momentum states within the 2p2h excitations of the shell model type method to describe the tensor correlation explicitly. We found that the solutions show a good convergence and the obtained wave function has the large tensor correlation. We also found that three 2p2h configurations are largely coupled with (0s)4 one to describe the tensor correlation, which is understood from the selectivity of the tensor operator. This tensor correlation is also important to describe the scattering phenomena of the 4 He +n system including the higher partial waves consistently.

3α resonance excited states of 12C in a microscopic cluster model

Three-alpha resonance excited states has been theoretically explored by means of the α+α+α microscopic cluster model. The resonance parameters is determined by employing the Complex Scaling Method (CSM). Our model space is extended by including higher partial waves than the RGM+CSM calculation by Pichler1. Our model has given the third 0+ state at 4~5MeV above the three-body threshold but the broad 0+ state, which was recently reported experimentally and overlapping with the 2+ state2, has not been localized between the second and the third 0+ states. On the other hands, our model has given the second 2+ state about 2MeV and the third at 4~5MeV.

The high partial wave phenomenon of spin changing atomic transitions

The collisional transition between two highly excited atomic states with different spin is investigated theoretically. Taking helium-like n1S–n3P as an example, it is found that the transition is driven in the highly ionized Fe ion purely by exchange, and the cross section becomes increasingly dominated by partial waves of high orbital angular momentum as the scattering energy increases. Whereas for the near-neutral Li ion the transition is dominated by channel coupling in low partial waves. Analytical benchmarks and numerical methods are developed for the accurate calculation of the exchange integral at high angular momentum. It is shown how the partial wave and energy dependence of the collision strength for high n spin changing transitions in the highly ionized ion is related to the overlap of the extended atomic orbitals.

New calculation schemes for proton-deuteron scattering including the Coulomb interaction

The Coulomb interaction between the protons is included in the description of proton-deuteron scattering using the screening and renormalization approach in the framework of momentum-space integral equations. Two new calculational schemes are presented that confirm the reliability of the perturbative approach for treating the screened Coulomb interaction in high partial waves, used by us in earlier works.

Calculation of absolute scattering phase shifts

Use of a simple semiclassical estimate of Bessel function phase for arbitrary argument avoids the modulo π errors which the conventional approach tends to introduce into the calculation of absolute quantal phase shifts for high partial waves. This has significant implications for the direct quantum mechanical calculation of second virial coefficients at high temperatures.

Renormalization of one-pion exchange and power counting

The renormalization of the chiral nuclear interactions is studied. In leading order, the cutoff dependence is related to the singular tensor interaction of the one-pion exchange potential. In S waves and in higher partial waves where the tensor force is repulsive this cutoff dependence can be absorbed by counterterms expected at that order. In the other partial waves additional contact interactions are necessary. The implications of this finding for the effective field theory program in nuclear physics are discussed.

High partial wave resonances in positron hydrogen scattering

In this work, we present results for high-angular-momentum resonances in positron-hydrogen scattering obtained by using the method of complex-coordinate rotations. Resonance states with angular momenta of $L=3$ to 6 are calculated using highly correlated Hylleraas-type wave functions. Furthermore, for the $L=0$ and 1 states, we present our updated results. Comparisons with other calculations are made.

Phenomenology of thepp→ppηreaction close to threshold

The recent high statistics measurement of the pp -> pp eta reaction at an excess energy Q=15.5 MeV has been analysed by means of partial wave decomposition of the cross section. Guided by the dominance of the final state 1S0 pp interaction (FSI), we keep only terms involving the FSI enhancement factor. The measured p-p and p-eta effective mass spectra can be well reproduced by lifting the standard on-shell approximation in the enhancement factor and by allowing for a linear energy dependence in the leading 3P0->1S0,s partial wave amplitude. Higher partial waves seem to play only a marginal role.

Experimental study ofppηdynamics in thepp→ppηreaction

A high statistics measurement of the pp --> ppeta reaction at an excess energy of Q = 15.5 MeV has been performed at the internal beam facility COSY-11. The stochastically cooled proton beam and the used detection system allowed to determine the momenta of the outgoing protons with a precision of 4 MeV/c (sigma) in the center-of-mass frame. The determination of the four-momentum vectors of both outgoing protons allowed to derive the complete kinematical information of the ppeta-system. An unexpectedly large enhancement of the occupation density in the kinematical regions of low proton-eta relative momenta is observed. A description taking the proton-proton and the eta-proton interaction into account and assuming an on-shell incoherent pairwise interaction among the produced particles fails to explain this strong effect. Its understanding will require a rigorous three-body approach to the ppeta system and the precise determination of contributions from higher partial waves. We also present an invariant mass spectrum of the proton-proton system determined at Q = 4.5 MeV. Interestingly, the enhancement at large relative momenta between protons is visible also at such a small excess energy. In contrast to all other determined angular distributions, the orientation of the emission plane with respect to the beam direction is extracted to be anisotropic.

Lower limit in semiclassical form for the number of bound states in a central potential

We identify a class of potentials for which the semiclassical estimate N (semi) =(1/π)∫ 0 ∞dr −V(r)θ[−V(r)] of the number N of (S-wave) bound states provides a (rigorous) lower limit: N⩾{{ N (semi)}}, where the double braces denote the integer part. Higher partial waves can be included via the standard replacement of the potential V( r) with the effective ℓ-wave potential V ℓ (eff)( r)= V( r)+ℓ(ℓ+1)/ r 2. An analogous upper limit is also provided for a different class of potentials, which is however quite severely restricted.

Quadratic momentum dependence in the nucleon-nucleon interaction

We investigate different choices for the quadratic momentum dependence required in nucleon-nucleon potentials to fit phase shifts in high partial waves. In the Argonne ${v}_{18}$ potential ${\mathbf{L}}^{2}$ and ${(\mathbf{L}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S})}^{2}$ operators are used to represent this dependence. The ${v}_{18}$ potential is simple to use in many-body calculations since it has no quadratic momentum-dependent terms in $S$ waves. However, ${\mathbf{p}}^{2}$ rather than ${\mathbf{L}}^{2}$ dependence occurs naturally in meson-exchange models of nuclear forces. We construct an alternate version of the Argonne potential, designated Argonne ${v}_{18pq}$, in which the ${\mathbf{L}}^{2}$ and ${(\mathbf{L}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S})}^{2}$ operators are replaced by ${\mathbf{p}}^{2}$ and ${Q}_{ij}$ operators, respectively. The quadratic momentum-dependent terms are smaller in the ${v}_{18pq}$ than in the ${v}_{18}$ interaction. Results for the ground-state binding energies of $^{3}\text{H}$, $^{3}\text{He}$, and $^{4}\text{He}$, obtained with the variational Monte Carlo method, are presented for both the models with and without three-nucleon interactions. We find that the nuclear wave functions obtained with ${v}_{18pq}$ are slightly larger than those with ${v}_{18}$ at interparticle distances $<1\phantom{\rule{0.3em}{0ex}}\text{fm}$. The two models provide essentially the same binding in the light nuclei, although ${v}_{18pq}$ gains less attraction when a fixed three-nucleon potential is added.

An upper bound on the total cross-section for electroweak baryon number violation

An upper bound on the total cross-section of s-wave electroweak instanton/sphaleron induced baryon plus lepton number violating processes is presented. It is obtained by exploiting a recently reported lower bound on the corresponding tunneling suppression exponent and by estimating the pre-exponential factor. We find that the present knowledge about electroweak baryon plus lepton number violating processes still allows their eventual observability at the Very Large Hadron Collider, even as pure s-wave scattering. A possibly observable rate at cosmic ray facilities and neutrino telescopes is presently not excluded, but requires a substantial contribution from higher partial waves.

On the absorption by near-extremal black branes

We study the absorption of a minimally coupled scalar in the gravitational background created by a stack of near-extremal black three-branes, and more generally by M2-, M5- and D p-branes. The absorption probability has the form P( l)= P 0( l) f l ( λ), where P 0( l) is the partial wave's absorption probability in the extremal case, and the thermal factor f l ( λ) depends on the ratio of the frequency of the incoming wave and the Hawking temperature, λ= ω/ πT. Using Langer–Olver's method, we obtain a low-temperature ( λ⪢1) asymptotic expansion for P( l) with coefficients determined recursively. This expansion, which turns out to be a fairly good approximation even for λ∼1, accounts for all power-like finite-temperature corrections to P 0( l), and we calculate a few terms explicitly. We also show that at low temperature the absorption probability contains exponentially suppressed terms, and attempt to develop an approximation scheme to calculate those. The high-temperature expansion is also considered. For the s-wave, the low-temperature gravity result is consistent with the free finite-temperature field theory calculation, while for high temperature and higher partial waves we find a disagreement. As a check of the approximation methods used, we apply them to the D1–D5-brane system, and compare results to the known exact solution.

Electron impact ionization of He above the threshold

Near-threshold ionization of He has beenstudied by using a uniform semiclassical wavefunction for thetwo outgoing electrons in the final channel. The quantum mechanical transition amplitude for the direct and exchangescattering derived earlier by using the Kohn variationalprinciple has been used to calculate the triple differentialcross sections. Contributions from singlets and triplets arecritically examined near the threshold for coplanar asymmetricgeometry with equal energy sharing by the two outgoingelectrons. It is found that in general the triplet contributionis much smaller compared to its singlet counterpart. However, atunequal scattering angles such as θ1 = 60°,θ2 = 120° the smaller peaks in the triplet contributionenhance both primary and secondary TDCS peaks. Significantimprovements of the primary peak in the TDCS are obtained forthe singlet results both in symmetric and asymmetric geometryindicating the need to treat the classical action variableswithout any approximation. Convergence of these cross sectionsare also achieved against the higher partial waves. Presentresults are compared with absolute and relative measurements ofRösel et al (1992Phys. Rev. A 46 2539) and Selles et al(1987 J. Phys. B. At. Mol. Phys. 20 5195) respectively.

Chiral quark model of theNNsystem within a Lippmann-Schwinger resonating group method

We analyze the two-nucleon system below the pion threshold, using a chiral quark cluster model. We solve multichannel resonating group method equations in momentum space, treating them as a set of Lippmann-Schwinger equations. Deuteron data and scattering phase shifts up to a total angular momentum $J=6$ are presented. Full couplings to $N\ensuremath{\Delta}$ and $\ensuremath{\Delta}\ensuremath{\Delta}$ channels are considered and analyzed. High angular momentum partial waves $(Lg2)$ provide a detailed test of chiral symmetry in the two-nucleon system. D waves still show important short-range effects. Low angular momentum partial waves and deuteron observables are in good agreement with the experimental data, showing that the underlying quark structure provides the required short-range potential behavior.

Partial-wave dispersion relations: Exact left-handE-plane discontinuity computed from the Born series

We show that for a superposition of Yukawa potentials, the exact left-hand cut discontinuity in the complex-energy plane of the (S-wave) scattering amplitude is given, in an interval depending on n, by the discontinuity of the Born series stopped at order n. This establishes an inverse and unexpected correspondence of the Born series at positive high energies and negative low energies. With the discontinuity on the left-hand axis elucidated, we can construct a viable dispersion relation (DR) for the partial (S-) wave amplitude. The DR is numerically verified for the exponential potential at zero scattering energy. Generalization to higher partial waves, and extension of these ideas to field theory are discussed.

Implications for the πNN coupling constant from pp and np spin transfer measurements

A complete set of spin-transfer coefficients for forward-angle pp elastic scattering at 198 MeV has been measured at the Indiana University Cyclotron Facility, with uncertainties far smaller than previous measurements. These particular observables, and this kinematic regime, were specifically chosen to maximize the sensitivity of these measurements to the neutral pion-nucleon coupling constant, a fundamental quantity in low and intermediate energy nuclear physics whose value remains highly controversial. To achieve the desired experimental uncertainty, several components of the apparatus required calibration at a higher level of precision than had been previously achieved, and new procedures in data acquisition and analysis were developed in order to minimize many of the possible sources of systematic error. Our primary conclusion from this work is that our results provide strong support for modern potential models of the NN interaction in which a relatively weak pion coupling is employed (g02 ≈ 13.6). Moreover, our data deviate significantly from the predictions of older potentials in which g02 is ~14.4. Calculations carried out in a one-boson exchange framework, using the Bonn B potential, suggest that most of these differences can be accounted for by simply reducing the πNN coupling from 14.4 to 13.6 for the long-range (higher partial wave) pion contributions in these models.

Analysis of discrepancies between quantal and semiclassical calculations of electron impact broadening in plasmas

In this work we analyse the serious discrepancies found between quantal calculations and non-perturbative semiclassical calculations of electron impact broadening in the case of B 2+2 s–2 p. We use the Coulomb Bethe (CB) approximation to calculate both electron impact broadening and excitation of 2 s–2 p for comparison with the other methods. We find good agreement between CB and the non-perturbative semiclassical method for the line width contributions of individual partial waves, except for low L, where strong collision effects enter. We also find good agreement between CB and the R-matrix and Coulomb Born methods for the excitation cross section partial wave contributions, again except for low L. There is disagreement for the high partial wave cross sections between the non-perturbative semiclassical method and all of the quantum methods; this is resolved by applying a symmetrized method, for which we demonstrate excellent agreement with CB. The area in which the semiclassical, Coulomb–Born and R-matrix methods disagree has been reduced to the first three partial waves, and the disagreement must be due to the treatment of strong collisions.