# Nearside-farside, local angular momentum and resummation theories: Useful tools for understanding the dynamics of complex-mode reactions

## Abstract

A valuable tool for understanding the dynamics of direct reactions is Nearside-Farside (NF) scattering theory. It makes a decomposition of the (resummed) partial wave series for the scattering amplitude, both for the differential cross section (DCS) and the Local Angular Momentum (LAM). This paper makes the first combined application of these techniques to complex-mode reactions. We ask if NF theory is a useful tool for their identification, in particular, can it distinguish complex-mode from direct-mode reactions? We also ask whether NF theory can identify NF interference oscillations in the full DCSs of complex-mode reactions. Our investigation exploits the fact that accurate quantum scattering matrix elements have recently become available for complex-mode reactions. We first apply NF theory to two simple models for the scattering amplitude of a complex-mode reaction: One involves a single Legendre polynomial; the other involves a single Legendre function of the first kind, whose form is suggested by complex angular momentum theory. We then study, at fixed translational energies, four state-to-state complex-mode reactions. They are: S({sup 1}D) + HD → SH + D, S({sup 1}D) + DH → SD + H, N({sup 2}D) +H{sub 2} → NH + H, and H{sup +} + D{sub 2} → HDmore »

- Authors:

- Centre for Computational Molecular Science, Australian Institute for Bioengineering and Nanotechnology, The University of Queensland, Brisbane, QLD 4072 (Australia)
- School of Chemistry, The University of Manchester, Manchester M13 9PL (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22492265

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Advances; Journal Volume: 5; Journal Issue: 7; Other Information: (c) 2015 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR MOMENTUM; COMPARATIVE EVALUATIONS; DEUTERIUM; DIFFERENTIAL CROSS SECTIONS; DIRECT REACTIONS; HYDROGEN; HYDROGEN IONS 1 PLUS; INTERFERENCE; LEGENDRE POLYNOMIALS; MATRIX ELEMENTS; OSCILLATIONS; PARTIAL WAVES; S MATRIX; SCATTERING; SCATTERING AMPLITUDES; SULFUR

### Citation Formats

```
Hankel, Marlies, E-mail: m.hankel@uq.edu.au, E-mail: j.n.l.connor@manchester.ac.uk, and Connor, J. N. L., E-mail: m.hankel@uq.edu.au, E-mail: j.n.l.connor@manchester.ac.uk.
```*Nearside-farside, local angular momentum and resummation theories: Useful tools for understanding the dynamics of complex-mode reactions*. United States: N. p., 2015.
Web. doi:10.1063/1.4927506.

```
Hankel, Marlies, E-mail: m.hankel@uq.edu.au, E-mail: j.n.l.connor@manchester.ac.uk, & Connor, J. N. L., E-mail: m.hankel@uq.edu.au, E-mail: j.n.l.connor@manchester.ac.uk.
```*Nearside-farside, local angular momentum and resummation theories: Useful tools for understanding the dynamics of complex-mode reactions*. United States. doi:10.1063/1.4927506.

```
Hankel, Marlies, E-mail: m.hankel@uq.edu.au, E-mail: j.n.l.connor@manchester.ac.uk, and Connor, J. N. L., E-mail: m.hankel@uq.edu.au, E-mail: j.n.l.connor@manchester.ac.uk. Wed .
"Nearside-farside, local angular momentum and resummation theories: Useful tools for understanding the dynamics of complex-mode reactions". United States. doi:10.1063/1.4927506.
```

```
@article{osti_22492265,
```

title = {Nearside-farside, local angular momentum and resummation theories: Useful tools for understanding the dynamics of complex-mode reactions},

author = {Hankel, Marlies, E-mail: m.hankel@uq.edu.au, E-mail: j.n.l.connor@manchester.ac.uk and Connor, J. N. L., E-mail: m.hankel@uq.edu.au, E-mail: j.n.l.connor@manchester.ac.uk},

abstractNote = {A valuable tool for understanding the dynamics of direct reactions is Nearside-Farside (NF) scattering theory. It makes a decomposition of the (resummed) partial wave series for the scattering amplitude, both for the differential cross section (DCS) and the Local Angular Momentum (LAM). This paper makes the first combined application of these techniques to complex-mode reactions. We ask if NF theory is a useful tool for their identification, in particular, can it distinguish complex-mode from direct-mode reactions? We also ask whether NF theory can identify NF interference oscillations in the full DCSs of complex-mode reactions. Our investigation exploits the fact that accurate quantum scattering matrix elements have recently become available for complex-mode reactions. We first apply NF theory to two simple models for the scattering amplitude of a complex-mode reaction: One involves a single Legendre polynomial; the other involves a single Legendre function of the first kind, whose form is suggested by complex angular momentum theory. We then study, at fixed translational energies, four state-to-state complex-mode reactions. They are: S({sup 1}D) + HD → SH + D, S({sup 1}D) + DH → SD + H, N({sup 2}D) +H{sub 2} → NH + H, and H{sup +} + D{sub 2} → HD + D{sup +}. We compare the NF results for the DCSs and LAMs with those for a state-to-state direct reaction, namely, F + H{sub 2} → FH + H. We demonstrate that NF theory is a valuable tool for identifying and analyzing the dynamics of complex-mode reactions.},

doi = {10.1063/1.4927506},

journal = {AIP Advances},

number = 7,

volume = 5,

place = {United States},

year = {Wed Jul 15 00:00:00 EDT 2015},

month = {Wed Jul 15 00:00:00 EDT 2015}

}