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Resonance Regge poles and the state-to-state F + H2 reaction: QP decomposition, parametrized S matrix, and semiclassical complex angular momentum analysis of the angular scattering
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10.1063/1.4794859
/content/aip/journal/jcp/138/12/10.1063/1.4794859
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4794859

Figures

Image of FIG. 1.
FIG. 1.

(a) versus J, and (b) versus J. Black solid circles: Numerical S matrix. Pink solid circles: Parametrized S matrix as given by Eq. (43a) . Note that is undefined in both cases because . The black solid circles and pink solid circles have been joined by black and pink straight lines, respectively.

Image of FIG. 2.
FIG. 2.

Linear plot of PWS σ(θR) versus θR. Black curve: Numerical S matrix. Pink curve: Parametrized S matrix as given by Eq. (43) .

Image of FIG. 3.
FIG. 3.

Plot of five different versus J, all using the numerical S matrix. Black solid circles: . Orange open squares: . Orange solid circles: . Green open squares: . Green solid circles: . In all cases the black, orange and green symbols have been joined by straight lines.

Image of FIG. 4.
FIG. 4.

Linear plot of PWS σ(θR) versus θR. All four curves use the numerical S matrix. Black solid curve: . Orange solid curve: . Green solid curve: . The inset shows in more detail the forward angular range, 0° ⩽ θR ⩽ 40°, where the purple dashed curve uses but keeping only the leading (n = 0) pole in the sum (17) .

Image of FIG. 5.
FIG. 5.

NF analysis for the Qmod subamplitude showing (a) logarithmic plot of full and N,F PWS σ(θR) versus θR, and (b) linear plot of full and N,F PWS LAM(θR) versus θR. Orange curves: full Qmod. Red curves: Qmod/N (r = 1). Blue curves: Qmod/F (r = 1). All six curves use the numerical S matrix.

Image of FIG. 6.
FIG. 6.

NF analysis for the Pmod subamplitude showing (a) logarithmic plot of full and N,F PWS σ(θR) versus θR, and (b) linear plot of full and N,F PWS LAM(θR) versus θR. Green curves: full Pmod. Red curves: Pmod/N (r = 1). Blue curves: Pmod/F (r = 1). All six curves use the numerical S matrix.

Image of FIG. 7.
FIG. 7.

(a) versus J, and (b) versus J. Black solid circles: Numerical Q matrix. Pink solid circles: The parametrized Q matrix as given by Eq. (42) . The black solid circles and pink solid circles have been joined by black and pink straight lines, respectively.

Image of FIG. 8.
FIG. 8.

Schematic drawing of contours in the CAM plane. Γ is the contour that occurs in the background integral (48) . is the contour that passes through the real saddle point, (solid circle), of the background integral. The open circles show schematically the positions of four poles, J 0, J 1, J 2, and J 3, in the CAM plane.

Image of FIG. 9.
FIG. 9.

Linear plot of σ(θR) versus θR for the parametrized S matrix. Black curves: PWS. Red curves: Uniform semiclassical CAM theory. The green arrows denote the position of the rainbow angle, .

Image of FIG. 10.
FIG. 10.

Logarithmic plot of σ(θR) versus θR for the parametrized S matrix. Black curve: PWS. Green curve: Pole DCS. Orange curve: Direct semiclassical DCS. Blue curve: Residue semiclassical DCS. Purple curve: Erfc semiclassical DCS.

Image of FIG. 11.
FIG. 11.

Logarithmic plot of σ(θR) versus θR for the parametrized S matrix. (a) Black curve: PWS. Light-blue curve: (residue + erfc) semiclassical DCS. (b) Black curve: PWS. Yellow curve: (residue + direct) semiclassical DCS.

Image of FIG. 12.
FIG. 12.

Logarithmic plot of σ(θR) versus θR for the parametrized S matrix. (a) Black solid curve: PWS. Green solid curve: Pole DCS including n = 0, 1, 2, and 3 poles. Orange dashed curves: Individual pole DCSs for n = 0, 1, 2, and 3. Red dashed curve: Nearside DCS for the n = 0 pole. Blue dashed curve: Farside DCS for the n = 0 pole. (b) Black solid curve: PWS. Blue solid curve: Residue DCS including n = 0, 1, 2, and 3 poles. Blue dashed curves: Individual residue DCSs for n = 0, 1, 2, and 3. (c) Black solid curve: PWS. Dark-purple solid curve: Erfc DCS including n = 0, 1, 2, and 3 poles. Light-purple dashed curves: Individual erfc DCSs for n = 0, 1, 2, and 3.

Image of FIG. 13.
FIG. 13.

(a) Logarithmic plot of σ(θR) versus θR, and (b) Plot of LAM(θR) versus θR. In both (a) and (b), the plots are for the parametrized S matrix. In addition, black solid curves: PWS. Green solid curves: CAM with n = 0, 1, 2, and 3 poles. Red solid curves: Nearside CAM with n = 0, 1, 2, and 3 poles. Blue solid curves: Farside CAM with n = 0, 1, 2, and 3 poles. Red dashed curves: N r = 1 PWS. Blue dashed curves: F r = 1 PWS.

Image of FIG. 14.
FIG. 14.

Linear plot of σ(θR) versus θR for the parametrized S matrix with 0° ⩽ θR ⩽ 40°. Black curve: PWS. Orange curve: Uniform semiclassical CAM theory using the nearside refc subamplitude plus the farside n = 0 pole sub-subamplitude. Blue dashed curve: Uniform semiclassical CAM theory using the farside n = 0 pole sub-subamplitude. Red dashed curve: Uniform semiclassical CAM theory using the nearside refc subamplitude. The green arrows denote the position of the rainbow angle, .

Image of FIG. 15.
FIG. 15.

Linear plot of σ(θR) versus θR for the parametrized S matrix. Black curve: PWS, including all partial waves. Red curve: PWS, including all partial waves except J = 0.

Tables

Generic image for table
Table I.

Values of Regge pole positions, J n , partial residues, , quantum life-angles, , and full residues, , for n = 0, 1, 2, 3, for the SCT Padé data. a In addition, a = −0.0637, b = π − 0.1777, c = 1.33708. b These data also apply to , the analytic continuation of .

Generic image for table
Table II.

Values of the parameters in Eq. (42) for .

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/content/aip/journal/jcp/138/12/10.1063/1.4794859
2013-03-28
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Resonance Regge poles and the state-to-state F + H2 reaction: QP decomposition, parametrized S matrix, and semiclassical complex angular momentum analysis of the angular scattering
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/12/10.1063/1.4794859
10.1063/1.4794859
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