Multiparticle partial-wave amplitudes and inelastic unitarity. IV. A scattering model with production and its characteristic operator function

Klink, William H.; Johnson, Lloyd E.

doi:10.1103/physrevd.9.1057

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1975

1982

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“…For the use of Fredholm methods. Other relevant papers are W. H. Klink (1971 and; H. Rabitz (1971); Conn and Rabitz (1973). P. Reinhardt (1970).…”

Section: 2mentioning

confidence: 99%

Scattering Theory of Waves and Particles

Newton¹

1982

2,956

3,254

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“…For the use of Fredholm methods. Other relevant papers are W. H. Klink (1971 and; H. Rabitz (1971); Conn and Rabitz (1973). P. Reinhardt (1970).…”

Section: 2mentioning

confidence: 99%

Scattering Theory of Waves and Particles

Newton¹

1982

2,956

3,254

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Crossing in 2 → 3 partial-wave amplitudes

Klink¹

1975

Phys. Rev. D

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Crossing in 2 -i 3 reactions is investigated, and it is shown that by using canonical variables we can express crossing in a particularly simple form.The most general five-particle amplitude involvAssuming parity invariance and using center-ofing spinless arbitrary-mass particles requires five m a s s variables, one can write relativistically invariant variables plus a "sign"invariant. That is, if the two incoming particles (~1~2 1 , % S12, ~1 3 ) a r e labeled 1' and 2', and the t h r e e outgoing par--; i . ' 2"3 -( s 1 ' 2 ' , tl'33 t 2 ' 3 3 S 1 2 , ~1 3 ) ticles 1 , 2 , and 3 , then the reaction 1' + 2 ' -1 + 2 + 3 i s conventionally described by an atnplitudef the total angular momentum and r l l the spin projection chosen along the direction of particle 3. where s i j = ( p i +pj),, t i f = ( p i -p j ) ' , and "sgn 1" i? i s the unit vector relating the direction of p a rdenotes the sign of the quantity in brackets. If particle 1' relative to the plane formed by particles ity invariance i s assumed, i t i s possible to elimi-1 , 2 , and 3 in their c.m. frame; it i s defined nate the dependence of F'2'3 on the "sgn" variable. through the polar angle 0 and azimuthal angle cp: (sit ,, T M1t -1 k f 2 , 2 ) (~1~ + -~~t~ -1~~' ) -S I 2 ) + 2s11 ,f(tll -A ' /~( S~, ,1,1%f1, 2,M2t 2 ) h 1 / 2 (~1~2~, s~~,~~~) T coscp = The notation i3,j(k,j means the angle betw$en particles i and j in the f r a m e where $, +c, = 0. If the parentheses (kl) a r e dropped, i t i s understood that the angle is evaluated in the c.m. frame. In o r d e r to define cp uniquely--rather than just coscp--it i s necessary to specify the sign of the invariantThe function is the usual triangle function.' Now to implement crosssing from the 1 1 + 2 ' -1 + 2 + 3 channel to the l f + 2 ' + 9 -1 + 2 channel in the most convenient manner, we choose another variable in place of the s,, subenergy, namely cos'd,,( ,,), that i s , the angle between particles 1 and 3 in the f r a m e where particles 1 and 2 have equal and opposite momenta-the so-called helicity angle. This angle is readily expressed in t e r m s of relativistic invariants to be and the amplitude in this new variable becomes

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Multiparticle partial-wave amplitudes and inelastic unitarity. IV. A scattering model with production and its characteristic operator function

Cited by 2 publications

References 15 publications

Scattering Theory of Waves and Particles

Scattering Theory of Waves and Particles

Crossing in 2 → 3 partial-wave amplitudes

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