<i>Kinematics of Nuclear Reactions</i>

Балдин, Александр Михайлович; Goldanskii, V. I.; Rozenthal, I. L.; Jones, William E.; Feshbach, Herman

doi:10.1063/1.3058191

Cited by 35 publications

(8 citation statements)

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“…and then to the respective particle rest frames. 4 The relativistic spin rotation is the purely kinematical effect: the angles of the space rotation coincide with the angles between the vectors of the resulting velocities at the relativistic addition of velocities v l and V in the direct and reverse orders [11]. …”

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Effect of the relativistic spin rotation on two-particle spin composition

2004

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The effect of the relativistic spin rotation on two-particle spin states, conditioned by the setting of the spins of the particles in their rest frames and by the noncommutativity of the Lorentz transformations along noncolinear directions, is discussed. Particularly, the transition from the c.m.s. of two spin-1/2 particles to the laboratory is considered. When the vectors of the c.m.s. particle velocities are not colinear with the velocity vector of the c.m.s., the angles of the relativistic spin rotation for the two particles are different. As a result, the relative fractions of the singlet and triplet states in the relativistic system of two spin-1/2 particles with a nonzero vector of relative momentum depend on the concrete frame in which the two-particle system is analyzed.1. Earlier the spin correlations in two-particle quantum systems were analyzed in detail as a tool allowing one to measure the space-time characteristics of particle production [1][2][3][4][5], to study the two-particle interaction and the production dynamics (see [3,4] and references therein) and to verify the consequences of the quantum-mechanical coherence with the help of Bell-type inequalities [4].The spin state of the system of two particles in an arbitrary frame is described by the two-particle density matrix, the elements of which, ρ(1,2) m1m1 ′ ; m2m2 ′ , are given in the representation of the spin projections of the first and second particle in the corresponding rest frames onto the common coordinate axis z (see, e.g., [3,5]).1 However, one should take into account the relativistic spin rotation conditioned by the additional rotation of the spatial axes at the successive Lorentz transformations along noncolinear directions [7][8][9].2 As a result, the concrete description of a particle spin state depends on the frame from which the transition to the particle rest frame is performed. Particularly, the total spin composition of the two-particle state with a nonzero vector of relative momentum is generally frame-dependent due to different relativistic rotation angles of the two spins at the transition to the frame moving in the direction which is not colinear with the velocity vectors of both particles.Usually, it is convenient to consider the spin correlations in the center-of-mass system (c.m.s.) of the particle pair. This is natural at the addition of the two-particle total spin and the relative orbital angular momentum into the conserved total angular momentum. In some cases, however, it may be useful to make transition to the laboratory, e.g., in the case when the particle scatterings are used as their spin analyzers [1].3 Denoting M l and p l = ±k the masses and c.m.s. momenta of the two particles, l = 1, 2, their respective c.m.s. velocities in the units of the velocity of light (c = 1) are v l = ±k/ k 2 + M 2 l . Here and below the ± signs correspond to the first (l = 1) and second (l = 2) particle, respectively. We denote the corresponding laboratory velocities as v l and the laboratory velocity of the particle pair as V. ...

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Effect of the relativistic spin rotation on two-particle spin composition

2004

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“…Another way to get "probability in unit time" is given in books on quantum field theory, e.g., see [8], [11], [2], [4]. At first, one considers the lim U(T /2, −T /2) as T → ∞, i.e., the S-matrix (in our way the limit T → ∞ is carried out later, see (36), (37)).…”

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Wave packets in the quantum theory of collisions

Shirokov

2008

Phys. Part. Nuclei

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Two methodological troubles of the quantum theory of collisions are considered. The first is the undesirable interference of the incident and scattered waves in the stationary approach to scattering. The second concerns the nonstationary approach to the theory of collisions of the type a + b → c + d. In order to calculate the cross section one uses the matrix element cd|S|ab of the S-matrix. The element is proportional to δ-function expressing the energy conservation. The corresponding probability | cd|S|ab | 2 contains δ 2 which is mathematically senseless. The known regular way to overcome the difficulty seems to be unsatisfactory. In this paper, both the troubles are resolved using wave packets of incident particles.

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“…For coherent elastic scattering at zero angle, the initial and final values of neutron momenta and spin projections are equal to each other, k i = k f = k and µ i = µ f = µ.It is convenient to relate this matrix to the matrixR in the integral of motion representation of the S-matrix[17] …”

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confidence: 99%