Photoproduction of charged pions on neutrons

Ramachandran, G.; Keshavamurthy, R. S.; Murthy, M. V. N.

doi:10.1088/0305-4616/5/11/009

Cited by 8 publications

(8 citation statements)

References 35 publications

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“…One family of three-sections has an interesting geometric shape, namely, the obesetetrahedron, having symmetry that corresponds to the 24-element tetrahedral group T d familiar from the context of point groups. We study this family in considerable detail in Section 6, and trace this T d symmetry consisting of 'proper and improper' rotations to a discrete subgroup of proper rotations in SO(3) ⊂ SU (3). This is the subgroup for which the eight-dimensional adjoint representation of SU(3) reduces to direct sum of one two-dimensional and two (inequivalent) three-dimensional irreducible representations of T d .…”

Section: Introductionmentioning

confidence: 99%

Geometry of the generalized Bloch sphere for qutrits

Goyal¹,

Simon²,

Singh³

et al. 2016

J. Phys. A: Math. Theor.

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Abstract. The geometry of the generalized Bloch sphere Ω 3 , the state space of a qutrit, is studied. Closed form expressions for Ω 3 , its boundary ∂Ω 3 , and the set of extremals Ω are obtained by use of an elementary observation. These expressions and analytic methods are used to classify the 28 two-sections and the 56 three-sections of Ω 3 into unitary equivalence classes, completing the works of earlier authors. It is shown, in particular, that there are families of two-sections and of three-sections which are equivalent geometrically but not unitarily, a feature that does not appear to have been appreciated earlier. A family of three-sections of obese-tetrahedral shape whose symmetry corresponds to the 24-element tetrahedral point group T d is examined in detail. This symmetry is traced to the natural reduction of the adjoint representation of SU (3), the symmetry underlying Ω 3 , into direct sum of the two-dimensional and the two (inequivalent) three-dimensional irreducible representations of T d .

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Section: Introductionmentioning

confidence: 99%

Geometry of the generalized Bloch sphere for qutrits

Goyal¹,

Simon²,

Singh³

et al. 2016

J. Phys. A: Math. Theor.

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“…A non-oriented spin s state |ψ has been defined earlier [13] as one which can not be identified as eigen state of S z with any choice ofẑ−axis as the axis of quantization. We may therefore define a mixed non-oriented system as one where the eigen states |ψ 1 , |ψ 2 , .…”

Section: Non-oriented System (States)mentioning

confidence: 99%

“…It is worth noting here that in addition to the above representation for density matrix which uses spherical tensor operators, there also exist other representations such as the SU (n) representation [13], where the density matrix is expanded in terms of the generators of the Lie group SU (n) ,whose number is also n 2 − 1. This representation is advantageous since the diagonal form of ρ can be expressed in terms of the subset consisting of diagonal generators which are n − 1 in number.…”

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confidence: 99%

Spin squeezing of mixed systems

Mallesh

Sirsi

Sbaih

et al. 2001

J. Phys. A: Math. Gen.

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Abstract. The notion of spin squeezing has been discussed in this paper using the density matrix formalism. Extending the definition of squeezing for pure states given by Kitagawa and Ueda in an appropriate manner and employing the spherical tensor representation, we show that mixed spin states which are non-oriented and possess vector polarization indeed exhibit squeezing. We construct a mixed state of a spin 1 system using two spin 1/2 states and study its squeezing behaviour as a function of the individual polarizations of the two spinors. §

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“…The dominance of the first resonance viz., ∆ 33 (1232) is quite conspicuous in this energy region and as such attention has lately been focussed [6,7] on details such as the quadrupole deformation of this resonance and ratio of E 1+ over M 1+ . In view of the necessity of neutron multipoles [8] to determine F (+) , F (−) and F (0) and their importance to decide questions of time reversal violation [9] or the possible existence of isotensor term [10], a careful discussion of target asymmetry and effective neutron polarization was presented [11] as also detailed theoretical analyses to extract the neutron multipoles more precisely from experiments on hydrogen isotopes [12]. Photo pion production has been studied extensively and reviewed by several groups [13].…”

Section: Introductionmentioning

confidence: 99%

Irreducible tensor approach to spin observables in the photoproduction of mesons with arbitrary spin-paritysπ

2007

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A theoretical formalism leading to elegant derivation of formulae for all spin observables is outlined for photo production of mesons with arbitrary spin parity s π . The salient features of this formalism based on irreducible tensor techniques are i) the number of independent irreducible tensor amplitudes is 4(2s + 1), ii) a single compact formula is sufficient to express these amplitudes in terms of allowed electric and magnetic multipole amplitudes and iii) all the spin observables including beam analyzing powers as well as the differential cross section are expressible in terms of bilinear irreducible tensors of rank 0 to 2(s + 1). The relationship between the irreducible tensor amplitudes and the helicity amplitudes is elucidated in general and explicit expressions for the helicity amplitudes are given in terms of the irreducible tensor amplitudes in the particular cases of pseudoscalar and vector meson photo production. The connection between the irreducible tensor amplitudes introduced here and the well known CGLN amplitudes for photo production of pseudoscalar mesons is also established.

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Photoproduction of charged pions on neutrons

Cited by 8 publications

References 35 publications

Geometry of the generalized Bloch sphere for qutrits

Geometry of the generalized Bloch sphere for qutrits

Spin squeezing of mixed systems

Irreducible tensor approach to spin observables in the photoproduction of mesons with arbitrary spin-paritysπ

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