nucl-th digest · Jul 27, 2016

Siegert State Approach to Quantum Defect Theory

The Siegert states are approached in framework of Bloch-Lane-Robson formalism for quantum collisions. The Siegert state is not described by a pole of Wigner R- matrix but rather by the equation

1 - R_{nn} L_{n} = 0

, relating R- matrix element

R_{nn}

to decay channel logarithmic derivative

L_{n}

. Extension of Siegert state equation to multichannel system results into replacement of channel R- matrix element

R_{nn}

by its reduced counterpart

R_{nn}

. One proves the Siegert state is a pole,

(1 - R_{nn} L_{n})^{- 1}

, of multichannel collision matrix. The Siegert equation

1 - R_{nn} L_{n} = 0

, (

n

- Rydberg channel), implies basic results of Quantum Defect Theory as Seaton's theorem, complex quantum defect, channel resonances and threshold continuity of averaged multichannel collision matrix elements.

Subjects:: Atomic Physics (physics.atom-ph); Nuclear Theory (nucl-th)
arXiv:: 1607.07649 [pdf]

Eur.Phys.J.D(2020)·1 citation

[Submitted on 26 Jul 2016] (cross-list from hep-ph)

Ultrarelativistic transverse momentum distribution of the Tsallis statistics

A.S. Parvan🇷🇺

The analytical expressions for the ultrarelativistic transverse momentum distributions of the Tsallis and the Tsallis- $2$ statistics were obtained. We found that the transverse momentum distribution of the Tsallis-factorized statistics, which is now largely used to describe the experimental transverse momentum spectra of hadrons measured in $pp$ collisions at LHC and RHIC energies, in the ultrarelativistic case is not equivalent to the transverse momentum distributions of the Tsallis and the Tsallis- $2$ statistics. However, we revealed that this distribution exactly coincides with the transverse momentum distribution of the Tsallis- $2$ statistics in the zeroth term approximation and is transformed to the transverse momentum distribution of the Tsallis statistics in the zeroth term approximation by changing the parameter $q$ to $1/ q_{c}$ . We demonstrated analytically on the basis of the ultrarelativistic ideal gas that the Tsallis-factorized statistics is not equivalent to the Tsallis and the Tsallis- $2$ statistics. In the present paper the Tsallis statistics corresponds to the standard expectation values.

Comments:: 2 figures
Subjects:: High Energy Physics — Phenomenology (hep-ph); Nuclear Theory (nucl-th)
arXiv:: 1607.07670 [pdf]

EPJA(2017)·21 citations

Wednesday·July 27, 2016

Siegert State Approach to Quantum Defect Theory

Ultrarelativistic transverse momentum distribution of the Tsallis statistics

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